You grab two jelly beans from a jar at the same time. b you draw a card from a deck, replace it, and draw a second. c you draw a card and do not replace it. then you draw another. d you study english every night, and then you get an a on the next test.

2-3 6. use your equation to find how high tyler will have to climb to scale the peak. (4 points: 2 points for correctly substituting values, 2 points for the correct height)

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) = .

Which number is located at point a on the number line? a number line is shown from negative 10 to 10 with each interval mark on the number line representing one unit. point a is labeled one interval mark to the right of negative 5.