A bag contains a total of 20 balls. 12 are blue, and 8 are yellow. If three balls are drawn at random, one at a time without replacement, what is the probability that you draw two blue balls and one yellow, where the order is unimportant?

On the way home from visiting his family, vincent’s plane cruised at an altitude of 3.2 × 104 feet. he had heard that a man named felix baumgartner skydived from an altitude of 1.28 × 105 feet. vincent wants to know how much higher felix went on his skydiving trip. question 1 you have already seen how adding numbers works in either scientific notation or standard notation. but can you subtract numbers in scientific notation and get the same results as subtracting in standard notation? to find out, first solve vincent’s problem in standard notation. part a write the cruising altitude of vincent’s plane in standard notation.

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) = .

A(1,1) b(-3,0) c(-4,-1) d(3,-2) drag it to correct position