Nadia has a handful of coins, all of which are either dimes or quarters. She has a total of 23 coins in her hand and a total of $3.65 worth of coins. Let d equal the number of dimes Nadia has and let q represent the number of quarters she has. (Write a system of equations (again in terms of cents) that models this situation.)(Solve the system you wrote in (b). State a final conclusion that gives how many dimes and how many quarters Nadia has in her hand.)

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?