Jasmine uses a garden hose to fill her pool. It takes Jasmine 16 hours for the pool to fill completely. Unfortunately, Jasmine does not know there is a crack in her pool siding that can deplete a full pool in 24 hours. Starting with an empty pool, how many hours will it take Jasmine to fill the pool while the crack is still leaking?

Jack has a piece of red ribbon that is two times as long as his piece of blue ribbon. he says that he can use two different equation to find out how long his piece of red ribbon is compared to his piece of blue ribbon is. is he correct? explain his reasoning

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) = .

Nour and rana are shopping for a christmas tree. they are deciding between 2 22 different types of trees (real and fake) and 4 44 colors for the ornaments (white, silver, gold, and purple). they each created a display to represent the sample space of randomly picking a type of tree and a color for the ornaments. whose display correctly represents the sample space?