Project #45549 - Math Midterm Problems

1. An airplane travels 105 miles in 10 minutes. What is the speed of the airplane in feet per second?


2. If 17% of a radioactive substance decays in 5 hours, what is the half-life of the substance?


3. How many tablespoons are in a quart?


4. The CPI for 2000 was 172.2. The CPI for 2012 was 229.6. A haircut cost $15 in the year 2000. Taking inflation into account, how much would that haircut cost in 2012?


5. Suppose an account pays interest at a nominal rate of 8% per year. Find the effective annual yield if interest is compounded

a. Monthly

b. Continuously


6. You have a choice of two savings accounts. One pays 10.5% annual interest rate, compounded quarterly. The other pays 10.4% annual interest rate, compounded continuously. Which is better (that is, which would pay more interest)? (Note these are unrealistic interest rates nowadays.)


7. Jill is carpeting a room that is 20 feet by 30 feet. She chose a carpet that costs $32.50 per square yard (including installation and tax). Find Jill's total cost of carpeting the room. (Round to the nearest cent.)


8. I want to make regular monthly deposits into an interest-bearing account for 10 years. The investment will earn 6% annual interest rate, compounded monthly. At the end of 10 years, I want the account to be worth $100,000. How much should I invest each month?


9. Peter and Natalie are married and filed income taxes jointly. Their combined wages were $158,300. They received $7,500 in interest from a savings account and had the following deductible expenditures: $3,600 for interest on a home mortgage and $6,000 for contributions to charity. They have four dependent children. What is their taxable income (after all adjustments)? Assume the standard deduction is $11,400 and each exemption is worth $3,650 (per person).


10. I have a sum of money to deposit into a savings account that earns 3.25% annual interest, compounded monthly. APPROXIMATELY how long will it take my money to double?


11. Which of the following statements describes a linear relationship? (Choose all that apply.)

  1. The temperature is increasing at a rate of 3o per hour.

  2. The number of cats is decreasing at the rate of 8% per year.

  3. The price of a gizmo is increasing at the rate of 14% per year.

  4. The price of houses in this neighborhood is increasing at the rate of $15,000 per year.


12. Suppose the doubling time of a state’s population is 43 years. If there are 13 million people in the state now, about how many will there be in 20 years? 


13. Three years ago, you bought 200 shares of XYZ Corporation for $72 each. You just sold all your shares for $50,000. What was the annual return on investment as a %?


14. The value of a car purchased in 2006 is depreciating (decreasing) at a constant rate of $2000 per year. The value of the car is $16,000 in the year 2010.

a. Does this describe linear or exponential decay?
b. Write a function that models the value of the car
t years after 2006. (So t = 0 corresponds to 2006, t = 1 corresponds to 2007, and so on.)



15. Airto spends an average of $4.10 a day on his daily espresso and pays $600 a month in rent.

On an annual basis, what percent of his rent is Airto’s spending on espresso?


16. Tweedledee invests $6200 in a savings account that compounds interest monthly at an APR of 4.9%. Tweedledum invests $6300 in a savings account that compounds interest continuously at an APR of 4.7%. Who will have the higher balance after 5 years?


17. Suppose you have 30 months in which to save $3900 for a vacation cruise. If you can earn an APR of 4.1%, compounded monthly, how much should you deposit at the end of each month to reach your goal?


18. The population of a certain city is now 74,000 people. If the population doubles every 25 years, what will the population be after 125 years?


19. How many inches are in 76.2 centimeters? (Helpful information: There are 2.54 centimeters in 1 inch.)


20. The half-life of Cobalt-56 is 77 days. A 2-gram piece of Cobalt-56 has decayed until it contains only 0.2 grams. Has it been more than 183 days (six months) since it had 2 grams?


21. Determine whether the following statements are sensible or ridiculous and explain your answer.

  1. Barbie went to a concert that lasted 5400 seconds.

  2. The fish weighed 3 meters.

  3. I put a kilogram of sugar in my teacup.

  4. A 2-liter bottle of water weighs about 5 pounds.


22. FICA tax consists of Social Security tax and Medicare tax. Social Security tax is 6.2% of the first $113,700 of wages and salary. Medicare tax is 1.45% of wages and salary. Carmen is single with no dependents, has a $200,000 salary, and earns $3,000 in interest from savings accounts. How much does Carmen pay total in FICA tax? (For federal income tax, the standard deduction is $6,100 and each personal exemption is worth $3,900.)


23. The following table provides information about median incomes in four states for 1998 1999. Use this information to answer the questions that follow.

1998 1999 Median Income






















Source: US Census Bureau

a. Which of the state incomes is the reference value? How do you know?

b. The 1998 1999 median income for Tennessee was $35,560. Find the income index for Tennessee, using your reference value from part a.



24. The US population in the year 2000 was about 309 million. Assuming a growth rate of 0.5% per year, approximately what will the population be in the year 2050? (Round your answer to the nearest ten million.)


25. One teaspoon of mayonnaise has 30 calories. How many calories are in a cup of mayonnaise?

26. My family wants to decrease its yearly electric bill. Last year, our electric bills totaled $1200.

A. On average, what have we been paying for electricity each month?

B. Last month, our electric bill was $135.00, and we were pleased our electricity costs were going down. Explain how this could be true. (This is not meant to be a trick question; this is more about what kind of information do you need to solve a problem.)


27. How many kilograms are in 6400 ounces?


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29. You take out a car loan for $10,000 at a fixed APR of 9.000% compounded monthly. Your monthly payments are $500. How much of your first payment goes to pay interest on the loan? How much of your second payment goes to pay interest on the loan? (Answer to the nearest cent.)


30. You take out a five-year car loan for $10,000 at a fixed APR of 8.471% compounded monthly. What are your monthly payments? 

Subject Mathematics
Due By (Pacific Time) 10/31/2014 10:00 am
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