55. The Electronic Depot received 108 mp3 players, 12 of which are defective. In how many dif- ferent ways can 6 players be selected for display such that:
a. none are defective?
b. half are defective?
c. all are defective?

Rena is building a 1: 180 scale model of a real castle. her model has a rectangular base that is 3 feet wide and 4 feet long what is the area of the base of the actual castle in square feet

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) = .

Agroup of randomly selected members of the foodies food club were asked to pick their favorite type of food. the bar graph below shows the results of the survey. there are 244 members in the foodies.