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Unformatted text preview: MATH 130 Name:
Final Exam Problem 1. (a) Find the prime factorizations for“24, 36, 40, and 45. 24 =
36 =
40 =
45 =
(b) Use this information to ﬁnd GCF(24, 36, 40, 45) = LCM(24, 36, 40, 45) z Problem 2. Use Venn diagrams to prove or disprove the statement Au(BuC)=(AuB)u(AuC’). Problem 3. (a) Find a fraction equal to 0.6T? (b) The Value of a fraction is 1/2. If we subtract 3 from the numerator
and subtract 1 from the denominator, its value changes to 1/3. What was
the original fraction? Problem 4. HOW much 80% solution should be mixed with 3 gallons of 40%
solution to get a 50% solution? Problem 5. A collection of nickels and dimes is worth $1.25. There are 17
coins. How many of them are nickels? Problem 6. The fog horn blows every 25 minutes, the emergency lights blink
every 45 minutes, and warning siren sounds every 60 minutes. If all three
occur simultaneously at 4 am, when is the next simultaneous occurrence? Problem 7. The ratio of Tom’s money to Sam’s money was 7:3 at the start. Tom gave Sam $5 and the ratio became 3:2. How much money did Tom have
at the start? Problem 8. a) Use Euler’s algorithm to ﬁnd GCF(4400, 160) = b). Find the number of factors of 4400. Problem 9. Let U = {1,2,3,4,5,6, 7,8, 9, 10,11,12}, A = {2,3,5,6,11},
B = {1,3,5,8,12}, C = {1,5, 6, 7, 9}. (a) Draw a Venn diagram containing this information. (b) Find the following sets
(Ammucz (Ammué= Problem 10. In a school 60% of the students take math, 80% take science,
and 10% take neither. (21) Draw a Venn diagram containing this information. (b) What fraction of the science students take math? 10 Problem 11. (a) Construct the truth table for (‘p /\ q) —> ﬁp: (b) Suppose p and r are true and q is false. Circle the truth value of each
statement below. ~ ‘T F pVsq T F p/\(qu) T F (upVT)—>q
T F (pfHJWT T F (pA'r)~a—lq 11 Problem 12. (a) Construct the addition table in base ﬁve. (b) Construct the multiplication table in base ﬁve. 12 Problem 13. Calculate in baSe ﬁve: (a) 4332
+ 3343
(b)
4332
 3343
Problem 14. Calculate in base ﬁve:
(a)
314
x 42
(b) _
4313214 13 Problem 15. Make the conversions: (a) 423fi’ve : ten (a) 423,58" 2 five Problem 16. Determine the postages we cannot make with an unlimited
supply of 5 and 6 cent stamps. ‘ 14 Problem 17. Find the smallest number with exactly 16 factors. 15 Problem 18. The distance between Madison and Chicago is 120 miles.
When Fred drove to Chicago, the trafﬁc was light and his average speed was 60 mph. On the return he ran into heavy trafﬁc and his average speed was
40 mph. (a) How long did each trip take? Madison to Chicago: Chicago to Madison: (b) What was Fred’s average speed for the round trip? 16 Problem 19. Meg can paint a house in 8 days. Jane can paint it in 6 days.
After they worked together for 1 day, Meg was sent to another job. How
much additional time did it take Jane to ﬁnish the job? 17 Problem 20. A bowl contains red balls and white balls in two sizes. There
are 30% more red balls than white balls. Half the red balls and one quarter
of the white balls are small. . (a) Make a chart of explicit numbers which ﬁt the data. (b) What is the ratio of large white balls to large red balls? ((1) What is the ratio of large balls to small balls? 18 ...
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 Spring '07
 TERWILLIGER

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