A bag contains a variety of different colored marbles. P( red)= 1/2, P( green) = 1/4, and P( red and green) = 1/8 , which statement is true?

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) = .

Evaluate the discriminant of each equation. tell how many solutions each equation has and whether the solutions are real or imaginary. x^2 + 4x + 5 = 0

What is the interquartile range of this data set? 2, 5, 9, 11, 18, 30, 42, 48, 55, 73, 81