Prove each of the following statements using strong induction. (a) Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps. (b) Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps. (c) Prove that any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.\

An engineer is going to redesign an ejection seat for an airplane. the seat was designed for pilots weighing between 120 lb and 161 lb. the new population of pilots has normally distributed weights with a mean of 125 lb and a standard deviation of 28.1 lb. a)if a pilot is randomly selected, find the probability that his weight is between 120 lb and 161 lb. the probability is approximately? b. if 36 different pilots are randomly selected, find the probability that their mean weight is between 120 lb and 161 lb. the probability is approximately? c. when redesigning the ejection seat, which probability is more relevant? . part (b) because the seat performance for a single pilot is more important. b. part (b) because the seat performance for a sample of pilots is more important. c. part (a) because the seat performance for a sample of pilots is more important. d. part (a) because the seat performance for a single pilot is more important.