Kiersten runs a website that people learn programming. every month, kiersten receives a subscription fee of \$10$10 from each of the subscribers to her website. last month, the website had 100100 subscribers. this month, 3030 new members joined the website, and 1010 members cancelled their subscription.

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?

What is the location of point g, which partitions the directed line segment from d to f into a 5: 4 ratio? –1 0 2 3

Car a and car b were in a race .the driver of car b claimed that his car was twice as fast as car a