Application Assignment on Math

The written assignment draws mostly on even-numbered exercises from the textbook. Answer all assigned exercises, and show all work.

Each problem is worth 4 points. Please show work where appropriate for full credit.

Section 4.3 Problems 24, 26, 68

24. Convert the number to the numeral in the base indicated.

14 to base 2

14/2=7 Remainder 0

14 to base 2= 70

26. Convert the number to the numeral in the base indicated.

73 to base 3

73/3=24R1; 24/3=8R0

73 to base 3= 801

68: Computer Code. The ASCII code used by most computers uses the last seven positions of an eight-bit byte to represent all the characters on a standard keyboard. How many different orderings of 0's and 1's (or how many different characters) can be made by using the last seven positions of an eight-bit byte?

Section 8.1 Problems 44, 52, 62

44. Convert the given measurement to the unit indicated.

0.034 ml to liters

0.034/1000=0.000034 liters

52. Arrange the quantities in order from smallest to largest.

514 hm, 62 km, 680 m

Converting all to meters

51400 m, 62000 m, 680 m

Ascending order; 680 m, 514 hm, 62 km

62. Calcium Tablets. Sean takes two 250-mg chewable calcium tablets each day.

How many milligrams of calcium will Sean take in a week (7 days)?

2250 mg=500 mg daily, 7 days = 5007=3500 mg

How many grams of calcium will Sean take in a week (7 days)?

3500 mg=3500/1000 =3.5 grams

Section 8.2 Problems 74, 88, 94

74. Choose the best answer to indicate the volume of the following.

Air in a balloon with a diameter of about 17 meters

aa) 2600 m3b) 2600 cm3c) 2600 km3

88. Farmland. Kim Martello has purchased a farm that is in the shape of a rectangle. The dimensions of the piece of land are 1.4 km by 3.75 km.

How many square kilometers of land did she purchase?

1.43.75=5.25 km2

If 1 km2 equals 100 ha, determine the amount of land she purchased in hectares.

5.25100=525 ha

94.Hot-Water Heater. A cylindrical shaped hot-water heater has a diameter of 0.56 m and a height of 1.17 m. If the hot-water heater is filled, determine the volume of the water in the hot-water heater in

cubic meters

v=227r2h=2270.2821.17=0.288288m3liters

0.2882881000=288.288 liters

Section 8.4 Problems 12, 32, 42, 56

12.Convert the quantity to the indicated units. When appropriate, give your answer to the nearest hundredth.

9 lb to kilograms

= 90.45359237=4.08233133 kg

=4.08 kg

32.How far? Carol Ann Harle's new car traveled 105 mi on 5 gal of gasoline. How many kilometers can Carol Ann's car travel with the same amount of gasoline?

=1051.853=194.565

=194.57 km

42. Weight Restriction. The weight restriction on a road in Italy is 7.5 t.

7.5 t = 7500 kg

How many tons does this weight equal?

7500/1016.0469088=7.38 tons

How many pounds?

7500/0.45359237= 16534.67 pounds

56.Stomach Ache Remedy.The label on the bottle of Maximum Strength Pepto-Bismol indicates that each tablespoon contains 236 mg of the active ingredient bismuth subsalicylate.

Determine the amount of active ingredient in the recommended dosage of 2 tablespoons.

2362=472 mg

b)If the bottle contains 8 floz, determine the quantity of the active ingredient in the bottle.

Section 11.1 Problems 26, 28, 42, 56

26. Potassium. The U.S. Department of Agriculture's recommended daily allowance (USDRA) of potassium for adults is 3500 mg. One serving of Cheerios provides 95 mg of potassium. What percent of the US RDA of potassium does one serving of Cheerios provide?

=953500100=2.714%28. River Pollution. In a study of US rivers, 693,905 miles of river were studied. According to the U.S. Environmental Protection Agency, it was found that 36% of the total miles of river studied had impaired water quality. How many miles of rivers had impaired water quality?

=36100693905=249805.8miles42. United States Population. The population of the United states has been increasing since 1990. In 1990, the population of the United States was about 249 million. In 2010, the population was about 308 million. Determine the percent increase of the U.S. population during this time period.

=308-249=59million; 59249100=23.69%56. Employee Increase. The Fastlock Company hired 57 new employees, which increased its staff by 30%. What was the original number of employees.=1005730=190 employeesSection 11.2Problems 26, 30, 54

26. Business Loan. The city of Bradenton is offering simple interest loans to start-up businesses at a rate of 3.5%. Gaetano Cannata obtains one of these loans for $6000 for 3 years to help pay for start-up costs of his restaurant, Ortygia. Determine the amount of money Gaetano must repay the city after 3 years.

Interest=60003.53100=630;Total amount to be paid =630+6000=$66300

30. Credit Union Loan. Enrico Montoyo wants to borrow $350 for 6 months from his credit union, using his savings account as security. The credit union's policy is that the maximum amount a person can borrow is 80% of the amount in the person's savings account. The interest rate is 2 percentage point higher than the interest rate being paid on the savings account. The current rate on the savings account is 3.25%.

How much money must Enrico have in his account to borrow $350?

=10035080=$437.5

What is the rate of interest the credit union will charge for the loan?

=3.25+2=5.25%

Find the amount Enrico must repay in 6 months

interest=3506125.25100=$9.1875;total amount to berepaid=350+9.1875=$359.187554. Restaurant Loan. The Sweet Tooth Restaurant borrowed $3000 on a note dated May 15 with simple interest of 11%. The maturity date of the loan is September 1. The restaurant made partial payments of $875 on June 15 and $940 on August 1. Find the amount due on the maturity date of the loan.

Amount already paid; 875+940=$1815

Time=3.5 months

Total amount payable= 3000+3000111003.512=$3096.25Amount due on maturity date= 3096.25-1815=$1281.25

Section 11.3 Problems 26, 32, 36

26. Investing a Prize. David Buckley won a writing contest and invested the $10,000 cash prize in a 3-year CD paying 1.29% compounded daily (use n=360). What was the value of the CD after 3 years?

Amount=100001+1.291003360=million $10277.72132. Determining Effective Annual Yield. Determine the effective annual yield for $1 invested for 1 year at 4.75% compounded monthly.

Annual yield= accumulated amount initial amount

Annual yield=11+4.7510012-1=0.74521276=$0.75

36. Comparing Loan Sources. Tom Angelo needs to borrow $1500 to expand his farm implement maintenance business. He learns that the local bank will lend him the money for two years at a rate of 10% compounded quarterly. After hearing this rate, Tom's grandfather offers to lend him the money for 2 years with a simple interest rate of 7%. How much money will Tom save by borrowing the money from his grandfather?

Amount payable to grandfather= 1500 + (15007%2) =$1710

Amount payable to bank= 1500 (1+10/100)(24)=$3215.38

Section 11.5 Problems 12, 20

12. Buying a House.Sadaf Din is purchasing a house selling for $215,000. To obtain her mortgage, Sadaf must make a 20% down payment. The current mortgage rate is 4.5%.

Determine the amount of the required down payment.

20%215000=$43000

Determine the monthly principal and interest payment for a 25-year mortgage with a 20% down payment.

Principal amount= 172000

20. A 25-Year Convention Mortgage. Mr. & Mrs. Alan Bell obtain a 25-year, $110,000 conventional mortgage at 10.5% on a house selling for $160,000. Their monthly mortgage payment, including principal and interest, is $1038.60. They also pay 2 points at closing.

a) Determine the total amount the Bells will pay for their house.

Deposit= 160000-110000=$50000

Total monthly installments=1038.602512=$311580

Points=21720001/100=$3440

Total amount=50000+311580+3440

=$365020

b) How much of the cost will be interest (including the two points)?

Interest=311580-110000+3440

=$205020

c) How much of the first payment on the mortgage is applied to the principal?

First payment= 17200010.5/1001/12=$1505

Amount applied to mortgage= 1505-1038.60=$466.40

References

Torrence, B. F., & Torrence, E. A. (2009). The student's introduction to Mathematica: A handbook for precalculus, calculus, and linear algebra. Cambridge: Cambridge University Press.