Mr. Cheung set up an account in an investment company at the beginning of this year. He makes an investment on the first day of each month. He invested $4000 in the first month and increased the monthly investment by 5% in each subsequent month. (a) How much will he invest in the last month of this year?

(b) Find the total amount that he will invest in this year.

(c) If the monthly return on his investment is 3%, find the total amount that he will get at the end of the year.

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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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