Cameron is designing a table for his game room. He wants the table to have a
square top with triangular leaves that fold on hinges.
1. Cameron makes a sketch of the tabletop, with the leaves open, on the
coordinate plane as shown.
Part A
If each unit on the grid represents 1 foot, what are the
lengths of each side of each leaf? Round to the nearest
tenth of a foot.
Part B
What are the dimensions of the tabletop with the
leaves open? Round to the nearest tenth of a foot.

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?