math

1. Maria and John have been married for 2 years and just learned that they are pregnant.

They have been renting a small apartment but decide to purchase a house. The one they

have found has a selling price of $300,000. They will make a 20% down payment.

They are considering 2 financing options at their credit union:

Option 1: A 3.125% APR, 30-year mortgage:

Option 2: A 2.5% APR, 15-year mortgage:

Answer the following questions showing all your work to reach each answer.

A. Which option will result in a lower monthly payment if they take the full term of

the mortgage? What will that monthly payment be?

B. Which option will result in the most total interest if they take the full term of the

mortgage? What will that total interest be?

2. Maria and John decide to shop for furnishings for the new house. They choose items that

amount to $5600.00. The store has 2 fixed installment simple interest loan options for

purchasing:

Option 1: 20% down payment and financing at 5% simple interest per year for 3 years.

Option 2: no down payment and financing at 5.25% simple interest for 4 years.

Answer each of the following questions separately, showing all your work to reach

each answer.

A. Which option will result in smaller finance charge (interest)? What will that finance

charge/interest be?

B. Which option will result in the smaller monthly payment on this fixed installment

loan? What will that monthly payment be?

C. They decide to defer any purchases and invest a $5600 bonus that Maria will be

getting from work in a savings account. The APR is 21.6% compounded monthly.

How much interest will they earn in 4 years?

D. They decide to defer any purchases and loan the $5600 bonus to a needy relative at

1.5% simple interest per year. How long will the term of the loan need to be if they

want to earn $500 in interest (assuming the loan is not paid off early).

3. Maria and John have decided that once they live in a house, they want to have a pet. They

go to an animal shelter and find several pets that they would love to take home. There are

25 cats, 4 flat coat retrievers, 8 Labrador retrievers, and 10 mixed-breed dogs.

Answer each of the following questions separately, showing all your work to reach

each answer.

A. Since they can’t decide, they place all the adoption cards in a container and draw

one. What is the probability that they select a cat?

B. Since they can’t decide, they place all the adoption cards in a container and draw

one. What is the probability that they select either a flat coat retriever or a

labrador retriever?

C. Since they can’t decide, they place all the adoption cards in a container and draw

one. What is the probability that if they select a dog, that it is not a mixed breed?

D. If they decide to purposely choose 2 of the 22 available dogs rather than randomly

choosing any 2, how many combinations of 2 dogs are possible?

4. Answer the questions below for the data taken from the Top 15 COVID 19 Confirmed

cases by County – 9/20/20. (Source: Johns Hopkins University

https://coronavirus.jhu.edu/us-map)

Note: You don’t need to go to the website, it’s for citation.

Show your methods very clearly and completely.

A. What is the mean? Which county is closest to that mean?

B. What is the median? Which county is closest to that median?

C. What percentile is Bronx county?

D. What county is at the 90th percentile?

52,063 Orange

52,471 San Bernardino

52,598 Bronx

53,341 Bexar

56,681 Riverside

64,160 Clark

65,848 Kings

70,893 Queens

75,682 Broward

77,889 Dallas

123,817 Harris

139,088 Cook

139,856 Maricopa

166,881 Miami-Dade

260,797 Los Angeles

Provided below are the sizes of 15 farms, in acres, randomly selected from the

state of Oregon. The mean of this sample is 401 acres.

2560 465 116 313 203 491 156 131 287 199 372 201 153 116 252

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116 116 131 153 156 199 201 203 252 287 313 372 465 491 2560

a. Find the median of the sample and compare it to the mean and discuss the

difference?

The median is ?

The mean is ?

b. Find the mean and the median if you throw out the 2560 acre farm which has

the largest area by far. What does this tell you?

116 116 131 153 156 199 201 203 252 287 313 372 465 491

The mean is ?

The median is ?

Use inductive reasoning to conjecture the rule that relates the number you

selected to the final answer. Try to prove your conjecture using deductive

reasoning.

Select a number:

Multiply by 3:

Subtract 6 from the answer:

Divide by 3:

Subtract the original number: