1. There are 2 separate, equal-size boxes, and inside each box there are 5 separate small boxes, and inside each of the small boxes there are 3 even smaller boxes. How many boxes are there all together? 30 boxes b 32 . boxes c 42 . boxes d 40 . boxes e 44 . boxes a . 5 points Question 2 1. Use Euler circles to check the validity of the argument. All candy is fattening. All candy is delicious. Therefore, all fattening food is delicious. The argument is __________. not valid b valid a . . 5 points Question 3 1. Two persons are to run a race, but one can run 11 meters per second, whereas the other can run 6 meters per second. If the slower runner has a 55-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time? a 11 sec . b 11.5 . sec 9.17 sec d 10 sec c . . e . 9.5 sec 5 points Question 4 1. A certain test is worth 120 points. How many points (rounded to the nearest point) are needed to obtain a score of 80%? 150 points b 101 . points c 67 . points d 96 . points e 40 . points a . 5 points Question 5 1. Is the network in d) an Euler circuit? Can this network can be traversed? not an Euler circuit; traversable b an Euler circuit; traversable a . . c . an Euler circuit; not traversable d not an Euler circuit; not . traversable 5 points Question 6 1. A saleswoman wants to visit eastern cities, New York City, Boston, Cleveland, and Washington, D.C. Driving distances are as shown in the figure below. What is the shortest trip starting in New York that visits each of these cities, if using the brute-force method. , ? Find a solution 1810 mi b 2799 . mi c 1811 . mi d 1813 . mi e 1814 . mi a . 5 points Question 7 1. Find the minimum spanning tree for the of the graph. The sum of the numbers spanning tree is 151 b The sum of the numbers . spanning tree is 132 c The sum of the numbers . spanning tree is 119 d The sum of the numbers . spanning tree is 202 e The sum of the numbers . spanning tree is 179 a . associated with the edges of the minimum associated with the edges of the minimum associated with the edges of the minimum associated with the edges of the minimum associated with the edges of the minimum 5 points Question 8 1. If $12,000 is invested at 6.5% for 14 years, find the future value if the interest is compounded daily. $29,767. 91 b $29,789. . 86 c $29,804. . 53 d $29,809. . 46 e $29,810. . 40 a . 5 points Question 9 1. Karen and Wayne need to buy a refrigerator because theirs just broke. Unfortunately, their savings account is depleted, and they will need to borrow money in order to buy a new one. Sears offers them an installment loan at 16% (add-on rate). If the refrigerator at Sears costs $1,540 plus 5% sales tax, and Karen and Wayne plan to pay for the refrigerator for 3 years, what is the monthly payment? $66.4 8 b $59.8 . 3 c $73.1 . 2 d $63.3 . 1 e $49.9 . 6 a . 5 points Question 10 1. Find the 12th term of the sequence. a . b . c . d . e . 5 points Question 11 1. In voting among three candidates, the outcomes are reported as: (ABC) 6 (ACB) 8 (BAC) 3 (BCA) 3 (CAB) 7 (CBA) 2 2. Determine the winner, if any, using Hare method. aB . bC . cA . d none . of them 5 points Question 12 1. A focus group of 35 people for ABC TV were asked to rank the government spending priorities of education (E), military spending (M), health care (H), immigration (I), and lowering taxes (T). Here are the preferences: (EIHTM) 17 (MIEHT) 6 (HMETI) 6 (TMEIH) 6 2. Suppose that the losing issues of health care, lowering taxes, and immigration are removed from the table. Now, who is the winner using the Borda count method? a . E bM . c No . winner. 5 points Question 13 1. The fraternity is electing a national president and there are four candidates: Alberto (A), Bate (B), Carl (C), and Dave (D). The voter preferences are: (CADB) 114 (CABD) 134 (DABC) 144 (BADC) 164 Who wins the election using the Hare method? Does this violate any of the fairness criteria? a . Bate. Yes. Condorcet criterion. b Carl. Yes. Condorcet . criterion. c Dave. Yes. Condorcet . criterion. d Carl. No. . e . Bate. No. 5 points Question 14 1. Find a modified divisor that will give modified quotas to produce the desired number of seats. Use rounding down for the standard quotas. 10 seats Population 1st Precinct 2st Precinct 3st Precinct 4st Precinct TOTAL 35,000 22,000 15,000 46,000 118,000 a. 11,400 b. 9,500 c. 9,200 d. 11,100 e. 9,000 5 points Question 15 1. A moderately active 140-pound person will use 2100 calories per day to maintain that body weight. How many calories per day are necessary to maintain a moderately active 155-pound person? __________ calories 5 points Question 16 1. If the property tax on a $300,000 home is $2,220, what is the tax on a $100,000 home? Round to the nearest dollar. $__________ 5 points Question 17 1. If 6% of the 210 million adult Americans are unemployed, how many adult Americans are unemployed? Give your answer to two decimal places, if required. __________ million 5 points Question 18 1. An animal shelter has two purebred Labradors among the 54 dogs available for adoption. It is also known that 7/9 of the dogs are mongrels. How many of the dogs are purebreds? __________ dogs 5 points Question 19 1. Find the APR (rounded to the nearest tenth of a percent) for the loan. Purchase a living room set for $2,500 at 12% add-on interest for 2 years. __________% 5 points Question 20 1. Does the network in the picture below have Hamiltonian cycles? If the network has one, describe it. If not, answer not possible. 1. Evaluate the expression. a . 12 7 b 28 . c2 . d 25 . e 14 . 0 20 points Question 2 1. A newspaper reported that candidate Williams received 13,500 more votes that her opponebt Ms. Smith, and that 42,310 votes were cast in the election. How many votes were cast for each candidate? 20 points Question 3 1. Find the next number in the following pattern: 1 5 3 7 5 9 7 ... 20 points Question 4 1. Use the following pattern and inductive reasoning to predict the answer to . 6,666,666,60 6 b 66,666,666,0 . 39 c 133,333,332, . 120 d 66,666,666,0 . 57 e 66,666,666,0 . 60 a . 20 points Question 5 1. What is the sum of the fifth line from the below pattern 2=2 2+4=6 2 + 4 + 6 = 12 Answers 1. 42 boxes 2. Not valid 3. 11 sec t(11-6)=55 t=55/5=11 sec 4. 96 points 100x(x/120)=80 X=12x8=96 5. An euler circuit traversable 6. 2799 mi 7. The sum of the number associated with the edges of the minimum spanning tree is 179 8. Dollar 28,978.49 9. Total amount borrowed=1540+77=1617 16% of 1617=258.72 1617+258.72=1875.72 36 months in 3 years 1875.72/36=52.1 approximate as 49.96 10. S12=4(12)-3==48-3=45 S12=45 11) (CAB) 7 12) Ans: b.C 13) Ans:A 14)9500 15)2325 16)740 17)13.12 18)7/9x(54)=42;54-42=12 19) Ans:23 20) not possible 1) 1^2+2^2+3^2+4^2+5^2+6^2+7^2 1+4+9+16+25+36+49=140 2)28810 3)11 4) e)66666666060 123456789x540 000000000 495827156 617283945 66666666060 2=2 2+4=6 2+4+612 2+4+6+8=20 2+4+6+8+10=30 Ans:30 Answers 1. 42 boxes 2. Not valid 3. 11 sec t(11-6)=55 t=55/5=11 sec 4. 96 points 100x(x/120)=80 X=12x8=96 5. An euler circuit traversable 6. 2799 mi 7. The sum of the number associated with the edges of the minimum spanning tree is 179 8. Dollar 28,978.49 9. Total amount borrowed=1540+77=1617 16% of 1617=258.72 1617+258.72=1875.72 36 months in 3 years 1875.72/36=52.1 approximate as 49.96 10. S12=4(12)-3==48-3=45 S12=45 11) (CAB) 7 12) Ans: b.C 13) Ans:A 14)9500 15)2325 16)740 17)13.12 18)7/9x(54)=42;54-42=12 19) Ans:23 20) not possible 1) 1^2+2^2+3^2+4^2+5^2+6^2+7^2 1+4+9+16+25+36+49=140 2)28810 3)11 4) e)66666666060 123456789x540 000000000 495827156 617283945 66666666060 2=2 2+4=6 2+4+612 2+4+6+8=20 2+4+6+8+10=30 Ans:30