As a probe descends to the Kuril Trench in the Pacific Occan, it records the amount of dissolved oxygen in the water in units of parts per million (ppm). At depths below 2, 000 meters, the dissolved oxygen drops at a constant rate of d ppm for every change in depth of 100 meters, until it reaches zero. At a depth of 2,530 eters, the dissolved oxygen is measured to be 205 ppm. At a depth of 3, 030 meters, the dissolved oxygen is measured to be 65 ppm. What is the value of d?

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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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