8. II
Billy and Tommy are playing a dice game with a six-sided die. Billy needs to roll a 5 or higher to win the game. What is the probability
that Billy will roll a 5 or higher?

Select the correct answer. joshua likes to read. he read 6 books when he was 6 years old. every year he doubled the number of books he read the previous year. how many total books did he read between the ages of 6 and 10? a. 60 b. 90 c.186 d.187

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

The evening newspaper is delivered at a random time between 5: 30 and 6: 30 pm. dinner is at a random time between 6: 00 and 7: 00 pm. each spinner is spun 30 times and the newspaper arrived 19 times before dinner. determine the experimental probability of the newspaper arriving before dinner.