"We pay more attention to numerators, such as '16 adverse events,' than we do to denominators, such as 'per million vaccine doses,' " Dr. Buttenheim said.
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" He explained how he interprets the variables in his practice: Seth advises advisors, "Demonstrate how high your numerators are and how low your denominator is, and you've built high trust.
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We'll therefore stick to the data we have both good numerators and denominators for to answer an important question: What are your risks if you do get infected with the coronavirus?
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You can pick different numerators and denominators to get at the same concept — using just wages and salaries instead of total compensation, for example, or dividing by gross domestic product instead of the related concept of national income — but the same basic pattern reveals itself.
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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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And second, note that there are 20 fractions. Which fractions have 20 as denominator? The ones whose numerators are relatively prime to 20 (, , , , , , , ).
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The remainder of WV 131, along Saltwell Road, was County Route 13. The numerators of county routes spurring from WV 131 still reflect these former numbers.
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Similarly, investigators sometimes report the false positive rate (FPR) as well as the false negative rate (FNR). However, these rates are ratios that fail to reveal their numerators and denominators. The total operating characteristic (TOC) is an effective method to express a model's diagnostic ability. TOC shows the numerators and denominators of the previously mentioned rates, thus TOC provides more information than the commonly used receiver operating characteristic (ROC) and ROC's associated area under the curve (AUC).
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One may thus equate numerators with numerators and denominators with denominators, giving Euclid's formula : a = m^2 - n^2 ,\ \, b = 2mn ,\ \, c = m^2 + n^2 with m and n coprime and of opposite parities. A longer but more commonplace proof is given in Maor (2007)Maor, Eli, The Pythagorean Theorem, Princeton University Press, 2007: Appendix B. and Sierpiński (2003). Another proof is given in , as an instance of a general method that applies to every homogeneous Diophantine equation of degree two.
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It is a version of ITC Galliard with characters that support Central European languages. OpenType features include case sensitive forms, numerators/denominators, fractions, ligatures, lining/old style/proportional/tabular figures, localized forms, ordinals, scientific inferiors, superscript, small caps, diphthongs, stylistic alternates (set 1).
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Consider the multiplicative monoid of positive integers as a category with one object. In this category, the pullback of two positive integers and is just the pair , where the numerators are both the least common multiple of and . The same pair is also the pushout.
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It is a version of Trade Gothic Next with rounded corners and terminals. The family includes nine fonts in three weights (regular, bold, heavy) and three widths and one style (roman). OpenType features include numerators/denominators, fractions, standard/discretionary ligatures, localized forms, sub/superscript, proportional figures.
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Superscripted numerals are used for the numerators of diagonal fractions, like ¾ or the signs for percent %, permille ‰, and basis point ‱. Certain standard abbreviations are also composed as diagonal fractions, such as ℅ (care of), ℀ (account of), ℁ (addressed to the subject), or in Spanish ℆ (cada uno/a, "each one").
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All points of the ellipse are given, except for (−1,1), which corresponds to t = ∞; the entire curve is parameterized therefore by the real projective line. Such a rational parameterization may be considered in the projective space by equating the first projective coordinates to the numerators of the parameterization and the last one to the common denominator.
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Thus, the diatomic sequence forms both the sequence of numerators and the sequence of denominators of the numbers in the Calkin–Wilf sequence. The function is the number of odd binomial coefficients of the form , ,. and also counts the number of ways of writing as a sum of powers of two in which each power occurs at most twice.
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Now consider the numerators. The first fraction, two thirds, is twice as large as one third. Since one third of a quarter is one twelfth, two thirds of a quarter is two twelfth. The second fraction, three quarters, is three times as large as one quarter, so two thirds of three quarters is three times as large as two thirds of one quarter.
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Characters are classified with a Numeric type. Characters such as fractions, subscripts, superscripts, Roman numerals, currency numerators, encircled numbers, and script-specific digits are type Numeric. They have a numeric value that can be decimal, including zero and negatives, or a vulgar fraction. If there is not such a value, as with most of the characters, the numeric type is "None".
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The font family originally includes 14 fonts in 7 weights, with a complementary italic. OpenType features include numerators/denominators, fractions, ligatures, lining/old style/proportional and tabular figures, superscript, small capitals, stylistic alternates, stylistic sets 1 and 2 (Roman fonts only). Only one width is offered, without condensed or extended designs. OpenType Pro version supports all western European, most central European and many eastern European languages.
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Madhava's sine series is stated in verses 2.440 and 2.441 in Yukti- dipika commentary (Tantrasamgraha-vyakhya) by Sankara Variar. A translation of the verses follows. Multiply the arc by the square of the arc, and take the result of repeating that (any number of times). Divide (each of the above numerators) by the squares of the successive even numbers increased by that number and multiplied by the square of the radius.
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The Bernoulli numbers are related to Fermat's Last Theorem (FLT) by Kummer's theorem , which says: :If the odd prime does not divide any of the numerators of the Bernoulli numbers then has no solutions in nonzero integers. Prime numbers with this property are called regular primes. Another classical result of Kummer are the following congruences. :Let be an odd prime and an even number such that does not divide .
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Divide (each of the above numerators) by the square of the successive even numbers decreased by that number and multiplied by the square of the radius. But the first term is (now)(the one which is) divided by twice the radius. Place the successive results so obtained one below the other and subtract each from the one above. These together give the śara as collected together in the verse beginning with stena, stri, etc.
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3/5 + 4/5i and 5/13 + 12/13i (which correspond to the two most famous Pythagorean triples (3,4,5) and (5,12,13)) are rational points on the unit circle in the complex plane, and thus are elements of G. Their group product is −33/65 + 56/65i, which corresponds to the Pythagorean triple (33,56,65). The sum of the squares of the numerators 33 and 56 is 1089 + 3136 = 4225, which is the square of the denominator 65.
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This contradicts the common meaning of the words that are used, as denominator refers to fractions, and two fractions do not have any greatest common denominator (if two fractions have the same denominator, one obtains a greater common denominator by multiplying all numerators and denominators by the same integer). Historically, other names for the same concept have included greatest common measure.. This notion can be extended to polynomials (see Polynomial greatest common divisor) and other commutative rings (see below).
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Separation of a fractional algebraic expression into partial fractions is the reverse of the process of combining fractions by converting each fraction to the lowest common denominator (LCD) and adding the numerators. This separation can be accomplished by the Heaviside cover-up method, another method for determining the coefficients of a partial fraction. Case one has fractional expressions where factors in the denominator are unique. Case two has fractional expressions where some factors may repeat as powers of a binomial.
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A height function is a function that quantifies the complexity of mathematical objects. In Diophantine geometry, height functions quantify the size of solutions to Diophantine equations and are typically functions from a set of points on algebraic varieties (or a set of algebraic varieties) to the real numbers. For instance, the classical or naive height over the rational numbers is typically defined to be the maximum of the numerators and denominators of the coordinates (e.g. 3 for the coordinates ), but in a logarithmic scale.
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In integral calculus we would want to write a fractional algebraic expression as the sum of its partial fractions in order to take the integral of each simple fraction separately. Once the original denominator, D0, has been factored we set up a fraction for each factor in the denominator. We may use a subscripted D to represent the denominator of the respective partial fractions which are the factors in D0. Letters A, B, C, D, E, and so on will represent the numerators of the respective partial fractions.
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Designed by Lynne Yun of Monotype GmbH, this family is based on Trade Gothic Condensed Heavy, but with only capital glyphs for Latin texts. The different fonts can be used over each other in layers to create complex effects.Trade Gothic Display – new multi-layer styles for the popular design font The family include five fonts in one weight and one width, with five different styles inside glyph outlines. OpenType features include case-sensitive forms, numerators/denominators, fractions, standard ligatures, localized forms, sub/superscript, proportional/lining figures, glyph (de)composition, kerning, mark (to mark) positioning.
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Walter S. Johnson (1884–1978) was a notable businessman and philanthropist in San Francisco, California. He was one of the founders of the American Forest Products Corporation, a Fortune 500 company in the 1950s and 1960s, and of Friden, Inc., the Friden Calculating Machine Company, which developed and sold electro-mechanical numerators and office equipment, predecessors of today's computerized counterparts. As a philanthropist, Walter S. Johnson is most famous for his 1959 contribution to the preservation of the Palace of Fine Arts, an act that ensured the endurance of the iconic San Francisco landmark.
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One of the hallmarks of Context-Based Sustainability is its use of Context-Based Metrics (CBMs). Unlike other metrics used to measure, manage and report the sustainability performance of organizations (e.g., absolute and relative/intensity metrics), some CBMs, but not all, take the form of quotients that have two parts to them: 1) denominators that express organization-specific norms for what their impacts on vital capitals must be in order to be sustainable (i.e., equivalent to "allocations" as explained above), and 2) numerators that express their actual impacts on the same capitals.
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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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If is field of complex numbers, the fundamental theorem of algebra implies that all have degree one, and all numerators a_{ij} are constants. When is the field of real numbers, some of the may be quadratic, so, in the partial fraction decomposition, quotients of linear polynomials by powers of quadratic polynomials may also occur. In the preceding theorem, one may replace "distinct irreducible polynomials" by "pairwise coprime polynomials that are coprime with their derivative". For example, the may be the factors of the square-free factorization of .
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Its sequence of numerators (or, offset by one, denominators) is Stern's diatomic series, and can be computed by the fusc function. The Calkin–Wilf tree is named after Neil Calkin and Herbert Wilf, who considered it in their 2000 paper. The tree was introduced earlier by Jean Berstel and Aldo de Luca, Section 6. as Raney tree, since they drew some ideas from a paper by George N. Raney.. Stern's diatomic series was formulated much earlier by Moritz Abraham Stern, a 19th-century German mathematician who also invented the closely related Stern–Brocot tree.
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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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Industry Level and Aggregate Measures of Productivity Growth with Explicit Treatment of Taxes on Products. Statistics Finland. By construction, Domar weights sum up to a figure larger than 1.0, because the revenue of some firms comes from the sales of intermediate to other firms so some revenues are multiply counted in the firm by firm accounting, in the numerators of the Domar weights, but are netted out in GDP. Example: a tire-maker's sales might go mainly to the makers of cars, trucks, bicycles, and so forth who sell their products with tires included, so tire revenues are multiply counted.
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Followers of the Greek philosopher Pythagoras ( ) discovered that the square root of two cannot be expressed as a fraction of integers. (This is commonly though probably erroneously ascribed to Hippasus of Metapontum, who is said to have been executed for revealing this fact.) In Jain mathematicians in India wrote the "Sthananga Sutra", which contains work on the theory of numbers, arithmetical operations, and operations with fractions. A modern expression of fractions known as bhinnarasi seems to have originated in India in the work of Aryabhatta (), Brahmagupta (), and Bhaskara (). Their works form fractions by placing the numerators () over the denominators (), but without a bar between them.
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The one that is the simplest to describe is probably the so-called Hermite's method. As the degree of cij is bounded by the degree of pi, and the degree of b is the difference of the degrees of f and g (if this difference is non negative; otherwise, b=0), one may write these unknowns polynomials as polynomials with unknown coefficients. Reducing the two members of above formula to the same denominator and writing that the coefficients of each power of x are the same in the two numerators, one gets a system of linear equations which can be solved to obtain the desired values for the unknowns coefficients.
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If all numerators are 1 in a fraction written in this form, and all denominators are different from each other, the result is an Egyptian fraction representation of the number. This notation was also sometimes combined with the composite fraction notation: two composite fractions written next to each other would represent the sum of the fractions. The complexity of this notation allows numbers to be written in many different ways, and Fibonacci described several methods for converting from one style of representation to another. In particular, chapter II.7 contains a list of methods for converting an improper fraction to an Egyptian fraction, including the greedy algorithm for Egyptian fractions, also known as the Fibonacci–Sylvester expansion.
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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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Rotis serif Rotis semi-serif Rotis semi-sans Rotis sans-serif It is a version of Rotis Sans designed by Monotype Imaging senior designer Robin Nicholas, and freelance designer Alice Savoie. It expands the original with extra three font weights (Light, Semi Bold, and Black) and italics, along with revised letter spacing and kerning, a new set of numerals with similar height to the capitals.Font News: Rotis II Sans, expanded and improved The family includes 14 fonts in seven weights, with complementary italics. OpenType features include access all alternates, case-sensitive forms, numerators/denominators, fractions, standard ligatures, localized forms (OpenType Pro fonts only), proportional/tabular figures, scientific inferiors, superscript/subscript, stylistic alternates, stylistic sets 1, 2 and 3 (OpenType Std fonts only).
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The international standard symbol for inch is in (see ISO 31-1, Annex A) but traditionally the inch is denoted by a double prime, which is often approximated by double quotes, and the foot by a prime, which is often approximated by an apostrophe. For example, can be written as 3′ 2″. (This is akin to how the first and second "cuts" of the hour and degree are likewise indicated by prime and double prime symbols.) Subdivisions of an inch are typically written using dyadic fractions with odd number numerators; for example, would be written as ″ and not as 2.375″ nor as ″. However for engineering purposes fractions are commonly given to three or four places of decimals and have been for many years.
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Thus the difference between and is , in excess; between and , , in deficit; between and , , in excess; and so on. The result being, that by employing this series of differences we can express in another and very simple manner the fractions with which we are here concerned, by means of a second series of fractions of which the numerators are all unity and the denominators successively be the product of every two adjacent denominators. Instead of the fractions written above, we have thus the series: : + − + − ... The first term, as we see, is the first fraction; the first and second together give the second fraction, ; the first, the second and the third give the third fraction , and so on with the rest; the result being that the series entire is equivalent to the original value.
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Different plants arrange their leaves differently, for instance on alternating sides of the plant stem, or rotated from each other by other fractions of a full rotation between consecutive leaves. In these patterns, rotations by 1/2 of an angle, 1/3 of an angle, 3/8 of an angle, or 5/8 of an angle are common, and it does not appear to be coincidental that the numerators and denominators of these fractions are all Fibonacci numbers. Higher Fibonacci numbers often appear in the number of spiral arms in the spiraling patterns of sunflower seed heads, or the helical patterns of pineapple cells. The theme of Adler's work in this area, in the papers reproduced in this volume, was to find a mathematical model for plant development that would explain these patterns and the occurrence of the Fibonacci numbers and the golden ratio within them.
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