You are given the sample mean and the population standard deviation. use this information to construct the 90% and 95% confidence intervals for the population mean. interpret the results and compare the widths of the confidence intervals. if convenient, use technology to construct the confidence intervals.

Bruce is getting materials for a chemistry experiment his teacher gives him a container that has 0.25 liter of liquid in it.bruce need to use 0.4 of this liquid for the experiment. how much liquid will bruce use?

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) = .

52 cm radius = diameter = area = circumference = circumfer