For positive acute angles A
A and
B
,
B, it is known that
cos
⁡
A
=
4
5
cosA=
5
4
​
and
sin
⁡
B
=
15
17
.
sinB=
17
15
​
. Find the value of
cos
⁡
(
A
−
B
)
cos(A−B) in simplest form.

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?