John makes random guesses on his multiple-choice test, which has five options for each question. Let the random variable X be the number of guesses taken before guessing correctly.

An assembly consists of two mechanical components. suppose that the probabilities that the first and second components meet specifications are 0.87 and 0.84. assume that the components are independent. determine the probability mass function of the number of components in the assembly that meet specifications. x

Explain why the function is discontinuous at the given number a. (select all that apply.) f(x) = 1 x + 1 a = −1 f(−1) is undefined. lim x→−1+ f(x) and lim x→−1− f(x) exist, but are not equal. lim x→−1 f(x) does not exist. f(−1) and lim x→−1 f(x) exist, but are not equal. none of the above

The perimeter of a triangle is 69 cm. the first is 5 cm shorter than the second side. the third side is twice as long the first side. find the length of each side