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Terms are within the same expression and are combined by either addition or subtraction. For example, take the expression: + There are two terms in this expression. Notice that the two terms have a common factor, that is, both terms have an . This means that the common factor variable can be factored out, resulting in
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
In statistics, Somers’ D, sometimes incorrectly referred to as Somer’s D, is a measure of ordinal association between two possibly dependent random variables X and Y. Somers’ D takes values between − 1 {\displaystyle -1} when all pairs of the variables disagree and 1 {\displaystyle 1} when all pairs of the variables agree.
Terms that are either constants or have the same variables raised to the same powers are called like terms. If there are like terms in an expression, one can simplify the expression by combining the like terms. One adds the coefficients and keeps the same variable. + + = Any variable can be classified as being either a free variable or a bound ...
The unique pair of values a, b satisfying the first two equations is (a, b) = (1, 1); since these values also satisfy the third equation, there do in fact exist a, b such that a times the original first equation plus b times the original second equation equals the original third equation; we conclude that the third equation is linearly ...
A specific element x of X is a value of the variable, and the corresponding element of Y is the value of the function at x, or the image of x under the function. A function f , its domain X , and its codomain Y are often specified by the notation f : X → Y . {\displaystyle f:X\to Y.}
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
Multiplication symbols are usually omitted, and implied when there is no space between two variables or terms, or when a coefficient is used. For example, 3 × x 2 {\displaystyle 3\times x^{2}} is written as 3 x 2 {\displaystyle 3x^{2}} , and 2 × x × y {\displaystyle 2\times x\times y} may be written 2 x y {\displaystyle 2xy} .