Eric and Sue will randomly select from a treat bag containing 3 lollipops and 2 gum balls. Eric will select, replace it, and then select a second treat. Sue will select a treat, not replace it, and then select a second treat. Who has the greater probability? What is Sue’s probability? What is Eric’s probability

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) = .

Asmall business produces and sells balls. the fixed costs are $20 and each ball costs $4.32 to produce. each ball sells for $8.32. write the equations for the total cost, c, and the revenue, r, then use the graphing method to determine how many balls must be sold to break even.

Reduce fractions expressing probability to lowest terms. in 3,000 repetitions of an experiment, a random event occurred in 500 cases. the expected probability of this event is?