If a school wants student opinion on the course registration process, would a systematic sample polling every tenth student to register, a stratified sample polling five students in each academic discipline, or a random sample polling any fifty students be most effective? why?

Stratified random sampling is based on a subdivision of the sample framework into strata with the help of an observable variable that separates them. After forming the strata, each individual is located in one and only one stratum. The sample is established by selecting a certain number of individuals in each stratum, guaranteeing a contribution of each stratum in the information obtained.

The best sampling method, in this case, is Stratified Random.

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50- 250 is correct i did that one too

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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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