A set of cards consists of 3 red cards and 7 black cards. You shuffle cards thoroughly and you turn cards over, one at a time, beginning with the top card. Let Y be the number of cards you turn over until you observe the first red card. The variable Y has which of the following probability distributions?

Whose conclusion is correct? choose all that apply. (two max) elijah emily edward esme

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 radical expression is a rational number? a. √ 360 b. √ 644 c. √ 225 d. √ 122