A committee of three people is selected at random from a set consisting of five teachers, seven parents of students, and three alumni. a. What is the probability of the event that the committee consists of all teachers?
b. What is the probability of the event that the committee has no teachers?

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?

Awindow has the shape of a rectangle with a semi circle at the top. find the approximate area of the window using the dimensions shown. 4ft by 8ft

Solve for the equation x. 2x + 22 = 4(x + 3)