(a) If the area of a rectangle is 16, then the length is 8 and the width is 2. Counterexample: length = 0 width
-
O
(b) If the measures of ZP, 20, and acute.
Counterexample: mZP =
m20
= °, mZR = 1
(c) If the length of XZ is 52 and point Y lies on XZ, then XY= 26 and YZ = 26.
Counterexample: XY
yz = 0
(d) If 21 and 22 are supplementary angles, then one of them must be obtuse.
Counterexample: m41 = ', m2 2 =

F(n + 1) = f(n) – 8. if f(1) = 100, what is f(6)?

Solving algebraic equations 2m+3=11

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?