You are planning to purchase a house that will require some renovations

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Part 1. Be sure to clearly show all your steps to each solution.

 

You are planning to purchase a house that will require some renovations.

 

  1. You will have a $350,000 mortgage for 30 years at the rate of 2.39%.  What will your monthly payment be?

 

  1. You decide to do some remodeling in the kitchen. Your parents agree to lend you the money, but you insist on paying them interest.  The agreement is that they will lend you $8000.00 at a simple interest rate of 2% per year.  Once the interest amounts to $480, you agree to pay them back the $8000 plus the $480 interest.  How many months will it take you to pay back this loan if the interest amounts to $480.00?

 

  1. Suppose that $8000.00 was invested in a savings account that paid 2.5% interest compounded quarterly. How much interest would be earned after 3 years?

 

Part  2

 

A group of friends start a walking program.  The chart below shows each member’s self-reported walking time in May and June of 2021.

 

Person Minutes Walking in May 2021 Minutes walking in June 2021
YOU 650 300
B 400 250
C 500 600
D 600 500
E 350 900
F 700 550
G 500 650
H 550 200
I 800 100
K 900 350

 

Answer the following questions based on this data. Be sure to show all of your work for each question.

 

  1. What was the mean walking time in May 2021? Express your answer to the nearest hundredth.

 

  1. By what percent did YOU exceed or fall below the mean in May 2021? Express your answer rounded to the nearest hundredth.

 

  1. What was the median walking time in June 2021? Express your answer to the nearest hundredth.

 

  1. By what percent did YOU exceed or fall below median in June 2021? Express your answer rounded to the nearest hundredth.

Part 3.

 

Here is data for a math class:

 

Final Grade Women Men
A 6 5
B 4 8
C 3 3
D 1 1
F 1 1

 

Answer the following questions based on the above data for the math class.  Be sure to show all of your work.

 

 

  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?

 

  1. A focus group of 3 students from this class is going to be randomly chosen. In how many ways can the 3 students be chosen?

 

  1. What is the probability that the random choice will result in all women being chosen for this focus group of 3?

 

 

Part 4

 

For this part, you will find it helpful to use a Venn diagram.  You may submit a Venn diagram or thoroughly explain how you reached each answer.

 

In a math 105 class of 32 students, a survey showed that 20 students used the ALEKS e-text at least once, 10 used a video at least once, and 7 used both the e-text and a video at least once.

 

  1. How many students used only the e-text?

 

  1. How many students used neither the e-text nor the videos at least once?

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