A crew working with dynamite to clear a road blasted a large rock straight up with
an initial velocity of 140 ft/sec. The rock reaches a height of s(t) = -16t^2 +
140t after t seconds
a) What is the velocity of the rock att seconds?
(1)
b) What is the velocity of the rock after when it is 170 feet above the ground on the
way up?
(t) = 170
c) What is the velocity of the rock when it is again at 170 feet on the way down?
d) When does the rock hit the ground?
e) What is the velocity when it hits the ground?

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?