A staffing agency for in-home nurses and support staff places necessary personal at locations on a daily basis. Each placed nurse works 240 minutes per day at a rate of $90. Each support staff employee works 360 minutes per day at a daily rate of $120. a. On a given day, 3000 total minutes are worked by the nurses ans support staff that were placed. Write an equation that represents this relationship. b. On the same day, earning for nurses and support staff are totaled at $1050. Write an equation that represents this relationship. c. Solve the systemof equations, and interpret the solutionin the context of the situation.

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?