The first two steps in determining the solution set of the system of equations, y = -x2 + 4x + 12 and y=-3x + 24, algebraically are shown in the table.
Step
Equation
Step 1 |-x2 + 4x+12 --3x+24
Step 2
x? - 7x+12-0
Which represents the solution(s) of this system of equations?
(3, 15)
(4.36)
(3, 15) and (4, 12)
(-3, 33) and (-4, 36)

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?