Given that is a standard normal random variable, compute the following probabilities. round your answers to 4 decimal places. a. p(0 ≤ z ≤ 0.70) b. p(-1.57 ≤ z ≤ 0) c. p (z > 0.39) d. p(z ≥ -0.33) e. p(z< 2.10) f. p (z≤ -0.63)

Ateacher noticed 5/8 of the students were wearing either blue shorts or white shorts. write two different ways this could be done.

Simplify. −4x^2 (5x^4−3x^2+x−2) −20x^6−12x^4+8x^3−8x^2 −20x^6+12x^4−4x^3+8x^2 −20x^8+12x^4−4x^2+8x −20x^6+12x^4+4x^3−8x^2

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) = .