Use the identity LaTeX: \left(x+y\right)\left(x^2-xy+y^2\ri ght)=x^3+y^3 to find the sum of two numbers if the product of the numbers is 28, the sum of the squares is 65, and the sum of the cubes of the numbers is 407. Enter your answer as a number, like this: 42

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?