"prove for all integers n, that is even. state the proof technique you have used. justify each step in your proof."

i can work it out in my head that it must be, as n cubed will be even if n is even, and odd if n is odd. an even minus an even is still an even, an odd minus an odd is an even. but i can only prove that the equation is a multiple of 3? i'm using proof by induction.

The vice president of programming at nbc is finalizing the prime-time schedule for the fall. she has decided to include a hospital drama but is unsure which of two possibilities to select. she has a pilot called the surgeon and another called critical care. to her make a final decision, a sample of 20 viewers from throughout the united states was asked to watch the two pilots and indicate which show they prefer. the results were that 12 liked the surgeon, 7 liked critical care, and one had no preference. state the decision rule, using the 0.10 significance level. h0: π = 0.50 h1: π ≠ 0.50 1. reject h0 if number of + signs is either < = or > = 2. what is your decision regarding h0? is there a preference for one of the two shows?