7 people are having dinner at a restaurant and decide to split the cheque evenly between them. If the check came to a total of $381.50, what amount will each person need to pay?

Liz is shipping a package to her friend. the maximum weight of a medium flat-rate box is 20 pounds, including the box which weighs 6 ounces. write and solve an inequality to describe the possible weight ,w, of the contents that liz will ship to her friend if she must use a medium flat-rate box.

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) = .

Adesigner charges a one time fee of $200 plus $40 an hour for each project. write an expression to represent how much money the designer will make for a project