Let’s say someone has constructed 3 different confidence interval for a population mean based on samples of size 35 one interval is 99% confidence interval another is a 95% and the third one is a 99% confidence interval

Twenty-five percent of the customers entering a grocery store between 5 p. m. and 7 p. m. use an express checkout. consider five randomly selected customers, and let x denote the number among the five who use the express checkout.

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) = .

What adds to be the bottom number but also multiplies to be the top number with 8 on the bottom and 15 on top