Survey of MathPractice Final Exam

1. Express the following set using the roster method: � �

�

2. Construct a Venn diagram illustrating the following sets: �

(description: two circles with 5,6,7 in the overlap, 2 in A only, 1and3 in B only, 4 outside both circles

For problems 3 and 4, let �

3. Find �

�

4. Find �

�

x | x ∈N and 10 ≤ x < 24{ }

10,11,12,13,14,15,16,17,18,19,20,21,22,23{ }

A = 2,5,6,7{ }, B = 1,3,5,6,7{ }, and U = 1,2,3,4,5,6,7{ }

U = a,b,c,d,e, f ,g{ }A = b,c,d{ }B = a,c,d{ }C = a,e, f ,g{ }

A∪ B

a,b,c,d{ }

(A∩ B)∪C

a,c,d,e, f ,g{ }

5. Evaluate �

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6. Write 60,531 in expanded form.

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7. Express as a Hindu-Arabic numeral: �

20,593

In problems 8 and 9, perform the indicated operation.

8. �

�

9. �

�

10. Evaluate � when �

-8

75

16,807

6 ×104( )+ 5 ×102( )+ 3×10( )+ 1×1( )

2 ×104( )+ 5 ×102( )+ 9 ×10( )+ 3×1( )

454 six

+235six

1133six

23 four×3 four

201 four

x3 − 3 x + 2( )2 x = −2

11. If � , find �

0

12. Find the slope of the line passing through (-3,1) and (4,-1).

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13. Graph � using the slope and the y-intercept.

(description: y intercept at -5, then rise 2 and run 3, so another point at (3,-3))

f (x) = 3x2 + 2x −1 f (−1)

m = 1− (−1)−3− 4

= − 27

y = 23x − 5

14. Solve by substitution:

�

�

15. Solve by addition:

�

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16. A bicycle with an original price of $510 is on sale at 15% off. What is the sale price of the bike?

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x = y + 43x + 7y = −18

⎧⎨⎩3(y + 4)+ 7y = −183y +12 + 7y = −1810y = −30y = −3x = −3+ 4x = 1(1,−3)

5x + 4y = 103x + 5y = −7

⎧⎨⎩3(5x + 4y = 10)−5(3x + 5y = −7)

15x +12y = 30−15x − 25y = 35

−13y = 65y = −5

5x + 4(−5) = 105x − 20 = 105x = 30x = 6(6,−5)

$510(0.85) = $433.50

17. You would like to have $4000 in three years for a special vacation by making a lump-sum investment in an account that pays 4% compounded monthly. How much should you deposit now? Round to up to the next dollar.

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18. Suppose that you want to retire in 35 years. How much should you deposit at the end of each month in an IRA that pays 6.25% compounded monthly in order to have $2,500,000 in 35 years? Round up to the next dollar.

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19. Convert 681cm to m. (Using KHDBDCM), 681cm = 6.81m

20. Given 1 inch =2.54 centimeters, use dimensional analysis to convert 275 centimeters to inches.

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21. A right triangle has one leg of length 12 centimeters and a hypotenuse of length 13 centimeters. Find the length of the other leg.

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P = A

1+ rn

⎛⎝⎜

⎞⎠⎟nt =

4000

1+ 0.0412

⎛⎝⎜

⎞⎠⎟12(4)

= $3410

P =A r

n⎛⎝⎜

⎞⎠⎟

1+ rn

⎛⎝⎜

⎞⎠⎟nt

−1⎡

⎣⎢

⎤

⎦⎥

=2,500,000 0.0625

12⎛⎝⎜

⎞⎠⎟

1+ 0.062512

⎛⎝⎜

⎞⎠⎟12(35)

−1⎡

⎣⎢

⎤

⎦⎥

= $1657

275cm × 1in2.54cm

= 698.5in

a2 +122 = 132

a2 +144 = 169a2 = 25a = 5

22. Find the volume of a right circular cylinder with diameter 4 cm and height 10 cm.

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23. At a certain time of day, the angle of elevation of the sun is 42� . If a building casts a shadow measuring 70 feet, find the height of the building to the nearest foot.

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24. Six movies are scheduled to run in movie marathon. How many different ways are there to schedule the order of the movies?

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25. A human resource manager has 10 applicants to fill two different positions. Assuming that all applicants are equally qualified for either of the positions, in how many ways can this be done?

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V = πr2hV = π (42 )10V = 502.7cm3

°

tan42° = h70

h = 70 tan42°h = 63 ft

6!= 720

10C2 = 45

26. One student is selected at random from a group of 12 freshmen, 12 sophomores, 12 juniors, and 4 seniors. Find the probability the person selected is not a junior.

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27. One card is selected at random from a deck of 52 cards. Find the probability of selecting a black card or an eight.

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28. A box contains six red balls, seven green balls, and eight yellow balls. Suppose you select one ball at random from the box and do not replace it. Then you randomly select a second ball. Find the probability that both balls selected are yellow.

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29. A game is played by rolling a single die. The player wins the number of dollars equal to the number rolled. There is a $2 charge to play the game. What is the expected value and what does it mean?

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This means that if you play the game many times, on average each game will be worth $1.50.

30. A group is comprised of 10 freshmen and 15 sophomores. If one person is randomly selected from the group, find the odds for the person being a freshman.

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P(J ') = 1− P(J )

P(J ') = 1− 1240

P(J ') = 2840

= 710

P(B∪ 8) = P(B)+ P(8)− P(B∩ 8)

= 2652

+ 452

− 252

= 2852

= 713

P(YfirstYsecond ) = P(Yfirst ) ⋅P(Ysecond Yfirst )

= 821

⋅ 720

= 215

E = −1 16

⎛⎝⎜

⎞⎠⎟ + 0

16

⎛⎝⎜

⎞⎠⎟ +1

16

⎛⎝⎜

⎞⎠⎟ + 2

16

⎛⎝⎜

⎞⎠⎟ + 3

16

⎛⎝⎜

⎞⎠⎟ + 4

16

⎛⎝⎜

⎞⎠⎟

= − 16+ 16+ 26+ 36+ 46

= 96= $1.50

P(F) = 1025

= 25

, so odds for = 2:3