In this case, we would put $100 in the numerator.
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Or you can take less money to decrease the numerator.
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You start by putting the total amount you are spending in the numerator.
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"We know the numerator," said Gottlieb, who left the Food and Drug Administration in April 2019.
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The numerator in the SEC's ratio, CEO compensation, reflects employment on a full-time, annualized basis.
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Pull out a napkin, put a value in the numerator and make a guess at the denominator.
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Thanks to The Post, the numerator (number of citizens fatally shot) in the equation no longer is unknown.
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That means that the numerator in the "P/E" ratio has fallen, even as the denominator remains relatively static.
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But this reflects the denominator rising, not the numerator shrinking: investment relative to GDP is in line with 1990s levels.
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As a result, the denominator of the return on equity calculation – equity – is higher while the numerator — net income — is lower.
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However, these ratios reflect not just an unusually large numerator (the number of road deaths) but also an anomalously low denominator.
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Specifically, the formula can be done by entering your numerator value, pressing the division key, and then inputting the denominator value.
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As such, there's a little misdirection going on, in that Facebook is including Instagram in the numerator but not the denominator here.
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"Most grocery pickup shoppers, in general, are affluent, busy, young professionals often with children," writes Grocery Dive's Krishna Thacker, citing market research firm Numerator.
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Then, you can press the 1/x button to put that number in the denominator (the numerator will be 1), and get your fraction value.
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The mathematical characteristics of the answer were ostensibly simple— a fraction less than one that needed a numerator of possible outcomes and denominator of total outcomes.
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The numerator appears to be vastly understated, because of the hundreds of cases that either haven't been reported or haven't been directly linked to this coronavirus.
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Our workaround was to slightly tweak the calculation for Net SE, replacing the numerator (Net New ARR) with the intra-quarter difference in GAAP revenue multiplied by 263 (annualized).
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And, second, we need to figure out both the public-health numerator and the denominator — how many cases, how many deaths, how contagious, and how many truly are at risk.
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NPL ratios are stabilizing at a time when loan portfolios continue to contract, meaning that the improvement is not due to an expansion in lending but to factors affecting the ratio's numerator.
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It included the world premiere of "Numerator," Mr. Morris's dance setting — for six men — to Mr. Harrison's five-part Varied Trio for violin (Xiaofan Liu), piano (Michael James Smith) and percussion (Nick Sakakeeny).
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Four Fractions Find four different fractions, in each of which the numerator is one less than the denominator, so that when all four fractions are added together, their sum will be a whole number.
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The numerator is Americans who are unemployed, the people who told a survey taker that they do not have a job but want one and have actively sought a job in the last four weeks.
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"When the denominator is the 350 million Americans whose cell phones might become vulnerable if you introduced backdoors," said McAfee chief technology officer Steve Grobman, "it doesn't matter if the numerator is 1,000 or 7,000."
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Indeed, public investors pushed a broad basket of SaaS and cloud-focused companies to over 12x their trailing revenues, using enterprise value instead of market cap to calculate the numerator of that particular price/sales equation.
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If the speed of the object (v ) in the numerator is super small compared with the speed of light (c ) in the denominator—which it is for 51 Pegasi, you get only a minuscule wavelength shift.
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Here in the U.S., our Centers for Disease Control and Prevention (CDC) has evolved when it comes to identifying a disease and isolating its victims (the numerator) and those with whom they have been in contact (the denominator).
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A quick way of calculating implied probability involves taking the "denominator" (if the odds are 6/1 the denominator is the 1, if the odds are 5/2 it is the 333) and dividing by the denominator plus the numerator.
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"The new government wants to expand the denominator with business-friendly policies, and shrink the numerator," says Panos Tsakloglou, a professor at Athens University of Economics and Business, and a former chairman of the Greek government's council of economic advisers.
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The significantly lower coverage reported in the accounts results from KKB's NPLs net of specific reserves being added to Halyk's NPL denominator, while KKB's provisions (some of which were held against performing loans) are not added to Halyk's reserve numerator.
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The firm's CFO, Luca Maestri, accused Ms Vestager's team of "legal mumbo-jumbo" and poor maths: their calculation that Apple paid an Irish tax rate of under 1% for 2014 was arrived at using the "wrong denominator and the wrong numerator", he claimed.
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Often this kind of analysis will involve an intermediary step, whereby an analyst will "discount" this expected price back to the present by dividing it by a number accounting for the amount of risk and the number of years until the outcome in the numerator is achieved.
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It's not unusual, as a journalist, to hear public health scientists of a certain age dismiss a news story of a patient's experience as an "n of 1"—meaning a numerator of 1 over a denominator of some presumed large number, or, translated from jargon, as an anecdote that isn't statistically representative.
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These emergencies were the H22020 swine flu virus in 2009, the Ebola outbreak in West Africa in 2013, polio in 2014, Zika in 2016, and Ebola again in the Democratic Republic of Congo in 2019 WHO has a poor track record when it comes to predicting both the numerator and the denominator, however.
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Divide the numerator and denominator by 25. The reduced fraction is .
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Then each of these primes divides all but one of the numerator terms and hence does not divide the numerator itself; but each prime does divide the denominator. Thus the expression is irreducible and is non-integer.
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The following is a rule by which we can write down at once the convergent fractions which result from these quotients without developing the continued fraction. The first quotient, supposed divided by unity, will give the first fraction, which will be too small, namely, . Then, multiplying the numerator and denominator of this fraction by the second quotient and adding unity to the numerator, we shall have the second fraction, , which will be too large. Multiplying in like manner the numerator and denominator of this fraction by the third quotient, and adding to the numerator the numerator of the preceding fraction, and to the denominator the denominator of the preceding fraction, we shall have the third fraction, which will be too small.
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Multiplication in overscore notation is problematic for the same reason that addition is. Multiplication in quote notation proceeds exactly like positive integer multiplication, comparing each new sum to previous sums in order to detect the repetition. For multiplication, quote notation is superior to overscore notation, and may be slightly better than numerator- denominator notation. Division in numerator-denominator notation has the same complexity as multiplication in numerator-denominator notation.
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Red auxiliary numbers selected divisors of denominators mp that best summed to numerator mn.
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In an improper fraction the numerator of the fraction is larger than the denominator.
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The numerator of these formulas is the semi-latus rectum \ell=a (1-e^2).
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The most general data type for a rational number stores the numerator and denominator as integers.
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11 ÷ 4 = 2 remainder 3. # The quotient (without the remainder) becomes the whole number part of the mixed number. The remainder becomes the numerator of the fractional part. In the example, 2 is the whole number part and 3 is the numerator of the fractional part.
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In control theory, a proper transfer function is a transfer function in which the degree of the numerator does not exceed the degree of the denominator. A strictly proper transfer function is a transfer function where the degree of the numerator is less than the degree of the denominator. The difference between the degree of the denominator (number of poles) and degree of the numerator (number of zeros) is the relative degree of the transfer function.
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Three is a common factor of the left denominator and right numerator and is divided out of both.
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Then an element of R is even or odd if and only if its numerator is so in Z.
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Divide the numerator of a fraction by the denominator to determine if the fraction has a terminating or repeating decimal.
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If the degree of the numerator is more than 1 larger than the degree of the denominator, and the denominator does not divide the numerator, there will be a nonzero remainder that goes to zero as x increases, but the quotient will not be linear, and the function does not have an oblique asymptote.
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The above formulas lead to an efficient Cohen, pp. 29–31 algorithm for calculating the Jacobi symbol, analogous to the Euclidean algorithm for finding the gcd of two numbers. (This should not be surprising in light of rule 2.) # Reduce the "numerator" modulo the "denominator" using rule 2. # Extract any even "numerator" using rule 9.
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In a fraction, the number of equal parts being described is the numerator (from Latin ', "counter" or "numberer"), and the type or variety of the parts is the denominator (from Latin ', "thing that names or designates"). As an example, the fraction amounts to eight parts, each of which is of the type named "fifth". In terms of division, the numerator corresponds to the dividend, and the denominator corresponds to the divisor. Informally, the numerator and denominator may be distinguished by placement alone, but in formal contexts they are usually separated by a fraction bar.
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This differs from the standard MLE for the exponential distribution in that the any censored observations are considered only in the numerator.
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When the numerator is one, it may be omitted (as in "a tenth" or "each quarter"). The entire fraction may be expressed as a single composition, in which case it is hyphenated, or as a number of fractions with a numerator of one, in which case they are not. (For example, "two-fifths" is the fraction and "two fifths" is the same fraction understood as 2 instances of .) Fractions should always be hyphenated when used as adjectives. Alternatively, a fraction may be described by reading it out as the numerator "over" the denominator, with the denominator expressed as a cardinal number.
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Black: the graph of f(x)=(x^2+x+1)/(x+1). Red: the asymptote y=x. Green: difference between the graph and its asymptote for x=1,2,3,4,5,6 When the numerator of a rational function has degree exactly one greater than the denominator, the function has an oblique (slant) asymptote. The asymptote is the polynomial term after dividing the numerator and denominator.
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Thus, the third quotient being 15, we have for our numerator , and for our denominator, . The third convergent, therefore, is . We proceed in the same manner for the fourth convergent. The fourth quotient being 1, we say 333 times 1 is 333, and this plus 22, the numerator of the fraction preceding, is 355; similarly, 106 times 1 is 106, and this plus 7 is 113.
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To convert any percentage or fraction to the equivalent odds, the numerator is subtracted from the denominator and then this difference is divided by the numerator. For example, to convert 25%, or 1/4, 1 is subtracted from 4 to get 3 (or 25 from 100 to get 75) and then 3 is divided by 1 (or 75 by 25), giving 3, or 3:1.
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The simplest representation has no common factors between the numerator and the denominator. This allows the probability distribution of natural numbers may be extended to rational numbers.
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Treat the mean for each group as a score, and compute the variability (again, the sum of squares) of those three scores. When divided by its degrees of freedom (i.e., based on the number of groups), the numerator of the F ratio is obtained. Under the truth of the null hypothesis, the sampling distribution of the F ratio depends on the degrees of freedom for the numerator and the denominator.
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When a partial fraction term has a single (i.e. unrepeated) binomial in the denominator, the numerator is a residue of the function defined by the input fraction. We calculate each respective numerator by (1) taking the root of the denominator (i.e. the value of x that makes the denominator zero) and (2) then substituting this root into the original expression but ignoring the corresponding factor in the denominator.
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The difference between superscript/subscript and numerator/denominator glyphs. In many popular fonts the Unicode "superscript" and "subscript" characters are actually numerator and denominator glyphs. Unicode has subscripted and superscripted versions of a number of characters including a full set of Arabic numerals. These characters allow any polynomial, chemical and certain other equations to be represented in plain text without using any form of markup like HTML or TeX.
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The fraction form looks like a fraction, with a numerator and a denominator. The numerator consists of two parts separated by a dash. The prefix (no longer used in check processing, yet still printed on most checks) is a 1 or 2 digit code (P or PP) indicating the region where the bank is located. The numbers 1 to 49 are cities, assigned by size of the cities in 1910.
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If p (i.e. the retail price is less than the purchase price), the numerator becomes negative. In this situation, it isn't worth keeping any items in the inventory.
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The numerator corresponds to the likelihood of an observed outcome under the null hypothesis. The denominator corresponds to the maximum likelihood of an observed outcome, varying parameters over the whole parameter space. The numerator of this ratio is less than the denominator; so, the likelihood ratio is between 0 and 1. Low values of the likelihood ratio mean that the observed result was much less likely to occur under the null hypothesis as compared to the alternative.
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Whilst the other equations we have a numerator of pressure and voltage and the denominator is still temperature. This means lower than the level of molecules there are no definite stable units.
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Factorize the expression in the denominator. Set up a partial fraction for each factor in the denominator. Apply the cover- up rule to solve for the new numerator of each partial fraction.
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The notion of irreducible fraction generalizes to the field of fractions of any unique factorization domain: any element of such a field can be written as a fraction in which denominator and numerator are coprime, by dividing both by their greatest common divisor.. This applies notably to rational expressions over a field. The irreducible fraction for a given element is unique up to multiplication of denominator and numerator by the same invertible element. In the case of the rational numbers this means that any number has two irreducible fractions, related by a change of sign of both numerator and denominator; this ambiguity can be removed by requiring the denominator to be positive. In the case of rational functions the denominator could similarly be required to be a monic polynomial..
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A conversion factor is used to change the units of a measured quantity without changing its value. The unity bracket method of unit conversion consists of a fraction in which the denominator is equal to the numerator, but they are in different units. Because of the identity property of multiplication, the value of a quantity will not change as long as it is multiplied by one. Also, if the numerator and denominator of a fraction are equal to each other, then the fraction is equal to one.
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To change a common fraction to a decimal, do a long division of the decimal representations of the numerator by the denominator (this is idiomatically also phrased as "divide the denominator into the numerator"), and round the answer to the desired accuracy. For example, to change ¼ to a decimal, divide 1.00 by 4 ("4 into 1.00"), to obtain 0.25. To change ⅓ to a decimal, divide 1.000... by 3 ("3 into 1.0000..."), and stop when the desired accuracy is obtained, e.g., at 4 decimals with 0.3333.
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When factors of the denominator include powers of one expression we # Set up a partial fraction for each unique factor and each lower power of D; # Set up an equation showing the relation of the numerators if all were converted to the LCD. From the equation of numerators we solve for each numerator, A, B, C, D, and so on. This equation of the numerators is an absolute identity, true for all values of x. So, we may select any value of x and solve for the numerator.
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Thus, this measure uses deviations above the MAR in the numerator, rewarding performance above the MAR. In the denominator, it has deviations below the MAR, thus penalizing performance below the MAR. Thus, by rewarding desirable results in the numerator and penalizing undesirable results in the denominator, this measure attempts to serve as a pragmatic measure of the goodness of an investment portfolio's returns in a sense that is not just mathematically simple (a primary reason to use standard deviation as a risk measure), but one that considers the realities of investor psychology and behavior.
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To specify the exact variant of the Henry's law constant, two superscripts are used. They refer to the numerator and the denominator of the definition. For example, H^{cp} refers to the Henry solubility defined as c/p.
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To express fractions, the prefix sem- is added to the denominator number, followed by the connective -ə-, and then the word for the numerator. To express the fraction two-fifths, the word in Aimol is sem-rəŋə-ə-ənni.
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Algorithm: let the numerator be the product of separation of the poles and intersection from tip of pole, let the denominator be the difference of offsets. Add the height of pole to the quotient to obtain the height of pine tree.
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Note that the volume integral in the denominator of the Holstein–Herring formula is sub-dominant in R. Consequently this denominator is almost unity for sufficiently large internuclear distances R and only the surface integral of the numerator need be considered.
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Common fractions can be classified as either proper or improper. When the numerator and the denominator are both positive, the fraction is called proper if the numerator is less than the denominator, and improper otherwise. In general, a common fraction is said to be a proper fraction, if the absolute value of the fraction is strictly less than one—that is, if the fraction is greater than −1 and less than 1. It is said to be an improper fraction, or sometimes top-heavy fraction, if the absolute value of the fraction is greater than or equal to 1.
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The degree of the graph of a rational function is not the degree as defined above: it is the maximum of the degree of the numerator and one plus the degree of the denominator. In some contexts, such as in asymptotic analysis, the degree of a rational function is the difference between the degrees of the numerator and the denominator. In network synthesis and network analysis, a rational function of degree two (that is, the ratio of two polynomials of degree at most two) is often called a '.Glisson, Tildon H., Introduction to Circuit Analysis and Design, Springer, 2011 ISBN .
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In our usual sign-and-magnitude notation, to add the two integers 25 and −37, one first compares signs, and determines that the addition will be performed by subtracting the magnitudes. Then one compares the magnitudes to determine which will be subtracted from which, and to determine the sign of the result. In our usual fraction notation, to add 2/3 + 4/5 requires finding a common denominator, multiplying each numerator by the new factors in this common denominator, then adding the numerators, then dividing the numerator and denominator by any factors they have in common. In quote notation, to add, just add.
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Figure 1(a): The Bode plot for a first-order (one-pole) highpass filter; the straight-line approximations are labeled "Bode pole"; phase varies from 90° at low frequencies (due to the contribution of the numerator, which is 90° at all frequencies) to 0° at high frequencies (where the phase contribution of the denominator is −90° and cancels the contribution of the numerator). Figure 1(b): The Bode plot for a first-order (one-pole) lowpass filter; the straight- line approximations are labeled "Bode pole"; phase is 90° lower than for Figure 1(a) because the phase contribution of the numerator is 0° at all frequencies. In electrical engineering and control theory, a Bode plot is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift.
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The numerator of V_{2k+1} is handled in the same way. (Adding n does not change the result modulo n.) Observe that, for each term that we compute in the U sequence, we compute the corresponding term in the V sequence.
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The degree of a projective variety is the evaluation at of the numerator of the Hilbert series of its coordinate ring. It follows that, given the equations of the variety, the degree may be computed from a Gröbner basis of the ideal of these equations.
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In mathematics, Spijker's lemma is a result in the theory of rational mappings of the Riemann sphere. It states that the image of a circle under a complex rational map with numerator and denominator having degree at most n has length at most 2nπ.
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A system of equations is said to be incompatible or inconsistent when there are no solutions and it is called indeterminate when there is more than one solution. For linear equations, an indeterminate system will have infinitely many solutions (if it is over an infinite field), since the solutions can be expressed in terms of one or more parameters that can take arbitrary values. Cramer's rule applies to the case where the coefficient determinant is nonzero. In the 2×2 case, if the coefficient determinant is zero, then the system is incompatible if the numerator determinants are nonzero, or indeterminate if the numerator determinants are zero.
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For equal permeabilities (e.g., non-magnetic media), if and are complementary, we can substitute for and for so that the numerator in equation () becomes which is zero (by Snell's law). Hence and only the s-polarized component is reflected. This is what happens at the Brewster angle.
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A fraction when multiplied by (i.e. concatenated with) its denominator yields its numerator. As concatenation is not commutative, it makes a difference whether the denominator occurs to the left or right. The concatenation must be on the same side as the denominator for it to cancel out.
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To add two numbers in numerator-denominator notation, for example (+a/b) + (–c/d) , requires the following steps. • sign comparison to determine if we will be adding or subtracting; in our example, the signs differ so we will be subtracting • then 3 multiplications; in our example, a×d , b×c , b×d • then, if we are subtracting, a comparison of a×d to b×c to determine which is subtrahend and which is minuend, and what is the sign of the result; let's say a×d < b×c so the sign will be – • then the addition or subtraction; b×c – a×d and we have –(b×c – a×d)/(b×d) • finding the greatest common divisor of the new numerator and denominator • dividing numerator and denominator by their greatest common divisor to obtain a normalized result Normalizing the result is not necessary for correctness, but without it, the space requirements quickly grow during a sequence of operations. Subtraction is almost identical to addition. Adding two numbers in overscore notation is problematic because there is no right end to start at.
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A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n. Examples are 1/1, 1/2, 1/3, 1/4 ,1/5, etc.
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A Wolstenholme number is a number that is the numerator of the generalized harmonic number Hn,2. The first such numbers are 1, 5, 49, 205, 5269, 5369, 266681, 1077749, … . These numbers are named after Joseph Wolstenholme, who proved Wolstenholme's theorem on modular relations of the generalized harmonic numbers.
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Fractions are themselves singular or plural depending on the numerator (e.g. one eighth vs two eighths), and whatever they apply to can be singular or plural (e.g., three-quarters of the apple(s)), depending on whether it refers to a fraction of a single item or many items.
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Board of Governors of the Federal Reserve System-The Recent Decline in the Labor Force Participation Rate and Its Implications for Potential Labor Supply-See Figure 3-2006 The labor force participation rate decreases when the percentage increase in the defined population (denominator) is greater than the percentage increase in the labor force (i.e., the sum of employed and unemployed, the numerator). With respect to the unemployment rate, if the percentage increase in the number of unemployed (numerator) is greater than the percentage increase in the number in the labor force (denominator), the unemployment rate will rise.Peter Barth and Dennis Heffley "Taking Apart Taking Part: Local Labor Force Participation Rates" University of Connecticut, 2004.
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Coxeter's listing of degenerate Wythoffian uniform polyhedra, giving Wythoff symbols, vertex figures, and descriptions using Schläfli symbols. All the uniform polyhedra and all the degenerate Wythoffian uniform polyhedra are listed in this article. There are many relationships among the uniform polyhedra. The Wythoff construction is able to construct almost all of the uniform polyhedra from the acute and obtuse Schwarz triangles. The numbers that can be used for the sides of a non-dihedral acute or obtuse Schwarz triangle that does not necessarily lead to only degenerate uniform polyhedra are 2, 3, 3/2, 4, 4/3, 5, 5/2, 5/3, and 5/4 (but numbers with numerator 4 and those with numerator 5 may not occur together).
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Fractional odds are also known as British odds, UK odds, or, in that country, traditional odds. They are typically represented with a "/" but can also be represented with a "-", e.g. 4/1 or 4-1. Odds with a denominator of 1 are often presented in listings as the numerator only.
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For example, a quadratic for the numerator and a cubic for the denominator is identified as a quadratic/cubic rational function. The rational function model is a generalization of the polynomial model: rational function models contain polynomial models as a subset (i.e., the case when the denominator is a constant).
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355 = 5 × 71, Smith number, Mertens function returns 0, divisible by the number of primes below it. the numerator of the best simplified rational approximation of pi having a denominator of four digits or fewer. This fraction (355/113) is known as Milü and provides an extremely accurate approximation for pi.
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This form of fraction with numerator on top and denominator at bottom without a horizontal bar was also used by al-Uqlidisi and by al-Kāshī in his work "Arithmetic Key". File:Stevin-decimal notation.svg A forerunner of modern European decimal notation was introduced by Simon Stevin in the 16th century.
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Because the total energy must be real, the numerator must also be imaginary: i.e. the rest mass m must be imaginary, as a pure imaginary number divided by another pure imaginary number is a real number. In some modern formulations of the theory, the mass of tachyons is regarded as real.
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This gamma function is a meromorphic function of its argument with simple poles at x=-n, n=0,1,2,.... Thus the expression for S (the gamma function in the numerator) possesses poles at precisely those points which are given by the above expression for the Regge trajectories; hence the name Regge poles.
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Line chart showing unemployment rate trends from 2000 to 2017, for the U3 and U6 measures. Analyzing employment ratios for prime working age (25–54 yrs) helps remove the effects of aging demographics. Both ratios have the same denominator, the civilian population. The numerator of the upper line is the labor force (i.e.
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The normalization model is an influential model of responses of neurons in primary visual cortex. David Heeger developed the model in the early 1990s, and later refined it together with Matteo Carandini and J. Anthony Movshon. The model involves a divisive stage. In the numerator is the output of the classical receptive field.
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Finding averages may involve using weighted averages and possibly using the harmonic mean. A ratio r=a/b has both a numerator "a" and a denominator "b". The value of a and/or b may be a real number or integer. The inverse of a ratio r is 1/r = b/a.
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Note that, for each , f^{(j)}(a)=P^{(j)}(a). Hence each of the first k−1 derivatives of the numerator in h_k(x) vanishes at x=a, and the same is true of the denominator. Also, since the condition that the function f be k times differentiable at a point requires differentiability up to order k−1 in a neighborhood of said point (this is true, because differentiability requires a function to be defined in a whole neighborhood of a point), the numerator and its k − 2 derivatives are differentiable in a neighborhood of a. Clearly, the denominator also satisfies said condition, and additionally, doesn't vanish unless x=a, therefore all conditions necessary for L'Hopital's rule are fulfilled, and its use is justified.
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His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞. Although the rule did not originate with l'Hôpital, it appeared in print for the first time in his treatise on the infinitesimal calculus, entitled Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes.Answering l'Hôpital's question, in a letter of 22 July 1694 Johann Bernoulli described the rule of computing the limit of a fraction whose numerator and denominator tend to 0 by differentiating the numerator and denominator. A commonly made claim that l'Hôpital attempted to get credit for discovering the l'Hôpital's rule is inaccurate, since in the preface to his textbook, l'Hôpital generally acknowledged Leibniz, Jakob Bernoulli and Johann Bernoulli as the sources of the results in it.
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It is obtained from the previous formula by multiplying denominator and numerator by !, so it is certainly computationally less efficient than that formula. The last formula can be understood directly, by considering the n! permutations of all the elements of S. Each such permutation gives a k-combination by selecting its first k elements.
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In probability theory, a 2-EPT probability density function is a class of probability density functions on the real line. The class contains the density functions of all distributions that have characteristic functions that are strictly proper rational functions (i.e., the degree of the numerator is strictly less than the degree of the denominator).
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Ernst Kummer showed that an equivalent criterion for regularity is that p does not divide the numerator of any of the Bernoulli numbers Bk for . Kummer's proof that this is equivalent to the class number definition is strengthened by the Herbrand–Ribet theorem, which states certain consequences of p dividing one of these Bernoulli numbers.
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Then the result may be roll-normalized by checking whether the first digit equals the first digit after the quote. Likewise for subtraction. For both addition and subtraction, quote notation is superior to the other two notations. Multiplication in numerator-denominator notation is two integer multiplications, finding a greatest common divisor, and then two divisions.
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After reproduction the best chromosome and the worst chromosome in the offspring are found out. The designed filter has non- separable numerator and separable denominator transfer function.A. Mazinani, M. Ahmadi, M. Shridhar and R. S. Lashkari, “A novel approach to the design of 2-D recursive digital filters”, Journal of the Franklin Institute, Pergamon Press Ltd, vol. 329, no.
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It is a version of Neue Frutiger compliant with the German standard DIN 1450, designed by Akira Kobayashi. The family includes eight fonts, in four weights (book, regular, medium, bold) and one width, with a complementary oblique. OpenType features include denominator/numerator, fractions, ligatures, localized forms, ordinals, proportional figures, subscript/superscript, scientific inferiors, stylistic alternates (two sets), ornaments, kerning.
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The text of the Suan shu shu is however much less systematic than the Nine Chapters, and appears to consist of a number of more or less independent short sections of text drawn from a number of sources. The Book of Computations contains many perquisites to problems that would be expanded upon in The Nine Chapters on the Mathematical Art. An example of the elementary mathematics in the Suàn shù shū, the square root is approximated by using false position method which says to "combine the excess and deficiency as the divisor; (taking) the deficiency numerator multiplied by the excess denominator and the excess numerator times the deficiency denominator, combine them as the dividend." Furthermore, The Book of Computations solves systems of two equations and two unknowns using the same false position method.
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Similarly, the ratios of a utonality share the same numerator. 7/4, 7/5, 7/6, and 1/1 (7/7) form a utonality, sometimes written as 1/(4:5:6:7), or as 7/(7:6:5:4). Every utonality is therefore composed of members of a subharmonic series. This term is used extensively by Harry Partch in _Genesis of a music_.
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Every rational number may be expressed in a unique way as an irreducible fraction , where and are coprime integers and . This is often called the canonical form of the rational number. Starting from a rational number , its canonical form may be obtained by dividing and by their greatest common divisor, and, if , changing the sign of the resulting numerator and denominator.
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Liu Hui's used a lot of calculations with fraction in Haidao Suanjing. This form of fraction with numerator on top and denominator at bottom without a horizontal bar in between, was transmitted to Arabic country in an 825AD book by al Khwarizmi via India, and in use by 10th century Abu'l-Hasan al-Uqlidisi and 15th century Jamshīd al-Kāshī's work "Arithematic Key".
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When v is larger than c, the denominator in the equation for the energy is "imaginary", as the value under the radical is negative. Because the total energy must be real, the numerator must also be imaginary: i.e. the rest mass m must be imaginary, as a pure imaginary number divided by another pure imaginary number is a real number.
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The West Virginia portion of the Bloomery Pike, WV 29 from U.S. Route 50 near Pleasant Dale to WV 127 in Forks of Cacapon as well as WV 127 from WV 29 to the state line, was once designated West Virginia Route 45. This explains why all Hampshire County secondary routes off WV 29 and WV 127 have 45 as their numerator.
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There is an "arithmetic" of tangles with addition, multiplication, and reciprocal operations. An algebraic tangle is obtained from the addition and multiplication of rational tangles. The numerator closure of a rational tangle is defined as the link obtained by joining the "north" endpoints together and the "south" endpoints also together. The denominator closure is defined similarly by grouping the "east" and "west" endpoints.
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The difference of these terms is the harmonic series representation of the interval in question (using harmonic numbers), whose bottom note 12n is a transposition of the tonic by n octaves. This suggests why descending interval ratios with denominator a power of two are final. A similar situation is seen if the term in the numerator is a power of two.
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In probability theory and statistics, an inverse distribution is the distribution of the reciprocal of a random variable. Inverse distributions arise in particular in the Bayesian context of prior distributions and posterior distributions for scale parameters. In the algebra of random variables, inverse distributions are special cases of the class of ratio distributions, in which the numerator random variable has a degenerate distribution.
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Finding the optimal weighted MMSE precoding is difficult, leading to approximate approaches where the weights are selected heuristically. A common approach is to concentrate on either the numerator or the denominator of the mentioned ratio; that is, maximum ratio transmission (MRT) and zero-forcing (ZF)N. Jindal, MIMO Broadcast Channels with Finite Rate Feedback, IEEE Transactions on Information Theory, vol. 52, no.
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Numbers between 0 and 102.3, 10.23, 1.023, etc. can be represented this way, in increments of 0.1, 0.01, 0.001, etc. Vulgar fractions can be represented by using one hand to represent the numerator and one hand to represent the denominator; a spectrum of rational numbers can be represented this way, ranging from 1/31 to 31/1 (as well as 0).
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The primitive pseudo-remainder sequence consists in taking for α the content of the numerator. Thus all the ri are primitive polynomials. The primitive pseudo- remainder sequence is the pseudo-remainder sequence, which generates the smallest coefficients. However it requires to compute a number of GCD's in Z, and therefore is not sufficiently efficient to be used in practice, especially when Z is itself a polynomial ring.
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Arithmetic values incorrectly assumed to be represented by parts of the Eye of Horus In Ancient Egypt, most fractions were written as the sum of two or more unit fractions (a fraction with 1 as the numerator), with scribes possessing tables of answers (see Rhind Mathematical Papyrus 2/n table).Zaslavsky, Claudia (1993). Multicultural Mathematics: Interdisciplinary Cooperative-Learning Activities, p. 20\. . Thus instead of , one would write + .
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This shows that the rule of 72 is most accurate for periodically compounded interests around 8%. Similarly, replacing the "R" in R/200 on the third line with 2.02 gives 70 on the numerator, showing the rule of 70 is most accurate for periodically compounded interests around 2%. Alternatively, the E-M rule is obtained if the second-order Taylor approximation is used directly.
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Arguments to the `DS` statement are the subroutine number and a subroutine scaling factor. There are no arguments to the `DF` statement. The scaling factor for a subroutine consists of a numerator followed by a denominator that will be applied to all values inside the subroutine. This scaling allows large numbers to be expressed with fewer digits and allows ease of rescaling a design.
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Further, reserves are resources that are economically recoverable under existing conditions. Reserves may change as a result of political change, or by manipulation. Consumption of many resources is not constant, but typically increases as the population grows and becomes more prosperous. Non-constant values for both the numerator and denominator of the ratio implies it may either overestimate or underestimate the remaining life of the resource.
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228 (two hundred [and] twenty-eight) is the natural number following 227 and preceding 229. 228 is a refactorable number, and a practical number. There are 228 matchings in a ladder graph with five rungs. 228 is the smallest even number n such that the numerator of the nth Bernoulli number is divisible by a nontrivial square number that is relatively prime to n.
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Division in overscore notation is problematic because it requires a sequence of subtractions, which are problematic in overscore notation. Division in quote notation proceeds just like multiplication in quote notation, producing the answer digits from right to left, each one determined by the rightmost digit of the current difference and divisor (trivial in binary). For division, quote notation is superior to both overscore and numerator-denominator notations.
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A fraction is in lowest terms if the only factor common to the numerator and the denominator is 1. An expression which is not in fractional form is an integral expression. An integral expression can always be written in fractional form by giving it the denominator 1. A mixed expression is the algebraic sum of one or more integral expressions and one or more fractional terms.
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The earliest form of kinship diagram that displays this is from 1871: Morgan's System of Consanguinity and Affinity of Human Family. W. H. R River's system migrated to big letters for male, small letters for female, while in algebreic-type equations, the numerator denotes male and the denominator female. Later, in C. G. Seligman's 1910 Dance Diagram, outlined circles illustrated females and shaded circles indicated males.
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With the Snellen chart, the visual acuity is recorded as a fraction with 20 in the numerator (top number) and values ranging from 10 to 600 in the denominator (bottom number). The denominator indicates the distance in feet at which a person with normal vision could stand to correctly identify the same symbols identified by the person tested. For example, a visual acuity of 20/20 is considered normal.
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When blood pressure is stated for medical purposes, it is usually written with the systolic and diastolic pressures separated by a slash, for example, 120/80 mmHg. This clinical notation is not a mathematical figure for a fraction or ratio, nor a display of a numerator over a denominator. Rather it is a medical notation showing the two clinically significant pressures involved (i.e., systolic-slash-diastolic, or 120/80).
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Just as the Taylor polynomial of degree has coefficients that depend on the function , the Padé approximation also has coefficients dependent on and its derivatives. More precisely, in any Padé approximant, the degrees of the numerator and denominator polynomials have to add to the order of the approximant. Therefore, b_d=0 has to hold. One could determine the Padé approximant starting from the Taylor polynomial of using Euclid's algorithm.
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For example, the decimal representation 3.1416 could be rounded from any number in the interval . The continued fraction representations of 3.14155 and 3.14165 are : : and the best rational between these two is : Thus, is the best rational number corresponding to the rounded decimal number 3.1416, in the sense that no other rational number that would be rounded to 3.1416 will have a smaller numerator or a smaller denominator.
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First, the denominator combines two types of cash flows, the investment I_0 and the management fees. Management fees are effectively a risk-free claim and should be discounted at a rate close to the risk-free rate. Second, the numerator contains the total proceeds net of carried interest. The carried interest is effectively a call option, making the LP's total payoff at maturity less risky than the underlying asset.
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2-bridge links are defined similarly as above, but each component will have one min and max. 2-bridge knots were classified by Horst Schubert, using the fact that the 2-sheeted branched cover of the 3-sphere over the knot is a lens space. The names rational knot and rational link were coined by John Conway who defined them as arising from numerator closures of rational tangles.
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Intuitively the ratio measures the steepness of the strokes, viewed from the side (e.g., assuming movement through a stationary fluid) – f is the stroke frequency, A is the amplitude, so the numerator fA is half the vertical speed of the wing tip, while the denominator V is the horizontal speed. Thus the graph of the wing tip forms an approximate sinusoid with aspect (maximal slope) twice the Strouhal constant.
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Such a subtraction can lose significant digits. Because and are always of opposite sign the “subtraction” in the numerator of the improved formula is effectively an addition (as is the subtraction in the denominator too). At iteration number , the number is calculated as above and then, if and have the same sign, set and , otherwise set and . This process is repeated until the root is approximated sufficiently well.
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Colloquially, decimal numbers are formed by saying chut (จุด, dot) where the decimal separator is located. For example, 1.01 is nueng chut sun nueng (หนึ่งจุดศูนย์หนึ่ง). Fractional numbers are formed by placing nai (ใน, in, of) between the numerator and denominator or using [set] x suan y ([เศษ] x ส่วน y, x parts of the whole y) to clearly indicate. For example, is nueng nai sam (หนึ่งในสาม) or [set] nueng suan sam ([เศษ]หนึ่งส่วนสาม).
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For a constant exponential distribution, the hazard, \lambda, is constant. In this case, the MBTF is :MTBF = 1 / \hat\lambda = \sum u_i / k, where \hat\lambda is the maximum likelihood estimate of \lambda, maximizing the likelihood given above. We see that the difference between the MTBF considering only failures and the MTBF including censored observations is that the censoring times add to the numerator but not the denominator in computing the MTBF..
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Snellen defined “standard vision” as the ability to recognize one of his optotypes when it subtended 5 minutes of arc. Thus the optotype can only be recognized if the person viewing it can discriminate a spatial pattern separated by a visual angle of one minute of arc. Outside the United States, the standard chart distance is , and normal acuity is designated "6/6". Other acuities are expressed as ratios with a numerator of 6.
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FENa is calculated in two parts—figuring out how much sodium is excreted in the urine, and then finding its ratio to the total amount of sodium that passed through (aka "filtered by") the kidney. First, the actual amount of sodium excreted is calculated by multiplying the urine sodium concentration by the urinary flow rate. This is the numerator in the equation. The denominator is the total amount of sodium filtered by the kidneys.
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In a fraction, the numerator is occasionally referred to as upstairs and the denominator downstairs, as in "bringing a term upstairs". ; up to, modulo, mod out by: An extension to mathematical discourse of the notions of modular arithmetic. A statement is true up to a condition if the establishment of that condition is the only impediment to the truth of the statement. Also used when working with members of equivalence classes, esp.
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Let Z(2) := { z / n : z, n ∈ Z, n odd }. Then the field of fractions of Z(2) is Q. Now, for any nonzero element r of Q, we can apply unique factorization to the numerator and denominator of r to write r as where z, n, and k are integers with z and n odd. In this case, we define ν(r)=k. Then Z(2) is the discrete valuation ring corresponding to ν.
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When the numerator is squared that prime will still not divide into it because of the unique factorization. Therefore, the square of a rational non-integer is always a non-integer; by contrapositive, the square root of an integer is always either another integer, or irrational. Euclid used a restricted version of the fundamental theorem and some careful argument to prove the theorem. His proof is in Euclid's Elements Book X Proposition 9.
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In some contexts it is desirable to round a given number to a "neat" fraction — that is, the nearest fraction = / whose numerator and denominator do not exceed a given maximum. This problem is fairly distinct from that of rounding a value to a fixed number of decimal or binary digits, or to a multiple of a given unit . This problem is related to Farey sequences, the Stern–Brocot tree, and continued fractions.
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Small Deborah numbers represent Newtonian flow, while non-Newtonian (with both viscous and elastic effects present) behaviour occurs for intermediate range Deborah numbers, and high Deborah numbers indicate an elastic/rigid solid. Since Deborah number is a relative quantity, the numerator or the denominator can alter the number. A very small Deborah number can be obtained for a fluid with extremely small relaxation time or a very large experimental time, for example.
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The latter fraction is the best possible rational approximation of using fewer than five decimal digits in the numerator and denominator. Zu Chongzhi's result surpasses the accuracy reached in Hellenistic mathematics, and would remain without improvement for close to a millennium. In Gupta-era India (6th century), mathematician Aryabhata in his astronomical treatise Āryabhaṭīya calculated the value of to five significant figures π ≈ = 3.1416.How Aryabhata got the earth's circumference right Āryabhaṭīya (): :.
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The F statistic is a ratio of a numerator to a denominator. Consider randomly selected subjects that are subsequently randomly assigned to groups A, B, and C. Under the truth of the null hypothesis, the variability (or sum of squares) of scores on some dependent variable will be the same within each group. When divided by the degrees of freedom (i.e., based on the number of subjects per group), the denominator of the F ratio is obtained.
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How do retailers' trading performance measures stack up?, Deloitte, March 2009 Sales density is a ratio computed dividing the total retail sales over a year by the total surface of all the stores owned by the retailer (potential wholesale/franchising sales are usually not included). It is disputed whether the online sales of the retailer should be included in the numerator of the ratio given the high interdependence in the marketing strategy of online sales and own stores sales.
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Duffin and Bott extended earlier work by Otto Brune that requisite functions of complex frequency s could be realized by a passive network of inductors and capacitors. The proof, relying on induction on the sum of the degrees of the polynomials in the numerator and denominator of the rational function, was published in Journal of Applied Physics, volume 20, page 816. In his 2000 interviewJackson, Allyn, "Interview with Raoul Bott", Notices of the American Mathematical Society 48 (2001), no.
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Typically, participation in extra credit can only improve one's grade. Points might be added to an existing activity, for example, if the student correctly answers a more difficult portion of a test that would be required to meet the objectives of a unit. Optional activities may also add points or marks used in overall grade computation. This may, for example, increase the numerator of the fraction used in computing an overall percentage, while leaving the denominator unchanged.
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Smoke rising in Lochcarron, Scotland, is stopped by a temperature inversion and its related overlying layer of warmer air It is often more difficult to forecast the erosion of a CAD event than its development. Numerical models tend to underestimate the event's duration. The bulk Richardson number, Ri, calculates vertical wind shear to help forecast erosion. The numerator corresponds to the strength of the inversion layer separating the CAD cold dome and the immediate atmosphere above.
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For 3×3 or higher systems, the only thing one can say when the coefficient determinant equals zero is that if any of the numerator determinants are nonzero, then the system must be incompatible. However, having all determinants zero does not imply that the system is indeterminate. A simple example where all determinants vanish (equal zero) but the system is still incompatible is the 3×3 system x+y+z=1, x+y+z=2, x+y+z=3.
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A relevant RR analysis would consist of the examination of the frequency of serious injury in 1000 randomly selected unbelted drivers exposed to a 20 mph frontal collision versus the frequency of serious injury in 1000 randomly selected restrained drivers exposed to the same collision severity and type. If the frequency of serious injury in the group exposed to the presumptive hazard (failure to use a seat belt) was 0.15 and the frequency in the unexposed (belted) group was 0.05, then the CRR would be the same thing as the RR of 0.15/0.05. The RR design of the analysis dictates that the populations that the numerator and denominator of the CRR are substantially similar in all respects, with the exception of the exposure to the investigated hazard, which was the failure to use a seat belt in the example. In some instances encountered in a legal setting, however, the numerator and denominator risk must be derived from dissimilar populations in order to fit the circumstances of an investigated injury or disease.
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The methodology is not an economic measure. It measures how much healthy life is lost. It does not assign a monetary value to any person or condition, and it does not measure how much productive work or money is lost as a result of death and disease. However, HALYs, including DALYs and QALYs, are especially useful in guiding the allocation of health resources as they provide a common numerator, allowing for the expression of utility in terms of dollar/DALY, or dollar/QALY.
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The plant is equipped with some KBA Super Simultan, KBA Super Numerator, KBA Giori Super Orloff Intaglio (Colour), KBA NotaSys, KBA Rapida, Roland Favorit. With this the company has the capacity to produce over 200 million pieces of banknotes per year. Fidelity Printers and Refinery also makes use of some digital printing systems like the OCE Prisma system for light commercial jobs. For card personalisation and recharge cards the company operates Atlantic Zeiser and KBA Universys and Muhlbauer HSO systems.
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These ratios are not in all contexts regarded as strictly just but they are the justest possible in 5-limit tuning. 7-limit tuning allows for the justest possible ratios (ratios with the smallest numerator and denominator), namely 7:5 for the A4 (about 582.5 cents, also known as septimal tritone) and 10:7 for the d5 (about 617.5 cents, also known as Euler's tritone).Haluska (2003). p. xxiii. "7:5 septimal or Huygens' tritone, Bohlen- Pierce fourth", "10:7 Euler's tritone".
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A similar phenomenon occurs with other numbers, such as 5/5809 (an example found independently by K. S. Brown and David Bailey) which has a 31-term expansion. Although the denominators of this expansion are difficult to compute due to their enormous size, the numerator sequence may be found relatively efficiently using modular arithmetic. describes several additional examples of this type found by Broadhurst, and notes that K. S. Brown has described methods for finding fractions with arbitrarily long expansions.
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Based on the original Basel Accord, banks using the basic indicator approach must hold capital for operational risk equal to the average over the previous three years of a fixed percentage of positive annual gross income. Figures for any year in which annual gross income is negative or zero should be excluded from both the numerator and denominator when calculating the average. A standard deviation is commonly also taken. The fixed percentage 'alpha' is typically 15 percent of annual gross income.
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The COP is a ratio with the same metric units of energy (joules) in both the numerator and denominator. They cancel out, leaving a dimensionless quantity. Formulas for the approximate conversion between SEER and EER or COP are available. : (1) SEER = EER ÷ 0.9 : (2) SEER = COP × 3.792 : (3) EER = COP × 3.413 From equation (2) above, a SEER of 13 is equivalent to a COP of 3.43, which means that 3.43 units of heat energy are pumped per unit of work energy.
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Using specially constructed cards, the choice can be tested a number of times. Let "B" denote the colour Black. By constructing a fraction with the denominator being the number of times "B" is on top, and the numerator being the number of times both sides are "B", the experimenter will probably find the ratio to be near . Note the logical fact that the B/B card contributes significantly more (in fact twice) to the number of times "B" is on top.
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In this case, the meter is sometimes characterized as "triple septuple time". It is also possible for a time signature to be used for an irregular, or "additive" metrical pattern, such as groupings of eighth notes. Septuple meter can also be notated by using regularly alternating bars of triple and duple or quadruple meters, for example + , or + + , or through the use of compound meters, in which two or three numerals take the place of the expected numerator 7, for example, , or .
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In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator an integer) is called "reducing a fraction". Rewriting a radical (or "root") expression with the smallest possible whole number under the radical symbol is called "reducing a radical". Minimizing the number of radicals that appear underneath other radicals in an expression is called denesting radicals.
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The formula describing a current divider is similar in form to that for the voltage divider. However, the ratio describing current division places the impedance of the considered branches in the denominator, unlike voltage division where the considered impedance is in the numerator. This is because in current dividers, total energy expended is minimized, resulting in currents that go through paths of least impedance, hence the inverse relationship with impedance. Comparatively, voltage divider is used to satisfy Kirchhoff's Voltage Law (KVL).
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Although almost all analog electronic filters are IIR, digital filters may be either IIR or FIR. The presence of feedback in the topology of a discrete-time filter (such as the block diagram shown below) generally creates an IIR response. The z domain transfer function of an IIR filter contains a non-trivial denominator, describing those feedback terms. The transfer function of an FIR filter, on the other hand, has only a numerator as expressed in the general form derived below.
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There are two types of derivatives with matrices that can be organized into a matrix of the same size. These are the derivative of a matrix by a scalar and the derivative of a scalar by a matrix. These can be useful in minimization problems found in many areas of applied mathematics and have adopted the names tangent matrix and gradient matrix respectively after their analogs for vectors. Note: The discussion in this section assumes the numerator layout convention for pedagogical purposes.
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Eric Hehner and Nigel Horspool proposed in 1979 the use of a -adic representation for rational numbers on computers called quote notation. The primary advantage of such a representation is that addition, subtraction, and multiplication can be done in a straightforward manner analogous to similar methods for binary integers; and division is even simpler, resembling multiplication. However, it has the disadvantage that representations can be much larger than simply storing the numerator and denominator in binary (for more details see ).
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The original proof of the irrationality of the non-square natural numbers depends on Euclid's lemma. Many proofs of the irrationality of the square roots of non-square natural numbers implicitly assume the fundamental theorem of arithmetic, which was first proven by Carl Friedrich Gauss in his Disquisitiones Arithmeticae. This asserts that every integer has a unique factorization into primes. For any rational non-integer in lowest terms there must be a prime in the denominator which does not divide into the numerator.
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This approximation can be extremely inaccurate in some cases where a zero in the numerator is near in frequency. The method also uses a simplified method for finding the term linear in frequency based upon summing the RC-products for each capacitor in the circuit, where the resistor R for a selected capacitor is the resistance found by inserting a test source at its site and setting all other capacitors to zero. Hence the name zero- value time constant technique.
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There are two representations of the rational numbers in common use. One uses a sign ( + or – ), followed by a nonnegative integer (numerator), followed by a division symbol, followed by a positive integer (denominator). For example, –58/2975 . (If no sign is written, the sign is + .) The other is a sign followed by a sequence of digits, with a radix point (called a decimal point in base ten) somewhere in the sequence, and an overscore over one or more of the rightmost digits.
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Newton, who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396" (or "nearly 4 to 3"; for water). Hauksbee, who called it the "ratio of refraction", wrote it as a ratio with a fixed numerator, like "10000 to 7451.9" (for urine). Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1 (water). Young did not use a symbol for the index of refraction, in 1807.
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These superscripts typically share a baseline with numerator digits, the top of which are aligned with the top of the full-height numerals of the base font; lowercase ascenders may extend above. Ordinal indicators are sometimes written as superscripts (, , , , rather than 1st, 2nd, 3rd, 4th), although many English-language style guides recommend against this use. Other languages use a similar convention, such as 1er or 2e in French, or 4ª and 4º in Portuguese, Galician and Italian, or 4.ª and 4.
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However, a meaningful factorization for a rational number or a rational function can be obtained by writing it in lowest terms and separately factoring its numerator and denominator. Factorization was first considered by ancient Greek mathematicians in the case of integers. They proved the fundamental theorem of arithmetic, which asserts that every positive integer may be factored into a product of prime numbers, which cannot be further factored into integers greater than 1. Moreover, this factorization is unique up to the order of the factors.
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A common fraction is a division expression where both dividend and divisor are integers (although typically called the numerator and denominator), and there is no implication that the division needs to be evaluated further. A more basic way to show division is to use the obelus (or division sign) in this manner: :a \div b. This form is infrequent except in basic arithmetic. The obelus is also used alone to represent the division operation itself, for instance, as a label on a key of a calculator.
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Because vectors are matrices with only one column, the simplest matrix derivatives are vector derivatives. The notations developed here can accommodate the usual operations of vector calculus by identifying the space M(n,1) of n-vectors with the Euclidean space Rn, and the scalar M(1,1) is identified with R. The corresponding concept from vector calculus is indicated at the end of each subsection. NOTE: The discussion in this section assumes the numerator layout convention for pedagogical purposes. Some authors use different conventions.
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The reserves-to-production ratio (RPR or R/P) is the remaining amount of a non-renewable resource, expressed in time. While applicable to all natural resources, the RPR is most commonly applied to fossil fuels, particularly petroleum and natural gas. The reserve portion (numerator) of the ratio is the amount of a resource known to exist in an area and to be economically recoverable (proven reserves). The production portion (denominator) of the ratio is the amount of resource produced in one year at the current rate.
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In mathematics, the Herbrand–Ribet theorem is a result on the class group of certain number fields. It is a strengthening of Ernst Kummer's theorem to the effect that the prime p divides the class number of the cyclotomic field of p-th roots of unity if and only if p divides the numerator of the n-th Bernoulli number Bn for some n, 0 < n < p − 1\. The Herbrand–Ribet theorem specifies what, in particular, it means when p divides such an Bn.
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If the denominator of the ratio is expressed as a single unit of one of these quantities, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable. One common type of rate is "per unit of time", such as speed, heart rate and flux. Ratios that have a non-time denominator include exchange rates, literacy rates, and electric field (in volts per meter).
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This tempts the analyst to ignore the problem. However (s)he must consider whether a set of large beta coefficients reflect strong preferences (a large true beta) or consistency in choices (a large true lambda), or some combination of the two. Dividing all estimates by one other – typically that of the price variable – cancels the confounded lambda term from numerator and denominator. This solves the problem, with the added benefit that it provides economists with the respondent's willingness to pay for each attribute level.
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Although the program is part of the Ministry of Education, it has been criticized for being "too Mayan". Although PRONEBI attempts to prevent the use of Spanish loanwords (Hispanicisms) in bilingual classrooms, bilingual teachers often express concepts which do not exist in the Mayan languages (like "flashlight" or "numerator") with Spanish loanwords. PRONEBI aims to retain the "purity" of the Mayan languages by encouraging the development of neologisms, using Mayan- language lexicons to express foreign concepts. However, some Mayan intellectuals and activists believe that PRONEBI is not sufficiently representative of Mayan identity.
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If the order of q and β were to be reversed the result would not in general be α. The quaternion q can be thought of as an operator that changes β into α, by first rotating it, formerly an act of version and then changing the length of it, formerly call an act of tension. Also by definition the quotient of two vectors is equal to the numerator times the reciprocal of the denominator. Since multiplication of vectors is not commutative, the order cannot be changed in the following expression.
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Partch chose the 11 limit (i.e. all rational numbers with odd factors of numerator and denominator not exceeding 11) as the basis of his music, because the 11th harmonic is the first that is utterly foreign to Western ears. The seventh harmonic is poorly approximated by 12-tone equal temperament, but it appears in ancient Greek scales, is well-approximated by meantone temperament, and it is familiar from the barbershop quartet;Abbott, Lynn (1992): Play That Barber Shop Chord: A Case for the African-American Origin of Barbershop Harmony. American Music 10, no.
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The coefficients change each season based upon how often each event occurs. Because the coefficients are derived from expected run value, we can use wOBA to estimate a few more things about a player's production and baseball as a whole. When using the formula (shown below), the numerator side on its own will give us an estimate of how many runs a player is worth to his team. Similarly, a team's wOBA is a good estimator of team runs scored, and deviations from predicted runs scored indicate a combination of situational hitting and base running.
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The aim is to include the values of people that are often excluded from markets in the same terms as used in markets, that is money, in order to give people a voice in resource allocation decisions. Some SROI users employ a version of the method that does not require that all impacts be assigned a financial proxy. Instead the "numerator" includes monetized, quantitative but not monetized, qualitative, and narrative types of information about value. A network was formed in 2008 to facilitate the continued evolution of the method.
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Another 2006 study, led by Simon Chapman, found that after this law was enacted in 1996 in Australia, the country went more than a decade without any mass shootings, and gun-related deaths (especially suicides) declined dramatically. The latter of these studies also criticized the former for using a time-series analysis despite the fact that, according to Chapman et al., "calculating mortality rates and then treating them as a number in a time series ignores the natural variability inherent in the counts that make up the numerator of the rate." Chapman et al.
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149 is the 35th prime number, and with the next prime number, 151, is a twin prime, thus 149 is a Chen prime. 149 is an emirp, since the number 941 is also prime. 149 is a strong prime in the sense that it is more than the arithmetic mean of its two neighboring primes. 149 is an irregular prime since it divides the numerator of the Bernoulli number B130. 149 is an Eisenstein prime with no imaginary part and a real part of the form 3n - 1.
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With the card B/W there is always a 50% chance W being on top, thus in 50% of the cases card B/W is drawn, the draw affects neither numerator nor denominator and effectively does not count (this is also true for all times W/W is drawn, so that card might as well be removed from the set altogether). Conclusively, the cards B/B and B/W are not of equal chances, because in the 50% of the cases B/W is drawn, this card is simply "disqualified".
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OpenType features include automatic ligature sets, numerals (tabular, proportional, oldstyle and lining), numerator, denominator, scientific inferior subscripts, and small caps. It is also distributed with Microsoft Excel Viewer, Microsoft PowerPoint Viewer,Excel ViewerPowerpoint Viewer the Microsoft Office Compatibility PackMicrosoft Office Compatibility Pack for Word, Excel, and PowerPoint File Formats for Microsoft Windows and the Open XML File Format Converter for Mac.Open XML File Format Converter for Mac 1.2.1 It is not available as a freeware for use in other operating systems such as GNU/Linux, cross-platform use, and web use.
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A decimal fraction is a fraction whose denominator is not given explicitly, but is understood to be an integer power of ten. Decimal fractions are commonly expressed using decimal notation in which the implied denominator is determined by the number of digits to the right of a decimal separator, the appearance of which (e.g., a period, a raised period (•), a comma) depends on the locale (for examples, see decimal separator). Thus for 0.75 the numerator is 75 and the implied denominator is 10 to the second power, viz.
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The rotational angle from leaf to leaf in a repeating spiral can be represented by a fraction of a full rotation around the stem. Alternate distichous leaves will have an angle of 1/2 of a full rotation. In beech and hazel the angle is 1/3, in oak and apricot it is 2/5, in sunflowers, poplar, and pear, it is 3/8, and in willow and almond the angle is 5/13. The numerator and denominator normally consist of a Fibonacci number and its second successor.
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Nowadays fractions, unlike inline division, are often given using smaller numbers, superscript, and subscript (e.g., 23⁄43). This notation is responsible for the current form of the percent , permille , and permyriad signs, developed from the horizontal form which represented an early modern corruption of an Italian abbreviation of per cento.. Many fonts draw the fraction slash (and the division slash) less vertical than the slash. The separate encoding is also intended to permit automatic formatting of the preceding and succeeding digits by glyph substitution with numerator and denominator glyphs (e.g.
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The slope of a linear demand curve is constant. The elasticity of demand changes continuously as one moves down the demand curve because the ratio of price to quantity continuously falls. At the point the demand curve intersects the y-axis PED is infinitely elastic, because the variable Q appearing in the denominator of the elasticity formula is zero there. At the point the demand curve intersects the x-axis PED is zero, because the variable P appearing in the numerator of the elasticity formula is zero there.
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If the limit exists, meaning that there is a way of choosing a value for that makes a continuous function, then the function is differentiable at , and its derivative at equals . In practice, the existence of a continuous extension of the difference quotient to is shown by modifying the numerator to cancel in the denominator. Such manipulations can make the limit value of for small clear even though is still not defined at . This process can be long and tedious for complicated functions, and many shortcuts are commonly used to simplify the process.
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The stat was invented in 1979 by writer Daniel Okrent, who called the metric "innings pitched ratio" at the time. Okrent excluded hit batsmen from the numerator of baserunners allowed since Sunday newspapers did not include hit batsmen in their statistical updates. WHIP is one of the few sabermetric statistics to enter mainstream baseball usage. In addition to its use in live games, the WHIP is one of the most commonly used statistics in fantasy baseball, and is standard in fantasy leagues that employ 4×4, 5×5, and 6×6 formats.
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Height functions allow mathematicians to count objects, such as rational points, that are otherwise infinite in quantity. For instance, the set of rational numbers of naive height (the maximum of the numerator and denominator when expressed in lowest terms) below any given constant is finite despite the set of rational numbers being infinite. In this sense, height functions can be used to prove asymptotic results such as Baker's theorem in transcendental number theory which was proved by . In other cases, height functions can distinguish some objects based on their complexity.
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Cancelling out is a mathematical process used for removing subexpressions from a mathematical expression, when this removal does not change the meaning or the value of the expression because the subexpressions have equal and opposing effects. For example, a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator. As another example, if a×b=a×c, then the multiplicative term a can be canceled out if a≠0, resulting in the equivalent expression b=c; this is equivalent to dividing through by a.
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One method of deriving Millman's theorem starts by converting all the branches to current sources (which can be done using Norton's theorem). A branch that is already a current source is simply not converted. In the expression above, this is equivalent to replacing the e_k/R_k term in the numerator of the expression above with the current of the current generator, where the kth branch is the branch with the current generator. The parallel conductance of the current source is added to the denominator as for the series conductance of the voltage sources.
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Formulas typically used in railway engineering in general compute the resistance as inversely proportional to the radius of curvature (thus, they neglect the fact that the resistance is dependent on both speed and superelevation). For example, in the USSR, the standard formula is Wr (curve resistance in parts per thousand or kgf/tonne) = 700/R where R is the radius of the curve in meters. Other countries often use the same formula, but with a different numerator-constant. For example, the US used 446/R, Italy 800/R, England 600/R, China 573/R, etc.
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Let K be a number field with ring of integers R. Let S be a finite set of prime ideals of R. An element x of K is an S-unit if the principal fractional ideal (x) is a product of primes in S (to positive or negative powers). For the ring of rational integers Z one may take S to be a finite set of prime numbers and define an S-unit to be a rational number whose numerator and denominator are divisible only by the primes in S.
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Since 4 would be the minimum possible even factor in the numerator and 2 would be the maximum possible even factor in the denominator, this would imply a to be even despite defining it as odd. Thus one of m and n is odd and the other is even, and the numerators of the two fractions with denominator 2mn are odd. Thus these fractions are fully reduced (an odd prime dividing this denominator divides one of m and n but not the other; thus it does not divide m2 ± n2).
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When this happens the numerator is large, the denominator is small, and the result is a delta ratio which is high [ > 2 ]. This means a combined high anion gap metabolic acidosis and a pre-existing either respiratory acidosis or metabolic alkalosis (causing the high bicarbonate) – i.e. a mixed acid-base metabolic acidosis. Result 3: if there is a pure HAGMA, the bicarb would be expected to fall at a similar rate as the anion gap rises, since one molecule of acid combines with one molecule of bicarb buffer.
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In practice, the method of cross-multiplying means that we multiply the numerator of each (or one) side by the denominator of the other side, effectively crossing the terms over. :\frac a b warrow \frac c d \quad \frac a b earrow \frac c d. The mathematical justification for the method is from the following longer mathematical procedure. If we start with the basic equation: :\frac a b = \frac c d we can multiply the terms on each side by the same number and the terms will remain equal.
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Rules governing the use of zero appeared in Brahmagupta's Brahmasputha Siddhanta (7th century), which states the sum of zero with itself as zero, and incorrectly division by zero as:Algebra with Arithmetic of Brahmagupta and Bhaskara, translated to English by Henry Thomas Colebrooke (1817) London > A positive or negative number when divided by zero is a fraction with the > zero as denominator. Zero divided by a negative or positive number is either > zero or is expressed as a fraction with zero as numerator and the finite > quantity as denominator. Zero divided by zero is zero.
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Gini coefficient, income distribution by country. The Gini coefficient is a measure of statistical dispersion most prominently used as a measure of inequality of income distribution or inequality of wealth distribution. It is defined as a ratio with values between 0 and 1: the numerator is the area between the Lorenz curve of the distribution and the uniform distribution line; the denominator is the area under the uniform distribution line. Thus, a low Gini coefficient indicates more equal income or wealth distribution, while a high Gini coefficient indicates more unequal distribution.
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When blood pressure is stated for medical purposes, it is usually written with the systolic and diastolic pressures separated by a slash, for example, 120/80 mmHg. This clinical notation is not a mathematical figure for a fraction or ratio, nor a display of a numerator over a denominator. Rather, it is a medical notation showing the two clinically significant pressures involved (systole followed by diastole). It is often shown followed by a third number, the value of the heart rate (in beats per minute), which typically is measured jointly with blood pressure readings.
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Analysis assists those conducting the study to verify and help define the term MSP. For the indicator MSP, WHO has defined a summary of what it measures, rationale for the indicator, numerator, denominator and calculation, recommended measurement tools, measurement, frequency, and the strengths and weaknesses of the indicator. WHO's definition of MSP has some strengths and weaknesses The quantification is an indicator and a picture of the levels of higher-risk sex in a locale. If those surveyed changed their activity to one sexual partner, the change will be quantified by changes in the indicator.
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Saturday, 24 August 2019 Visual acuity is a quantitative measure of the ability to identify black symbols on a white background at a standardized distance as the size of the symbols is varied. It is the most common clinical measurement of visual function. In the term "20/20 vision" the numerator refers to the distance in feet from which a person can reliably distinguish a pair of objects. The denominator is the distance from which an 'average' person would be able to distinguish —the distance at which their separation angle is 1 arc minute.
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Also in this regard, note that the VIS term in the numerator of NDVI only scales the result, thereby creating negative values. NDVI is functionally and linearly equivalent to the ratio NIR / (NIR+VIS), which ranges from 0 to 1 and is thus never negative nor limitless in range.Crippen, R.E. (1990) 'Calculating the vegetation index faster,' Remote Sensing of Environment, 34, 71-73. But the most important concept in the understanding of the NDVI algebraic formula is that, despite its name, it is a transformation of a spectral ratio (NIR/VIS), and it has no functional relationship to a spectral difference (NIR-VIS).
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The Japanese invasion money used in the Netherlands Indies was first denominated in Gulden (1942) and later in Roepiah (1944–45). The Gulden issue bears the payment obligation "De Japansche Regeering Betaalt Aan Toonder" (The Japanese Government pays to the bearer) on notes one-half Gulden and above. On smaller change notes (1–10 cents) it is shortened to “De Japansche Regeering”. All Japanese invasion money used in the Netherlands Indies bear the block prefix letter “S” either followed by a number (lower denominations, 1–10 cents), a second letter, or as the numerator in a fractional block layout.
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Since the hyperbolic functions are rational functions of whose numerator and denominator are of degree at most two, these functions may be solved in terms of , by using the quadratic formula; then, taking the natural logarithm gives the following expressions for the inverse hyperbolic functions. For complex arguments, the inverse hyperbolic functions, the square root and the logarithm are multi-valued functions, and the equalities of the next subsections may be viewed as equalities of multi-valued functions. For all inverse hyperbolic functions (save the inverse hyperbolic cotangent and the inverse hyperbolic cosecant), the domain of the real function is connected.
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The Persian mathematician Jamshīd al-Kāshī made the same discovery of decimal fractions in the 15th century. Al Khwarizmi introduced fractions to Islamic countries in the early 9th century; his fraction presentation was similar to the traditional Chinese mathematical fractions from Sunzi Suanjing.Lam Lay Yong, "The Development of Hindu-Arabic and Traditional Chinese Arithmetic", Chinese Science, 1996 p38, Kurt Vogel notation This form of fraction with numerator on top and denominator at bottom without a horizontal bar was also used by 10th century Abu'l-Hasan al-Uqlidisi and 15th century Jamshīd al-Kāshī's work "Arithmetic Key". File:Stevin-decimal notation.
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Al-Hassar or Abu Bakr Muhammad ibn Abdallah ibn Ayyash al-Hassar ()was a Muslim mathematician from Morocco, living in the 12th century. He is the author of two books Kitab al-bayan wat-tadhkar (Book of Demonstration and Memorization), a manual of calculation and Kitab al-kamil fi sinaat al-adad (Complete Book on the Art of Numbers), on the breakdown of numbers. The first book is lost and only a part of the second book remains. Al-Hassar developed the modern symbolic mathematical notation for fractions, where the numerator and denominator are separated by a horizontal bar.
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The proof above for the square root of two can be generalized using the fundamental theorem of arithmetic. This asserts that every integer has a unique factorization into primes. Using it we can show that if a rational number is not an integer then no integral power of it can be an integer, as in lowest terms there must be a prime in the denominator that does not divide into the numerator whatever power each is raised to. Therefore, if an integer is not an exact th power of another integer, then that first integer's th root is irrational.
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In most contexts, both numbers are restricted to be positive. A ratio may be specified either by giving both constituting numbers, written as "a to b" or "a∶b", or by giving just the value of their quotient Equal quotients correspond to equal ratios. Consequently, a ratio may be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator, or as the value denoted by this fraction. Ratios of counts, given by (non-zero) natural numbers, are rational numbers, and may sometimes be natural numbers.
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The numbers 50 to 99 are states, assigned in a rough spatial geographic order, and are used for banks located outside one of the 49 numbered cities. The second part of the numerator (after the dash) is the bank's ABA Institution Identifier, which also forms digits 5 to 8 of the nine digit routing number (YYYY). The denominator is also part of the routing number; by adding leading zeroes to make up four digits where necessary (e.g. 212 is written as 0212, 31 is written as 0031, etc.), it forms the first four digits of the routing number (XXXX).
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Mathematical notation was decimal, and based on hieroglyphic signs for each power of ten up to one million. Each of these could be written as many times as necessary to add up to the desired number; so to write the number eighty or eight hundred, the symbol for ten or one hundred was written eight times respectively. Because their methods of calculation could not handle most fractions with a numerator greater than one, they had to write fractions as the sum of several fractions. For example, they resolved the fraction two-fifths into the sum of one-third + one-fifteenth.
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Avenir Next Rounded is a version of Avenir Next with rounded terminals, designed by Akira Kobayashi and Sandra Winter.A new form of an old friend: Avenir Next RoundedNeues Schriftdesign Avenir Next Rounded von Akira Kobayashi – gut lesbar, vielseitig und sympathisch – 6. Februar 2013 - Die neue Avenir Next Rounded ist die weichere Interpretation der serifenlosen Avenir Next The family includes 8 fonts in 4 weights (regular, medium, demi, and bold) and 1 width (based on normal width), with complementary italics. OpenType features include numerator and denominator, fractions, standard ligatures, lining and old-style figures, localized forms, scientific inferiors, subscript and superscript, and small caps.
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Chemotherapy and other medications dispensed in a physician's office are reimbursed according to the Average Sales Price, a number computed by taking the total dollar sales of a drug as the numerator and the number of units sold nationwide as the denominator. The current reimbursement formula is known as "ASP+6" since it reimburses physicians at 106% of the ASP of drugs. Pharmaceutical company discounts and rebates are included in the calculation of ASP, and tend to reduce it. In addition, Medicare pays 80% of ASP+6, which is the equivalent of 84.8% of the actual average cost of the drug.
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For example: When dividends are both taxed as income, and also generate a tax credit in the UK and Canadian system, the effective tax rate is the net effect of both - the net tax divided by the actual dividend's value. For example: When contributions are made to Tax Deferred Accounts the reduced tax base will result in reduced taxes calculated at the statutory marginal rate. But the reduction in the tax base may also affect qualification for other government benefits. The difference in those benefits is added to the numerator to increase the effective marginal rate due to the contribution.
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So the equation above should be balanced as the change in the AG away from normal [12 ] is similar to the change in bicarb away from normal [24]. Mathematically, if the change in the numerator is similar to the change in the denominator, the delta ratio will be close to 1. Since the anions are unable to diffuse out of the bloodstream, while bicarbonate and hydrogen ions diffuse with ease (as H₂CO₃, carbonic acid), the usual result will be closer to a delta ratio of 1 to 2. Lactic acidosis usually causes a ratio of 1.6.
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In probability theory and statistics, the noncentral F-distribution is a continuous probability distribution that is a noncentral generalization of the (ordinary) F-distribution. It describes the distribution of the quotient (X/n1)/(Y/n2), where the numerator X has a noncentral chi-squared distribution with n1 degrees of freedom and the denominator Y has a central chi-squared distribution with n2 degrees of freedom. It is also required that X and Y are statistically independent of each other. It is the distribution of the test statistic in analysis of variance problems when the null hypothesis is false.
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The oxygenation index is a calculation used in intensive care medicine to measure the fraction of inspired oxygen (FiO2) and its usage within the body. A lower oxygenation index is better - this can be inferred by the equation itself. As the oxygenation of a person improves, they will be able to achieve a higher PaO2 at a lower FiO2. This would be reflected on the formula as a decrease in the numerator or an increase in the denominator - thus lowering the OI. Typically an OI threshold is set for when a neonate should be placed on ECMO, for example >40.
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In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. The importance of the partial fraction decomposition lies in the fact that it provides algorithms for various computations with rational functions, including the explicit computation of antiderivatives,Horowitz, Ellis. "Algorithms for partial fraction decomposition and rational function integration." Proceedings of the second ACM symposium on Symbolic and algebraic manipulation.
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Each of these could be written as many times as necessary to add up to the desired number; so to write the number eighty or eight hundred, the symbol for ten or one hundred was written eight times respectively.Clarke, Somers (1990); p. 217. Because their methods of calculation could not handle most fractions with a numerator greater than one, ancient Egyptian fractions had to be written as the sum of several fractions. For example, the fraction two-fifths was resolved into the sum of one-third + one-fifteenth; this was facilitated by standard tables of values.Clarke, Somers (1990); p. 218.
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But the numerator then has a noncentral chi-squared distribution, and consequently the quotient as a whole has a non-central F-distribution. One uses this F-statistic to test the null hypothesis that the linear model is correct. Since the non-central F-distribution is stochastically larger than the (central) F-distribution, one rejects the null hypothesis if the F-statistic is larger than the critical F value. The critical value corresponds to the cumulative distribution function of the F distribution with x equal to the desired confidence level, and degrees of freedom d1 = (n − p) and d2 = (N − n).
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Intuitively, a meromorphic function is a ratio of two well-behaved (holomorphic) functions. Such a function will still be well-behaved, except possibly at the points where the denominator of the fraction is zero. If the denominator has a zero at z and the numerator does not, then the value of the function will approach infinity; if both parts have a zero at z, then one must compare the multiplicity of these zeros. From an algebraic point of view, if the function's domain is connected, then the set of meromorphic functions is the field of fractions of the integral domain of the set of holomorphic functions.
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Cost-effectiveness analysis (CEA) is a form of economic analysis that compares the relative costs and outcomes (effects) of different courses of action. Cost-effectiveness analysis is distinct from cost–benefit analysis, which assigns a monetary value to the measure of effect. Cost-effectiveness analysis is often used in the field of health services, where it may be inappropriate to monetize health effect. Typically the CEA is expressed in terms of a ratio where the denominator is a gain in health from a measure (years of life, premature births averted, sight-years gained) and the numerator is the cost associated with the health gain.
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Rational function models have the following disadvantages: #The properties of the rational function family are not as well known to engineers and scientists as are those of the polynomial family. The literature on the rational function family is also more limited. Because the properties of the family are often not well understood, it can be difficult to answer the following modeling question: Given that data has a certain shape, what values should be chosen for the degree of the numerator and the degree on the denominator? #Unconstrained rational function fitting can, at times, result in undesired vertical asymptotes due to roots in the denominator polynomial.
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So to test whether a point in the s-plane is on the root locus, only the angles to all the open loop poles and zeros need be considered. This is known as the angle condition. Similarly, the magnitude of the result of the rational polynomial is the product of all the magnitudes in the numerator divided by the product of all the magnitudes in the denominator. It turns out that the calculation of the magnitude is not needed to determine if a point in the s-plane is part of the root locus because K varies and can take an arbitrary real value.
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This formula is determined by taking the unpaid amount and any costs associated with incarcerating the accused as the numerator and eight times the provincial minimum wage as the denominator. For example, an unpaid fine of $640 in a jurisdiction with a minimum wage of $8 hourly would be approximately 10 days. In addition, unless waived by the court, the defendant is required to pay a victim fine surcharge in addition to whatever else the judge imposes as sentence. The surcharge is 30% of the fine imposed or, if no fine is imposed, $100 for an indictable offence and $50 for an offence punishable on summary conviction.
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When using valuation multiples such as EV/EBITDA and EV/EBIT, the numerator should correspond to the denominator. The EV should, therefore, correspond to the market value of the assets that were used to generate the profits in question, excluding assets acquired (and including assets disposed) during a different financial reporting period. This requires restating EV for any mergers and acquisitions (whether paid in cash or equity), significant capital investments or significant changes in working capital occurring after or during the reporting period being examined. Ideally, multiples should be calculated using the market value of the weighted average capital employed of the company during the comparable financial period.
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Arbitrary-precision arithmetic in most computer software is implemented by calling an external library that provides data types and subroutines to store numbers with the requested precision and to perform computations. Different libraries have different ways of representing arbitrary-precision numbers, some libraries work only with integer numbers, others store floating point numbers in a variety of bases (decimal or binary powers). Rather than representing a number as single value, some store numbers as a numerator/denominator pair (rationals) and some can fully represent computable numbers, though only up to some storage limit. Fundamentally, Turing machines cannot represent all real numbers, as the cardinality of exceeds the cardinality of .
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One property he discovered was that the denominators of the fractions of Bernoulli numbers are always divisible by six. He also devised a method of calculating based on previous Bernoulli numbers. One of these methods follows: It will be observed that if n is even but not equal to zero, # is a fraction and the numerator of in its lowest terms is a prime number, # the denominator of contains each of the factors 2 and 3 once and only once, # is an integer and consequently is an odd integer. In his 17-page paper "Some Properties of Bernoulli's Numbers" (1911), Ramanujan gave three proofs, two corollaries and three conjectures.
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Like measurements of prevalence of periodontitis, the measurement of incidence will vary depending upon the case definition of the disease. Often “incidence” refers to new sites that meet the definition of periodontitis, even if they occur within a person that already has other diseased sites. Beck 1997 found that past disease predicted subsequent CAL, although not usually at the same site. Also, persons with greater attachment loss at baseline were more likely to lose teeth over the next 5 years. Beck 1997 – looked at incidence density such that the numerator was attachment loss greater or equal to 3mm while the denominator was the time at risk for each site.
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Twill weave is often designated as a fraction, such as , in which the numerator indicates the number of harnesses that are raised (and thus threads crossed: in this example, two), and the denominator indicates the number of harnesses that are lowered when a filling yarn is inserted (in this example, one). The fraction is read as "two up, one down" (the fraction for plain weave is .). The minimum number of harnesses needed to produce a twill can be determined by totaling the numbers in the fraction; for the example described, the number of harnesses is three. Twill weave can be identified by its diagonal lines.
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A Steiner chain for two disjoint circles is a finite cyclic sequence of additional circles, each of which is tangent to the two given circles and to its two neighbors in the chain. Steiner's porism states that if two circles have a Steiner chain, they have infinitely many such chains. The chain is allowed to wrap more than once around the two circles, and can be characterized by a rational number p whose numerator is the number of circles in the chain and whose denominator is the number of times it wraps around. All chains for the same two circles have the same value of p.
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Thus, in either case, the parent is a fraction with a smaller sum of numerator and denominator, so repeated reduction of this type must eventually reach the number 1. As a graph with one outgoing edge per vertex and one root reachable by all other vertices, the Calkin–Wilf tree must indeed be a tree. The children of any vertex in the Calkin–Wilf tree may be computed by inverting the formula for the parents of a vertex. Each vertex has one child whose value is less than 1, , because this is the only value less than 1 whose parent formula leads back to .
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A series of entropy production formulas can be derived. : ∆S heat= [(1/T)a-(1/T)b] x ∆ thermal energy : ∆S expansion= [(pressure/T)a-(pressure/T)b] x ∆ volume : ∆S electric = [(voltage/T)a-(voltage/T)b] x ∆ current These equations have the form : ∆Ss = [(intensive)a -(intensive)b] x ∆ extensive where the a and b are two different regions. This is the long version of Prigogine’s equation : ∆Ss = XsJs where Xs is the entropic force and Js is the entropic flux. It is possible to derive a number of different energy forms from Prigogine’s equation. Note that in thermal energy in the entropy production equation the intensive factor’s numerator is 1.
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The Islamic law of inheritance served as an impetus behind the development of algebra (derived from the Arabic al-jabr) by Muhammad ibn Mūsā al-Khwārizmī and other medieval Islamic mathematicians. Al-Khwārizmī's Hisab al-jabr w’al- muqabala, the foundational text of algebra, devoted its third and longest chapter to solving problems related to Islamic inheritance using algebra. He formulated the rules of inheritance as linear equations, hence his knowledge of quadratic equations was not required. Al-Hassār, a mathematician from the Maghreb (North Africa) specializing in Islamic inheritance jurisprudence during the 12th century, developed the modern symbolic mathematical notation for fractions, where the numerator and denominator are separated by a horizontal bar.
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For an example of an ordered field that is not Archimedean, take the field of rational functions with real coefficients. (A rational function is any function that can be expressed as one polynomial divided by another polynomial; we will assume in what follows that this has been done in such a way that the leading coefficient of the denominator is positive.) To make this an ordered field, one must assign an ordering compatible with the addition and multiplication operations. Now if and only if f − g > 0, so we only have to say which rational functions are considered positive. Call the function positive if the leading coefficient of the numerator is positive.
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Charles Roy Henderson ( – ) was an American statistician and a pioneer in animal breeding — the application of quantitative methods for the genetic evaluation of domestic livestock. This is critically important because it allows farmers and geneticists to predict whether a crop or animal will have a desired trait, and to what extent the trait will be expressed. He developed mixed model equations to obtain best linear unbiased predictions of breeding values and, in general, any random effect. He invented three methods for the estimation of variance components in unbalanced settings of mixed models, and invented a method for constructing the inverse of Wright's numerator relationship matrix based on a simple list of pedigree information.
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A rational that falls within the interval , for , can be found with the continued fractions for and . When both and are irrational and : : where and have identical continued fraction expansions up through , a rational that falls within the interval is given by the finite continued fraction, : This rational will be best in the sense that no other rational in will have a smaller numerator or a smaller denominator. If is rational, it will have two continued fraction representations that are finite, and , and similarly a rational will have two representations, and . The coefficients beyond the last in any of these representations should be interpreted as ; and the best rational will be one of , , , or .
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If scope is changed during execution, that change should be input into the VBS, the numerator in computing the Actual DIPP adjusted, and the DIPP Progress Index thus updated. Unlike cost, which can be summed up the branches of a WBS to provide an overall budget, value cannot similarly be summed in a VBS. If the value of an automobile is $25,000, there are many components and activities that are mandatory in generating that value – leave any of them out, and the value of the project approaches zero. Therefore, the fact that the engine, driveshaft and wheels are all mandatory, and each therefore has a value-added of $25,000 does NOT make the value of the automobile $75,000.
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Al-Hassār, a mathematician from Morocco specializing in Islamic inheritance jurisprudence during the 12th century, developed the modern symbolic mathematical notation for fractions, where the numerator and denominator are separated by a horizontal bar. This same fractional notation appeared soon after in the work of Fibonacci in the 13th century. Abū al-Hasan ibn Alī al-Qalasādī (1412–1486) was the last major medieval Arab algebraist, who made the first attempt at creating an algebraic notation since Ibn al- Banna two centuries earlier, who was himself the first to make such an attempt since Diophantus and Brahmagupta in ancient times. The syncopated notations of his predecessors, however, lacked symbols for mathematical operations.
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Division can only be performed if the result has no remainder (i.e., the divisor is a factor of the numerator). Fractions are not allowed, and only positive integers may be obtained as a result at any stage of the calculation. As in the letters rounds, any contestant who does not write down their calculations in time must go first if both declare the same result, and both contestants must show their work to each other if their results and calculations are identical. Only the contestant whose result is closer to the target number scores points: 10 for reaching it exactly, 7 for being 1–5 away, 5 for being 6–10 away.
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Thomas > Sutton and George Dawson, A Dictionary of Photography, London: Sampson Low, > Son & Marston, 1867, (p. 122). In 1874, John Henry Dallmeyer called the ratio 1/N the "intensity ratio" of a lens: > The rapidity of a lens depends upon the relation or ratio of the aperture to > the equivalent focus. To ascertain this, divide the equivalent focus by the > diameter of the actual working aperture of the lens in question; and note > down the quotient as the denominator with 1, or unity, for the numerator. > Thus to find the ratio of a lens of 2 inches diameter and 6 inches focus, > divide the focus by the aperture, or 6 divided by 2 equals 3; i.e.
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The ocean is the largest sink or reservoir of atmospheric carbon dioxide (CO2), continually taking in carbon from the air. This CO2 is then dissolved and reacts with water to form carbonic acid, which reacts further to generate carbonate (CO32−), bicarbonate (HCO3−), and hydrogen (H+) ions. The saturation state of seawater refers to how saturated (or unsaturated) the water is with these ions, and this determines if an organism will calcify or if the already calcified crystals will dissolve. The saturation state for calcium carbonate (CaCO3) can be determined using the equation: Ω = ([Ca2+][CO32−])/ Ksp Where the numerator denotes the concentrations of calcium ions to carbonate ions, and the denominator Ksp refers to the stoichiometric solubility product for the mineral (solid) phase of calcium carbonate.
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Now take S to be the set of sequences of k elements selected from our n-element set without repetition. On one hand, there is an easy bijection of S with the Cartesian product corresponding to the numerator n(n-1)\cdots(n-k+1), and on the other hand there is a bijection from the set C of pairs of a k-combination and a permutation σ of k to S, by taking the elements of C in increasing order, and then permuting this sequence by σ to obtain an element of S. The two ways of counting give the equation :n(n-1)\cdots(n-k+1)=\binom nk k!, and after division by k! this leads to the stated formula for \tbinom nk.
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Under these conditions, the system can be described by a "one-plus" rate law where the numerator consists of all rate constants and species required to go from starting material to product, and the denominator consists of a sum of terms describing each of the states in which the catalyst exists (and 1 corresponds to the free catalyst). For the simplest case where one substrate goes to one product through a single intermediate: : = In the slightly more complex situation where two substrates bind in sequence followed by product release: : = In the case of the simple pre-equilibrium conditions described above, the catalyst resting state is either entirely or partially (depending on the magnitude of the equilibrium constant) the substrate bound complex.
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The most commonly used example of this is the kernel Fisher discriminant. LDA can be generalized to multiple discriminant analysis, where c becomes a categorical variable with N possible states, instead of only two. Analogously, if the class-conditional densities p(\vec x\mid c=i) are normal with shared covariances, the sufficient statistic for P(c\mid\vec x) are the values of N projections, which are the subspace spanned by the N means, affine projected by the inverse covariance matrix. These projections can be found by solving a generalized eigenvalue problem, where the numerator is the covariance matrix formed by treating the means as the samples, and the denominator is the shared covariance matrix. See “Multiclass LDA” above for details.
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The information ratio is often annualized. While it is then common for the numerator to be calculated as the arithmetic difference between the annualized portfolio return and the annualized benchmark return, this is an approximation because the annualization of an arithmetic difference between terms is not the arithmetic difference of the annualized terms.“The Annualization of Attribution” by Andre Mirabelli in Advanced Portfolio Attribution Analysis edited by Carl Bacon. Since the denominator is here taken to be the annualized standard deviation of the arithmetic difference of these series, which is a standard measure of annualized risk, and since the ratio of annualized terms is the annualization of their ratio, the annualized information ratio provides the annualized risk-adjusted active return of the portfolio relative to the benchmark.
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The mediant is the fraction between two fractions a/c and b/d whose numerator is the sum of the numerators, a+b, and whose denominator is the sum of the denominators, c+d. That is, the mediant of the fractions a/c and b/d is the fraction (a+b)/(c+d). In his paper Haros demonstrated that the mediant is always irreducible and, more importantly for this purposes, if one starts with the sequence of fractions :1/99, 1/98, 1/97, ..., 1/4, 1/3, 1/2, 2/3, 3/4, 5/6, ..., 96/97, 97/98, 98/99 and just keeps applying the rule, only keeping the result if the denominator is less than one-hundred, then they generate all 3,003.
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In a letter to Cipriano de Rore dated from around 1563, Benedetti proposed a new theory of the cause of consonance, arguing that since sound consists of air waves or vibrations, in the more consonant intervals the shorter, more frequent waves concurred with the longer, less frequent waves at regular intervals. Isaac Beeckman and Marin Mersenne both adopted this theory in the next century. In the same letter, he proposed a measure of consonance by taking the product of the numerator and the denominator of a rational interval in lowest terms. James Tenney also used this method to develop his measure of "harmonic distance" (log2(ab) is the harmonic distance for the ratio b/a measured from an arbitrary tonal center 1/1).
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In accounting practice, the tax numerator in the above equation usually includes taxes at federal, state, provincial, and municipal levels. Marginal tax rates are applied to income in countries with progressive taxation schemes, with incremental increases in income taxed in progressively higher tax brackets, resulting in the tax burden being distributed amongst those who can most easily afford it. Marginal taxes are valuable as they allow governments to generate revenue to fund social services in a way that only affects those who will be the least negatively affected. In economics, one heavily disputed theory is that marginal tax rates will impact the incentive of increased income, meaning that higher marginal tax rates cause individuals to have less incentive to earn more.
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The equation for the Filtration rate, Q: ::(1) Q = (πbρKΩ^2(r_b^2 - r_p^2))/(μ([r_b/r_p])+(KR_m)/r_b) ::(2) αKp_s = 1 Where µ and ρ are viscosity and liquid density, respectively. Ω is the angular speed, K is the average cake permeability, which is related to equation 2, rp,rc, and rb are the radius of the liquid surface, cake surface and filter medium adjacent to the perforated bowl respectively, Rm is the combined resistance, α is the specific resistance and ρs is the solid density. The numerator describes the pusher's driving force, which is due to the hydrostatic pressure difference across the wall and the liquid surface. The denominator describes the resistance due to the cake layer and the filter medium.
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The tonal complexity of ratios between these harmonics is said to get more complex with higher prime factors. To limit this tonal complexity, an interval is said to be n-limit when both its numerator and denominator are n-smooth. Furthermore, superparticular ratios are very important in just tuning theory as they represent ratios between adjacent members of the harmonic series. Størmer's theorem allows all possible superparticular ratios in a given limit to be found. For example, in the 3-limit (Pythagorean tuning), the only possible superparticular ratios are 2/1 (the octave), 3/2 (the perfect fifth), 4/3 (the perfect fourth), and 9/8 (the whole step). That is, the only pairs of consecutive integers that have only powers of two and three in their prime factorizations are (1,2), (2,3), (3,4), and (8,9).
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The energy efficiency ratio (EER) of a particular cooling device is the ratio of output cooling energy (in BTU/hr) to input electrical energy (in Watts) at a given operating point. EER is generally calculated using a 95 °F outside temp and an inside (actually return air) temp of 80 °F and 50% relative humidity. The EER is related to the coefficient of performance (COP) commonly used in thermodynamics, with the primary difference being that the COP of a cooling device is unit-less, because the numerator and denominator are expressed in the same units. The EER uses mixed units, so it doesn't have an immediate physical sense and is obtained by multiplying the COP (or EER) by the conversion factor from BTU/h to Watts: EER = 3.41214 × COP (see British thermal unit).
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In mathematics, a rational function is any function which can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K. In this case, one speaks of a rational function and a rational fraction over K. The values of the variables may be taken in any field L containing K. Then the domain of the function is the set of the values of the variables for which the denominator is not zero and the codomain is L. The set of rational functions over a field K is a field, the field of fractions of the ring of the polynomial functions over K.
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Any rational function (in other words, f(z) is the ratio of polynomial functions g(z) and h(z) of z with complex coefficients, such that g(z) and h(z) have no common factor) can be extended to a continuous function on the Riemann sphere. Specifically, if z0 is a complex number such that the denominator h(z0) is zero but the numerator g(z0) is nonzero, then f(z0) can be defined as ∞. Moreover, f(∞) can be defined as the limit of f(z) as , which may be finite or infinite. The set of complex rational functions — whose mathematical symbol is C(z) — form all possible holomorphic functions from the Riemann sphere to itself, when it is viewed as a Riemann surface, except for the constant function taking the value ∞ everywhere.
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A: The height of the island is four li and 55 steps, and it is 120 li and 50 steps from the pole. Algorithm: Let the numerator equals to the height of pole multiplied by the separation of poles, let denominator be the difference of offsets, add the quotient to the height of pole to obtain the height of island. As the distance of front pole to the island could not be measured directly, Liu Hui set up two poles of same height at a known distance apart and made two measurements. The pole was perpendicular to the ground, eye view from ground level when the tip of pole was on a straight line sight with the peak of island, the distance of eye to the pole was called front offset =DG, similarly, the back offset =FH, difference of offsets =FH-DG.
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The granularity-related inconsistency of means (GRIM) test is a simple statistical test used to identify inconsistencies in the analysis of data sets. The test relies on the fact that, given a dataset containing N integer values, the arithmetic mean (commonly called simply the average) is restricted to a few possible values: it must always be expressible as a fraction with an integer numerator and a denominator N. If the reported mean does not fit this description, there must be an error somewhere; the preferred term for such errors is "inconsistencies", to emphasise that their origin is, on first discovery, typically unknown. GRIM inconsistencies can result from inadvertent data-entry or typographical errors or from scientific fraud. The GRIM test is most useful in fields such as psychology where researchers typically use small groups and measurements are often integers.
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In the study of harmony, many musical intervals can be expressed as a superparticular ratio (for example, due to octave equivalency, the ninth harmonic, 9/1, may be expressed as a superparticular ratio, 9/8). Indeed, whether a ratio was superparticular was the most important criterion in Ptolemy's formulation of musical harmony.. In this application, Størmer's theorem can be used to list all possible superparticular numbers for a given limit; that is, all ratios of this type in which both the numerator and denominator are smooth numbers. These ratios are also important in visual harmony. Aspect ratios of 4:3 and 3:2 are common in digital photography,. Ang also notes the 16:9 (widescreen) aspect ratio as another common choice for digital photography, but unlike 4:3 and 3:2 this ratio is not superparticular.
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In statistics, a sum of squares due to lack of fit, or more tersely a lack-of- fit sum of squares, is one of the components of a partition of the sum of squares of residuals in an analysis of variance, used in the numerator in an F-test of the null hypothesis that says that a proposed model fits well. The other component is the pure-error sum of squares. The pure-error sum of squares is the sum of squared deviations of each value of the dependent variable from the average value over all observations sharing its independent variable value(s). These are errors that could never be avoided by any predictive equation that assigned a predicted value for the dependent variable as a function of the value(s) of the independent variable(s).
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The alternate direct form II only needs N delay units, where N is the order of the filter – potentially half as much as direct form I. This structure is obtained by reversing the order of the numerator and denominator sections of Direct Form I, since they are in fact two linear systems, and the commutativity property applies. Then, one will notice that there are two columns of delays (z^{-1}) that tap off the center net, and these can be combined since they are redundant, yielding the implementation as shown below. The disadvantage is that direct form II increases the possibility of arithmetic overflow for filters of high Q or resonance.J. O. Smith III, Direct Form II It has been shown that as Q increases, the round-off noise of both direct form topologies increases without bounds.
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Although it is not encountered in practice, the equations can also apply to the case of two media with a common permittivity but different refractive indices due to different permeabilities. From equations () and (), if ϵ is fixed instead of μ, then becomes inversely proportional to , with the result that the subscripts 1 and 2 in equations () to () are interchanged (due to the additional step of multiplying the numerator and denominator by ). Hence, in () and (), the expressions for and in terms of refractive indices will be interchanged, so that Brewster's angle () will give instead of and any beam reflected at that angle will be p-polarized instead of s-polarized.More general Brewster angles, for which the angles of incidence and refraction are not necessarily complementary, are discussed in C.L. Giles and W.J. Wild, "Brewster angles for magnetic media", International Journal of Infrared and Millimeter Waves, vol.
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The simplest non-trivial moneyness is the ratio of these, either S/K or its reciprocal K/S, which is known as the (spot) simple moneyness, with analogous forward simple moneyness. Conventionally the fixed quantity is in the denominator, while the variable quantity is in the numerator, so S/K for a single option and varying spots, and K/S for different options at a given spot, such as when constructing a volatility surface. A volatility surface using coordinates a non-trivial moneyness M and time to expiry τ is called the relative volatility surface (with respect to the moneyness M). While the spot is often used by traders, the forward is preferred in theory, as it has better properties, thus F/K will be used in the sequel. In practice, for low interest rates and short tenors, spot versus forward makes little difference.
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While the two approaches are equivalent at the aggregate level, the NATA approach allows a more detailed analysis to be made of those who gain and those who lose as a result of a proposal. However the NATA approach raises issues regarding the precise definition of the impacts that are included in the numerator and denominator of the Benefit- Cost Ratio. As well as setting out methods for appraising transport proposals, WebTAG contains values that should be used to assess different types of impacts, including the value of time and vehicle operating costs. A UK Government Multi-Criteria Analysis (MCA) manual, originally produced by the former Department for Transport, Local Government and the Regions and now overseen by the Department for Communities and Local Government, highlights NATA as an example of MCA being applied in practice to a major area of UK Government policy.
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In such a case the CRR cannot be derived from either an RR or OR. An example of such a situation occurs when the numerator is a per event risk, and the denominator is a per-time risk (also known as a cumulative risk). An example of this type of analysis would be the investigation of a pulmonary embolism (PE) that occurred a week after a patient sustained a lower extremity fracture in a traffic crash. Such complications often result from blood clots forming in the legs and then traveling to the lungs. If the patient had a history of deep vein thrombosis (DVT) in the lower extremities prior to the crash, then a CRR might consist of the comparison between the risk of a PE following a lower extremity fracture (a per event rate) and the 1-week risk of PE in a patient with DVT (a time-dependent probability).
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If p is an irregular prime and p divides the numerator of the Bernoulli number B2k for , then is called an irregular pair. In other words, an irregular pair is a book-keeping device to record, for an irregular prime p, the particular indices of the Bernoulli numbers at which regularity fails. The first few irregular pairs (when ordered by k) are: : (691, 12), (3617, 16), (43867, 18), (283, 20), (617, 20), (131, 22), (593, 22), (103, 24), (2294797, 24), (657931, 26), (9349, 28), (362903, 28), ... . The smallest even k such that nth irregular prime divides Bk are :32, 44, 58, 68, 24, 22, 130, 62, 84, 164, 100, 84, 20, 156, 88, 292, 280, 186, 100, 200, 382, 126, 240, 366, 196, 130, 94, 292, 400, 86, 270, 222, 52, 90, 22, ... For a given prime p, the number of such pairs is called the index of irregularity of p.
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The SMC is very similar to the more popular Jaccard index. The main difference is that the SMC has the term M_{00} in its numerator and denominator, whereas the Jaccard index does not. Thus, the SMC counts both mutual presences (when an attribute is present in both sets) and mutual absence (when an attribute is absent in both sets) as matches and compares it to the total number of attributes in the universe, whereas the Jaccard index only counts mutual presence as matches and compares it to the number of attributes that have been chosen by at least one of the two sets. In market basket analysis, for example, the basket of two consumers who we wish to compare might only contain a small fraction of all the available products in the store, so the SMC will usually return very high values of similarities even when the baskets bear very little resemblance, thus making the Jaccard index a more appropriate measure of similarity in that context.
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Favoured by bookmakers in the United Kingdom and Ireland, and also common in horse racing, fractional odds quote the net total that will be paid out to the bettor, should he or she win, relative to the stake. Odds of 4/1 would imply that the bettor stands to make a £400 profit on a £100 stake. If the odds are 1/4, the bettor will make £25 on a £100 stake. In either case, having won, the bettor always receives the original stake back; so if the odds are 4/1 the bettor receives a total of £500 (£400 plus the original £100). Odds of 1/1 are known as evens or even money. The numerator and denominator of fractional odds are always integers, thus if the bookmaker's payout was to be £1.25 for every £1 stake, this would be equivalent to £5 for every £4 staked, and the odds would therefore be expressed as 5/4.
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Hipparchus's draconitic lunar motion cannot be solved by the lunar-four arguments that are sometimes proposed to explain his anomalistic motion. A solution that has produced the exact ratio is rejected by most historians though it uses the only anciently attested method of determining such ratios, and it automatically delivers the ratio's four-digit numerator and denominator. Hipparchus initially used (Almagest 6.9) his 141 BC eclipse with a Babylonian eclipse of 720 BC to find the less accurate ratio 7,160 synodic months = 7,770 draconitic months, simplified by him to 716 = 777 through division by 10. (He similarly found from the 345-year cycle the ratio 4267 synodic months = 4573 anomalistic months and divided by 17 to obtain the standard ratio 251 synodic months = 269 anomalistic months.) If he sought a longer time base for this draconitic investigation he could use his same 141 BC eclipse with a moonrise 1245 BC eclipse from Babylon, an interval of 13,645 synodic months = draconitic months ≈ anomalistic months.
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Typically, a root locus diagram will indicate the transfer function's pole locations for varying values of the parameter K. A root locus plot will be all those points in the s-plane where G(s)H(s) = -1 for any value of K. The factoring of K and the use of simple monomials means the evaluation of the rational polynomial can be done with vector techniques that add or subtract angles and multiply or divide magnitudes. The vector formulation arises from the fact that each monomial term (s-a) in the factored G(s)H(s) represents the vector from a to s in the s-plane. The polynomial can be evaluated by considering the magnitudes and angles of each of these vectors. According to vector mathematics, the angle of the result of the rational polynomial is the sum of all the angles in the numerator minus the sum of all the angles in the denominator.
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However, since division almost immediately introduces infinitely repeating sequences of digits (such as 4/7 in decimal, or 1/10 in binary), should this possibility arise then either the representation would be truncated at some satisfactory size or else rational numbers would be used: a large integer for the numerator and for the denominator. But even with the greatest common divisor divided out, arithmetic with rational numbers can become unwieldy very quickly: 1/99 − 1/100 = 1/9900, and if 1/101 is then added, the result is 10001/999900. The size of arbitrary- precision numbers is limited in practice by the total storage available, the variables used to index the digit strings, and computation time. A 32-bit operating system may limit available storage to less than 4 GB. A programming language using 32-bit integers can only index 4 GB. If multiplication is done with a algorithm, it would take on the order of steps to multiply two one- million-word numbers.
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Until the 1990s, Russia and the Soviet Union did not count, as a live birth or as an infant death, extremely premature infants (less than 1,000 g, less than 28 weeks gestational age, or less than 35 cm in length) that were born alive (breathed, had a heartbeat, or exhibited voluntary muscle movement) but failed to survive for at least seven days. Although such extremely premature infants typically accounted for only about 0.5% of all live-born children, their exclusion from both the numerator and the denominator in the reported IMR led to an estimated 22%–25% lower reported IMR.In 1990, the Baltic states moved to the WHO standard definition; in 1993 Russia also moved to this definition. In some cases, too, perhaps because hospitals or regional health departments were held accountable for lowering the IMR in their catchment area, infant deaths that occurred in the 12th month were "transferred" statistically to the 13th month (i.e.
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In the expression 6/x vision, the numerator (6) is the distance in metres between the subject and the chart and the denominator (x) the distance at which a person with 6/6 acuity would discern the same optotype. Thus, 6/12 means that a person with 6/6 vision would discern the same optotype from 12 metres away (i.e. at twice the distance). This is equivalent to saying that with 6/12 vision, the person possesses half the spatial resolution and needs twice the size to discern the optotype. A simple and efficient way to state acuity is by converting the fraction to a decimal: 6/6 then corresponds to an acuity (or a Visus) of 1.0 (see Expression below), while 6/3 corresponds to 2.0, which is often attained by well-corrected healthy young subjects with binocular vision. Stating acuity as a decimal number is the standard in European countries, as required by the European norm (EN ISO 8596, previously DIN 58220).
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When used for binary attributes, the Jaccard index is very similar to the simple matching coefficient. The main difference is that the SMC has the term M_{00} in its numerator and denominator, whereas the Jaccard index does not. Thus, the SMC counts both mutual presences (when an attribute is present in both sets) and mutual absence (when an attribute is absent in both sets) as matches and compares it to the total number of attributes in the universe, whereas the Jaccard index only counts mutual presence as matches and compares it to the number of attributes that have been chosen by at least one of the two sets. In market basket analysis, for example, the basket of two consumers who we wish to compare might only contain a small fraction of all the available products in the store, so the SMC will usually return very high values of similarities even when the baskets bear very little resemblance, thus making the Jaccard index a more appropriate measure of similarity in that context.
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The TI-36X Pro is an updated version of the European model, the TI-30X Pro MultiView, which was taken off the market shortly after its release in 2010 because of programming errors. While the 30X's bugs were fixed for relaunch as the 36X Pro, the updated version contains a notable software bug of its own, where it displays mixed numbers involving \pi incorrectly. In such cases, the display shows \pi in the numerator of the fraction, instead of as a separate coefficient. Converting ˚C to Kelvin within a fraction causes a display bug to appear (the K appears as a space instead) Conversions involving Kelvin incorrectly display ˚K, when it should just be K. In the main constants menu, there is a bug on the sixteenth menu entry for atomic mass unit, "u", which should display as "Atomic Mass U". When this entry is displayed in the top row, then scrolled down to the second row, the display incorrectly shows "Atomic Mass Ur", taking on the "r" from the next entry's last character.
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Its size is 27.264 cents, slightly larger than the Pythagorean comma. The composition of the septimal comma and the syntonic comma is 36/35, known as the septimal diesis. Its size is 48.8 cents, making it practically a quarter tone. The septimal diesis appears as the difference between many septimal intervals and their 5-limit counterparts: the minor seventh (9/5) and the seventh harmonic (7/4), the 8/7 septimal whole tone and the 10/9 minor whole tone, the 7/6 septimal minor third and the 6/5 minor third, the 9/7 septimal major third and the 5/4 major third, and many more. Other septimal commas include 49/48 (occasionally called the slendro diesis) (), which commonly appears as the difference between a ratio with 7 in the denominator and another with 7 in the numerator, like 8/7 and 7/6; and 50/49, called the tritonic diesis, because it is the difference between the two septimal tritones, 7/5 and 10/7, or Erlich's decatonic comma, because it plays an important role in the ten-tone scales of Paul Erlich (the intervals are tempered so that 50/49 vanishes).
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Beta(0,0): The Haldane prior probability expressing total ignorance about prior information, where we are not even sure whether it is physically possible for an experiment to yield either a success or a failure. As α, β → 0, the beta distribution approaches a two-point Bernoulli distribution with all probability density concentrated at each end, at 0 and 1, and nothing in between. A coin-toss: one face of the coin being at 0 and the other face being at 1. The Beta(0,0) distribution was proposed by J.B.S. Haldane, who suggested that the prior probability representing complete uncertainty should be proportional to p−1(1−p)−1. The function p−1(1−p)−1 can be viewed as the limit of the numerator of the beta distribution as both shape parameters approach zero: α, β → 0. The Beta function (in the denominator of the beta distribution) approaches infinity, for both parameters approaching zero, α, β → 0. Therefore, p−1(1−p)−1 divided by the Beta function approaches a 2-point Bernoulli distribution with equal probability 1/2 at each end, at 0 and 1, and nothing in between, as α, β → 0. A coin-toss: one face of the coin being at 0 and the other face being at 1.
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The conversion to a base b_2 of an integer represented in base b_1 can be done by a succession of Euclidean divisions by b_2: the right-most digit in base b_2 is the remainder of the division of by b_2; the second right-most digit is the remainder of the division of the quotient by b_2, and so on. More precisely, the th digit from the right is the remainder of the division by b_2 of the th quotient. For example: converting A10BHex to decimal (41227): 0xA10B/10 = 0x101A R: 7 (ones place) 0x101A/10 = 0x19C R: 2 (tens place) 0x19C/10 = 0x29 R: 2 (hundreds place) 0x29/10 = 0x4 R: 1 ... 0x4/10 = 0x0 R: 4 When converting to a larger base (such as from binary to decimal), the remainder represents b_2 as a single digit, using digits from b_1. For example: converting 0b11111001 (binary) to 249 (decimal): 0b11111001/10 = 0b11000 R: 0b1001 (0b1001 = "9" for ones place) 0b11000/10 = 0b10 R: 0b100 (0b100 = "4" for tens) 0b10/10 = 0b0 R: 0b10 (0b10 = "2" for hundreds) For the fractional part, conversion can be done by taking digits after the radix point (the numerator), and dividing it by the implied denominator in the target radix.
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