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1.

1. Evaluate the expression.

170P1

2. How many permutations are there of the following word?

COMBINATORICS

Permutations

3. Evaluate the expression.

(8/5)

4. Decide whether you would use a permutation, a combination, or neither. Next, write the solution using permutation notation or combination notation, if possible, and, finally, answer the question.

A club with 33 members is to select five officers (president, vice president, secretary, treasurer, and historian). In how many ways can this be done?

5. A state's license plates consist of four letters followed by three numerals, and 245 letter arrangements are not allowed. How many plates can the state issue?

6. Give the probability in decimal form (correct to two decimal places). A calculator may be helpful.

Last semester, a certain professor gave 21 As out of 207 grades. If one of the professor's students from last semester were selected randomly, what is the probability that student received an A? (Assume that each student receives one grade.)

7. A single card is selected from an ordinary deck of cards. The sample space is shown in the figure below. Find the probabilities. (Enter the probabilities as fractions.)

(a) P(three of hearts)

(b) P(three)

(c) P(heart)

8. An oil-drilling company knows that it costs $25,000 to sink a test well. If oil is hit, the income for the drilling company will be $425,000. If only natural gas is hit, the income will be $130,000. If nothing is hit, there will be no income. If the probability of hitting oil is 1/40 and if the probability of hitting gas is 1/20, what is the expectation for the drilling company?

Should the company sink the test well?

Yes or No

9. Find the requested probability. P(A) if P(A) = 0.8

P(A) =

10. Three fair coins are tossed. What is the probability that at least one is a head? (Enter the probability as a fraction.)

11. A single card is drawn from a standard deck of cards. Find the probability if the given information is known about the chosen card. A face card is a jack, queen, or king

P(face card|queen)

SECOND PART TO OTHER HOMEWORK WERE I STOP FROM

12. A class obtained the following scores on a test.

Test Score

Frequency

90

2

80

5

70

10

60

3

50

3

40

2

Find the mean, the median, the mode, and the range for the class. (If an answer does not exist, enter DNE.)

mean

median

mode range

13. Find the present value, using the present value formula and a calculator. (Round your answer to the nearest cent.)

Achieve $225,500 at 8.15% compounded continuously for 8 years, 135 days.

14. An artifact was found and tested for its carbon-14 content. If 75% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half-life of 5,730 years.)

15. Decide whether you would use a permutation, a combination, or neither. Next, write the solution using permutation notation or combination notation, if possible, and, finally, answer the question.

A club with 27 members is to select five officers (president, vice president, secretary, treasurer, and historian). In how many ways can this be done?

16. Tell what the output value is for the function machine for the given values.

(a) 2

(b) 9

(c) 8

(d) 3/2

(e) T

17. Find the range and the standard deviation (correct to two decimal places).

81, 90, 95, 95, 104

range

standard deviation

18. If f(x) = x 9,

find the following.

(a) f(14)

(B) f(5)

(C) f(p)

19. For the car loan described, give the following information.

A newspaper advertisement offers a $4,000 used car for nothing down and 36 easy monthly payments of $142.62.

(a) amount to be paid

(b) amount of interest

(c) interest rate (Round your answer to two decimal places.)

(d) APR (rounded to the nearest tenth percent)

20. Write each expression in terms of common logarithms, and then give a calculator approximation (correct to four decimal places).

(a) log2 10

exact value

approximation

(b) log3 312

exact value

approximation

21. Find three ordered pairs that satisfy the equation.

y = 2x 4

(x, y) = (0,

(x, y)=(1,

(x, y)=(2,

Use this information to graph the line.

22. Write the equations in logarithmic form.

(a) 343 = 73

(b) 16=(1/2-2 component 2

(c) a = bc

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