Profit is the difference between revenue and cost. the revenue, in dollars, of a company that manufactures televisions can be modeled by the polynomial 3x2 + 180x. the cost, in dollars, of producing the televisions can be modeled by 3x2 – 160x + 300. the variable x is the number of televisions sold.

if 150 televisions are sold, what is the profit?

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?