You own an ice-cream shop. Every day when you open the shop, there is an Exp( 1 10 ) random waiting time, in minutes, before the first customer arrives. 1. When the waiting time for the first customer exceeds 20 minutes, it is a bad day. Approximate the probability that you will have between 50 and 60 bad days in a year (365 days). Justify your use of this approximation approach. 2. When the waiting time for the first customer is shorter than 3 seconds (i. e., 0.05 minutes), it is a great day. Approximate the probability that you will have exactly 3 great days in a year (365 days). Justify your use of this approximation approach.

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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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