The school designed their vegetable garden to have a perimeter of 32 feet with the length measuring two feet more than twice the width. 1. Using l to represent the length of the garden and w to represent its width, complete the system of equations below that describes this situation.

Type the missing parts of the equations in the boxes below.

l=

= 32

2. Solve the system of equations.

What are the dimensions of the garden?

l=

w=

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?