MATH 105 Final Exam, Spring 2021 · This exam is worth 12 points toward your final grade in the course. · The exam has 3 Parts and each part has 6 questions. · The exam is available on the first day of...

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MATH 105 Final Exam, Spring 2021 · This exam is worth 12 points toward your final grade in the course. · The exam has 3 Parts and each part has 6 questions. · The exam is available on the first day of week 8. · You may take as long as you like on this exam, but you must complete and submit to your LEO classroom assignment folder by 11:59 pm on the last day of class. · The online text and the ALEKS lesson pages are a resource as you work on these problems. · Please submit your work in the LEO assignment folder as ONE single file · typed and saved as a single file and attached OR · neatly handwritten, scanned, and saved as a single file and attached. Be sure that the pages are right-side-up and in order · You MUST show all of your work to receive any credit. If you have questions about showing work, please ask. · The Final Exam is open book and open notes. You may refer to your textbook, notes, and online classroom materials. · Part 1 You are planning to purchase a house that will require a mortgage of $300,000. You find 2 mortgage offers both at the same rate of 2.5%. One is a 30-year mortgage and the other is a 20-year mortgage. 1. You know, without any computation, that the 30-year mortgage will have lower monthly payments than the 20-year mortgage since the rates are the same. A friend advised that before taking the 30-year mortgage offer, you do some mathematical calculations to see if your budget can handle the extra amount of monthly payment for the 20-year mortgage. a. What would be the monthly payment on the 30-year mortgage? b. What would be the monthly payment on the 20-year mortgage? 2. You ask your friend what advantage there is to be paying more per month on the 20-year mortgage. Your friend replies that it is all about total interest. a. What is the total interest you would pay over the full term of the 30-year mortgage? b. What is the total interest you would pay over the full term of the 20-year mortgage? 3. After you purchase the house, you decide to do some remodeling in the kitchen. You ask your parents if they would lend you money, but you insist on paying them interest. The agreement is that they will lend you $5000.00 at a simple interest rate of 2% per year. Once the interest amounts to $250, you agree to pay them back the $5000 plus the $250 interest. After how many months will you have to pay them back? 4. Suppose instead that the $5000.00 was invested in a savings account that paid 2% interest compounded quarterly. How much interest would be earned after 2.5 years? Part 2 You belong to two different walking groups. Here is data about each group’s walking in May 2020. Group A Person Minutes Walking in May 2020 YOU 630 B 400 C 500 D 650 E 350 F 700 G 500 H 550 I 800 K 900 Group B Person Minutes Walking in May 2020 YOU 400 X 250 Y 500 Z 450 Q 650 R 600 Answer the following questions based on this data. 1. What was the Group A mean walking time? 2. By what percent did YOU exceed or fall below the group A mean? Express your answer rounded to the nearest hundredth. 3. What was the Group B median walking time? 4. By what percent did YOU exceed or fall below the group B median? Express your answer rounded to the nearest hundredth. 5. Let’s suppose you want to draw a pie chart that shows information for the members of each group classified by a rating based on the amount of walking time. There will be 4 categories: excellent, very good, good, needs improvement. The Needs Improvement category is for the percentage of group members who walked for less than 400 minutes. Which group [A or B] has the smaller percentage of members in the Needs Improvement category? What is that percentage? Express your answer to the nearest hundredth. 6. One other way to look at the data is by percentiles. In which group was YOUR percentile rank higher? What is that percentile? Round the percentiles to the nearest whole number. Part 3. Here is data for a math class: Final Grade Women Men A 6 5 B 4 8 C 3 3 D 0 1 F 1 0 Answer the following questions based on the above data for the math class. 1. If one person is randomly chosen to participate in a focus group, what is the probability that the person will be a student who earned an A in the class? 2. If one person is randomly chosen to participate in a focus group, what is the probability that the student chosen will NOT have earned a C? 3. In how many ways can 2 women be chosen for a focus group? 4. In how many ways can 2 men be chosen for a focus group? 5. In how many ways can 4 students be chosen for a focus group? 6. What is the probability that the random selection of 4 students for the focus group will result in 2 women and 2 men being selected?