Johnson Electronics makes calculators. Consumer satisfaction is one of the top priorities of the company’s management. The company guarantees the refund of money or a replacement for any calculator that malfunctions within two years from the date of purchase. It is known from past data that despite all efforts, 12% of the calculators manufactured by this company malfunction within a 2-year period. The company recently mailed 550 such calculators to its customers. a. Find the probability that exactly 32 of the 550 calculators will be returned for refund or replacement within a 2-year period.
b. What is the probability that 30 or more of the 550 calculators will be returned for refund or replacement within a 2-year period?
a. What is the probability that 15 to 35 of the 550 calculators will be returned for refund or replacement within a 2-year period?

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answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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