Kenneth is answering a quadratic modeling problem. He knows that a ball was thrown from an initial height of 5 feet in the air, and reached a maximum height of 35 feet, 2 seconds later. He wants to find out how high it is after 3 seconds. He uses the quadratic model of y=a(x-5)(x-2), because he thinks he should be using factored form, and he picks 5 and 2, since they're the easiest numbers. He solves for a, and gets 3.5. So, that would give him an upward-opening parabola, and at that point, he's fairly sure he made a mistake, since the ball should follow a path that is a downward-opening parabola. Determine Kenneth's mistake, and correctly find the quadratic function for the flight of the ball. Then, find its height after 3 seconds. The correct graph is shown. *

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?