On his first three tests, Shaun scored 88, 98, and 79. What score must he get on his fourth test to have an average (mean) of 80 for all four tests?

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?

Suppose the equation ||x-a|-b|=2008 has 3 distinct real roots and a not =0. find the value of b.

Walter is to make cookies for a basketball tournament. he's made 15 cookies so far. his coach asked him to make at least 20 cookies but no more than 55. solve the inequality and interpret the solution. 20 ? x + 15 ? 55