le b. 51. Suppose that tan 0 = p/q, where p and q are positive ani 0° < 0 < 90°. Show that p sin0 q cos O p² – q° amtutmat p sin 0 + q cos 0 p² + q² +g² 52. This exercise shows how to obtain radical expressions for sin 15° and cos 15°. In the figure, assume that AB = BD = 2. %3D niwe 30° (a) In the right triangle BCD, note that DC = 1 because DC is opposite the 30° angle and BD = 2. Use the Pythagorean theorem to show that BC = V3. (b) Use the Pythagorean theorem to show that AD = 2\2 + V3. (c) Show that the expression for AD in part (b) is equal to V6 + V2. Hint: Two nonnegative quantities are 54. Thi %3D sin equal if and only if their squares are equal. (d) Explain why ZBAD = LBDA. (e) According to a theorem from geometry, an exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles. Apply this to AABD with exterior angle DBC = 30°, and show that ZBAD = 15°. (f) Using the figure and the values that you have obtained for the lengths, conclude that (a (b 1 2 + V3 sin 15° cos 15° = Võ + V2 (c (g) Rationalize the denominators in part (f) to obtain Võ + V2 sin 15° cos 15° 4 4. (h) Use your calculator to check the results in part (g). 3. The following foure chows a regular eleven-sided polygon

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.