Multiply the following using the vertical multiplication method:
3x^2 +5x + 1
x x^2 - 2x + 4

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?

Which of the following are independent events? a) knowing that it is going to rain tomorrow, and bringing an umbrella to schoolb) knowing that you have to get up early tomorrow, and going to bed before 9 p. mc) knowing that it is going to rain tomorrow, and going to bed before 9 p. md) knowing that you have a test in school tomorrow, and studying thw night before

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?