On which of the following intervals is the function f(x) = 4 cos(2x − π) decreasing? x = pi over 2 to x = π x = 0 to x = pi over 2 x = pi over 2 to x = 3 pi over 2 x = π to x = 3 pi over 2

Afunction is given: f(x)=3x+12 a. determine the inverse of this function and name it g(x) b. use composite functions to show that these functions are inverses. c. f(g(– explain: what is the domain?

You are a clerk at convenience store. a customer owes 11.69 for a bag of potatoes chips. she gives you a five dollar bill. how much change should the customer receive?

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?