Areality tv show features business owners who try to persuade investors to put money into their companies in exchange for partial ownership of the company.

to make a fair deal, the owner estimates the total value of the business and sets the amount of the investment based on the size of the share, as a percentage. for example, an investor could provide $3 million in exchange for 30 percent ownership stake in a company that is worth $10 million.

abbey owns a company that sells cat toys. she wants an investor to put $100,000 into her company so that she can expand the business.

which equation correctly relates an investor's share, s (as a percentage), to the total value of abbey's company, v?

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?