B 5
E
4
Points A, B, and Cform a triangle. Complete the statements to prove that the sum of the interior angles of AABC is 180°.
Statement
Reason
Points A, B, and C form a triangle.
given
Let DE be a line passing through B and parallel to AC. definition of parallel lines
23 – 25 and 21 - 24
m21 = m 24 and 23 = m25
m24+ m2 2 + 25 = 180°
mZ1 + Z2 + m23 = 180°
angle addition and definition of a straight line
substitution

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?