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This proposition is (sometimes) known as the law of the unconscious statistician because of a purported tendency to think of the aforementioned law as the very definition of the expected value of of a function g(X) and a random variable X, rather than (more formally) as a consequence of the true definition of expected value. [1]
Initial value theorem (integral transform) Inscribed angle theorem ; Integral representation theorem for classical Wiener space (measure theory) Intermediate value theorem ; Intercept theorem (Euclidean geometry) Intersecting chords theorem (Euclidean geometry) Intersecting secants theorem (Euclidean geometry)
Menelaus's theorem, case 1: line DEF passes inside triangle ABC. In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ABC, and a transversal line that crosses BC, AC, AB at points D, E, F respectively, with D, E, F distinct from A, B, C. A ...
For example, using Cartesian coordinates on the plane, the distance between two points (x 1, y 1) and (x 2, y 2) is defined by the formula = + (), which can be viewed as a version of the Pythagorean theorem. Similarly, the angle that a line makes with the horizontal can be defined by the formula = (), where m is the slope of the line.
A quadrilateral such as BCEF is called an adventitious quadrangle when the angles between its diagonals and sides are all rational angles, angles that give rational numbers when measured in degrees or other units for which the whole circle is a rational number. Numerous adventitious quadrangles beyond the one appearing in Langley's puzzle have ...
Stanley is recalling 2.6 million mugs sold in the U.S. after the company received dozens of consumer complaints, including some users who reported getting burned and requiring medical attention ...
To find an unknown angle, the law of cosines is safer than the law of sines. The reason is that the value of sine for the angle of the triangle does not uniquely determine this angle. For example, if sin β = 0.5, the angle β can equal either 30° or 150°. Using the law of cosines avoids this problem: within the interval from 0° to 180° the ...
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