For two figures to be considered congruent, their corresponding sides and angles must all be the same. Congruence can occur in any geometric figures, from simple line segments to complicated shapes with many sides and angles. Here’s another way to think about congruence: if you cut two figures out of paper, you could place one cutout on top of the other cutout and it would disappear. Consider that geometric figures are made up of an infinite number of points. When superimposed on top of each other, all of the points in one figure would match up with all of the points in the other figure. According to the passage, which of the following is not true?

A
Paper cutouts can be used to determine congruence.

B
Congruent figures have exactly the same size and shape.

C
Congruence only happens in three- or four-sided figures.

D
Two octagons can be congruent if their corresponding sides and angles match up.

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?