Suppose that you are currently making monthly payments on a $248,800 30-year mortgage at 567% interest compounded monthly. For the last 8 years, you have been paying the regular monthly payments. You now have the option to refinance your current mortgage with a new 25- year mortgage that has an interest rate of 4.5% compounded monthly. Note that the lender of the new loan has a closing cost fee of $1,300(for title insurance, home appraisal costs, etc.) for the new (refinanced) mortgage. The lender stipulates that closing cost must be paid in cash and cannot be part of the new loan. You are to determine whether you would save or lose money in interest if you were to refinance your home. Take the closing costs into account when determining if you would save or lose money. A group of 450 students that lived in on-campus housing were surveyed and asked if (1) they had access to a car and (2) whether they owned a television. Suppose that a person collecting the data likes puzzles and she has given you the following information about the results of the poll. 123 of the students responded that they had access to a car, 260 students did not own a television, and 184 students both did not have access to a car and did not own a television. Define the minimum number of basic sets needed to create the Venn diagram. (3 points) Write out the set theoretic notation for each piece of information that gives information about the number of students who responded to the various characteristics listed in the problem. (4 Points) Create the appropriate Venn diagram created using the above information. Define the minimum number of appropriate sets needed to answer this problem. (3 points) Write out a short step-by-step explanation (Step 1, step 2, step 3, ...) on how you found the values for each of the basic regions in the Venn diagram in the order that you found them. Include any calculations that you may have made in various steps. Use proper mathematical notation for the sets and the number of elements in the set of interest. Refer to the basic regions using the Roman numerals that are in Figure 1 (b) on page 201. (5 points) List the answers to the following questions: How many student owned a television but did not have access to a car? (1 point) Suppose that you are currently making monthly payments on a $248,800 30-year mortgage at 567% interest compounded monthly. For the last 8 years, you have been paying the regular monthly payments. You now have the option to refinance your current mortgage with a new 25- year mortgage that has an interest rate of 4.5% compounded monthly. Note that the lender of the new loan has a closing cost fee of $1,300(for title insurance, home appraisal costs, etc.) for the new (refinanced) mortgage. The lender stipulates that closing cost must be paid in cash and cannot be part of the new loan. You are to determine whether you would save or lose money in interest if you were to refinance your home. Take the closing costs into account when determining if you would save or lose money. A group of 450 students that lived in on-campus housing were surveyed and asked if (1) they had access to a car and (2) whether they owned a television. Suppose that a person collecting the data likes puzzles and she has given you the following information about the results of the poll. 123 of the students responded that they had access to a car, 260 students did not own a television, and 184 students both did not have access to a car and did not own a television. Define the minimum number of basic sets needed to create the Venn diagram. (3 points) Write out the set theoretic notation for each piece of information that gives information about the number of students who responded to the various characteristics listed in the problem. (4 Points) Create the appropriate Venn diagram created using the above information. Define the minimum number of appropriate sets needed to answer this problem. (3 points) Write out a short step-by-step explanation (Step 1, step 2, step 3, ...) on how you found the values for each of the basic regions in the Venn diagram in the order that you found them. Include any calculations that you may have made in various steps. Use proper mathematical notation for the sets and the number of elements in the set of interest. Refer to the basic regions using the Roman numerals that are in Figure 1 (b) on page 201. (5 points) List the answers to the following questions: How many student owned a television but did not have access to a car? (1 point)