I need help solving this problem. Please help me by answering and showing explanations.

Problem 4. Your grade point average is calculated as a weighted mean, Where classes with more credithours count more heavily. The formula for a weighted mean is Z wax.- Z w. where wi is the weight assigned to the the i-th data point (for GPA, it is the number of credit-hours for a class). Some universities (like UT) convert a letter grade (A, A, ...) into \"grade points\" (4.0, 3.7, ...), which are the $.- values in this formula. Other universities use \"decimal grading\" where there is no letter grade, and you are simply assigned a numerical grade for the class (e.g., you could get a 3.8 or 3.5 in a specic class). Assume that you are at such a university, and you have the following grades at the end of the semester: Course Credithours Grade points Probability and statistics 3 3.4 Statics 4 2.8 Differential equations 3 3.7 Elementary Dutch 5 4.0 Introduction to mountain unicycling 1 2.0 (a) Compute your GPA this semester. (b) You set out to improve your GPA by studying more for statics. How much would your statics grade need to rise to increase your GPA to 3.5? (Assume all the other classes have the same grade.) (c) If you instead improve your GPA by studying more for mountain unicycling, how much would your grade in that class need to rise to get a GPA of 3.5? (Again assume all other classes have the same grade as in the table.) (d) Prove that if all the weights are the same (nonzero) value, the weighted mean is the same as the regular mean