Math 213 – Quantitative Methods – Fall Term 2012-13

Final Exam: 18 December 2012

Directions. All work must be your individual effort. Write all work neatly and, in all instances, provide a careful explanation of your answer. No communication with any other student during the exam is permitted. You may use a calculator during the same; however, in all cases you are to provide an explanation of your work.

1. (10 points) Convert the following quantities into the indicated units. State the basic conversion formulas you are using.

a. 80 miles/hour into feet/second. b. 35 dollar/square foot into Euros/square meter.

c. 1.75 per Euros/liter into dollars per gallon. d. 100 Euros/cubic cm into dollar/cubic inch.

2. (10 points) Solve the system of equations 3x+2y=15 and 4x−2y=4.

3. (10 points) The relation between temperatures measured in the Fahrenheit scale (F) and the Celsius scale (C) is through the formula C = 5/9(F − 32). Find the temperature, in both F and C, where the numerical value in Fahrenheit is three times the numerical value in Celsius.

4. (10 points) Draw the Leontief diagrams which depict the model economy associated .15 .1 .10 .10

to the given technology matrx .20.1.15.10 .15 .15 .15 .05

.15 .15 .20 .15 5. (10 points) Consider the model economy whose technology matrix, according to the

Leontief model, is

.2 .15 .2 A=.1 .15 .35.

If the total production vector is

75 X = 50 ,

60 then compute the excess production vector Y .

.25 .05 .15

12

6. (10 points) For each of the following problems, compute the following numbers. a. What is 7!?

b. What is 1001!/996!? c. What is 100C98?

d. What is 40C38?

7. (10 points) How many committees of five people can be chosen from 9 math majors, 11 fashion majors, and 3 language majors

a. if at 2 math majors, 2 fashion majors, and 1 language major must be on each committee?

b. if exactly 2 fashion majors must be on each committee? c. if exactly 4 language majors must be on each committeeY?ou may leave your

answers in terms of the combinatorial coefficients nCr. Bonus points will be given for numerical evaluation of the answer.

8. (10 points) Suppose you are choosing committees of four people can be chosen from 8 math majors, 7 fashion majors, and 9 language majors.

a. What is the probability that the committee will have 2 math majors, 1 fashion major, and 1 language major?

b. What is the probability that the committee will have no fashion majors? You may leave your answers in terms of the combinatorial coefficients nCr.

9. (10 points) Suppose you save $325 per week in account which earns an annual interest rate of 3.25%. If the interest is compounded monthly, how much will you have after 45 years?

10. (10 points) Assume that in 45 years you wish you have an account with a balance of $2, 000, 000. If the account pays an annual interest rate of 4.5%, what must your monthly deposit equal in order to achieve your goal?

Summary of formulas Simply compounded interest: The basic formulas are

A=P+I where I=Prt

where

• P is the principle, or present value;; • r is the interest rate per year; • t is the time in years; • A is the amount after t years.

Compounded interest: The basic equation is F = P (1 + i)n

where

• P is the principle, or present value; • F is the future value; • i is the interest rate per compounding period; • n is the number of compounding periods.

Equivalently, one has the following formulas: P =F(1+i)−n;n=log(F/P)/log(1+i);i=(F/P)1/n −1.

Continuously compounded interest: The basic equation is F = Pert

where

• P is the principle, or present value; • F is the future value; • r is the interest rate per year; • t is the number of years.

Equivalently, one has the following formulas: P = Fe−rt;t = ln(F/P)/r;r = ln(F/P)/t.

Future value of an annuity formula: The formula is F = R((1 + i)n − 1)orR =F i

i(1 + i)n − 1

where

• R is the amount of the regular payment; • F is the future value of the annuity; • i is the interest rate per compounding period; • n is the number of compounding periods.

Present value of an annuity formula: The formula is P = R(1−(1+i)−n)orR=Pi

i 1−(1+i)−n

where

• R is the amount of the regular payment; • P is the present value of the annuity; • i is the interest rate per compounding period; • n is the number of compounding periods.

3

Subject | Mathematics |

Due By (Pacific Time) | 08/22/2013 12:00 am |

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