Let $g(x) = x^5 + x^4 + x^3 + x^2 + x + 1$. what is the remainder when the polynomial $g(x^{12})$ is divided by the polynomial $g(x)$?

Find three consecutive numbers such that the sum of one-fourth the first and one-fifth the second is five less than one-seventh the third

Use the quadratic formula to solve the equation. if necessary, round to the nearest hundredth. x^2 - 20 = x a. 5, 4 b. -5, -4 c. -5, 4 d. 5, -4

Out of five men and five women, we form a committee consisting of four different people. assuming that each committee of size four is equally likely, find the probabilities of the following events: 1. the committee consists of two men and two women 2. the committee has more women than men. 3. the committee has at least one man. for the remainder of the problem assume that alice and bob are among the ten people being considered. 4. both alice and bob are members of the committee.