Explain why every year must contain at least one Friday the 13th.

Avegetable garden and a surrounding path are shaped like a square together are 12 ft wide. the path is 1 feet wide. if one bag of gravel covers 8 square feet, how manu bags are needed to cover the path? round your answers to the nearest tenth.

1jessica's home town is a mid-sized city experiencing a decline in population. the following graph models the estimated population if the decline continues at the same rate. select the most appropriate unit for the measure of time that the graph represents. a. years b. hours c. days d. weeks

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) = .