Lydia is deciding between two different movie streaming sites to subscribe to. Plan A costs $5 per month plus $2.50 per movie watched. Plan B costs $24 per month plus $1.50 per movie watched. Let A represent the monthly cost of Plan A if Lydia watches : per month, and let B represent the monthly cost of Plan B if Lydia watches z movies per month. Write an equation for each situation, in terms of x, and determine which plan would be cheaper if Lydia plans on watching 21 movies each BE - iss cheaper than when watching 21 movies.​

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?