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Problems 1–6 compute divisions of a certain number of loaves of bread by 10 men and record the outcome in unit fractions. Problems 7–20 show how to multiply the expressions 1 + 1/2 + 1/4 = 7/4, and 1 + 2/3 + 1/3 = 2 by different fractions. Problems 21–23 are problems in completion, which in modern notation are simply subtraction problems.
The true odds against winning for each of the three horses are 1–1, 3–2 and 9–1, respectively. In order to generate a profit on the wagers accepted, the bookmaker may decide to increase the values to 60%, 50% and 20% for the three horses, respectively. This represents the odds against each, which are 4–6, 1–1 and 4–1, in order.
According to Betz's law, no wind turbine of any mechanism can capture more than 16/27 (59.3%) of the kinetic energy in wind. The factor 16/27 (0.593) is known as Betz's coefficient. Practical utility-scale wind turbines achieve at peak 75–80% of the Betz limit. [2] [3] The Betz limit is based on an open-disk actuator.
The golden ratio's negative −φ and reciprocal φ−1 are the two roots of the quadratic polynomial x2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. This quadratic polynomial has two roots, and. The golden ratio is also closely related to the polynomial.
Example of the optimal Kelly betting fraction, versus expected return of other fractional bets. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate.
When the prevalences of interest are those of individual chemical elements, rather than of compounds or other substances, the term mass fraction can also refer to the ratio of the mass of an element to the total mass of a sample. In these contexts an alternative term is mass percent composition. The mass fraction of an element in a compound can ...
The duty cycle is defined as the ratio between the pulse duration, or pulse width ( ) and the period ( ) of a rectangular waveform. Spectrum in relation to duty cycle. A duty cycle or power cycle is the fraction of one period in which a signal or system is active. [ 1][ 2][ 3] Duty cycle is commonly expressed as a percentage or a ratio. A ...
The coefficient of relationship is a measure of the degree of consanguinity (or biological relationship) between two individuals. The term coefficient of relationship was defined by Sewall Wright in 1922, and was derived from his definition of the coefficient of inbreeding of 1921. The measure is most commonly used in genetics and genealogy.