Math 113-All Sections Final Exam May 6, 2013

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1 Name Math 3-All Sections Final Exam May 6, 23 Answer questions on the scantron provided. The scantron should be the same color as this page. Be sure to encode your name, student number and SECTION NUMBER UNDER THE LAST COLUMN(S) UNDER SPECIAL CODE. The formula sheet is the last page of this exam, feel free to tear it off. This exam is double-sided. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the preference table to answer the question. ) Use Kruskal s Algorithm to find the weight of the minimal spanning tree: 5 8 A) 2 B) 6 C) D) 8 E) 7 2) Two marbles are drawn without replacement from a box with 5 white, 2 green, 2 red, and 3 blue marble. Find the probability that the first is white and the 2 nd is blue. A) 5/72 B) 8 C) 5/44 D) 5/66 E) 5/48 3) The top 5 NBA scorers of all time are listed along with the overall points scored. What is the mean number points scored?. Kareem Abdul-Jabbar A) B) C) D) E) Karl Malone 3. Michael Jordan 4. Kobe Bryant Wilt Chamberlain 349 4) Which vertices are adjacent to vertex B? A) A and C only B) A, E, and C only C) A, C, E, G only D) A and E only E) all vertices Math 3 Final Exam Blue Spring 23 page

2 5) Suppose that the generator matrix for a (4,8) code is as follows. Find the codeword corresponding to:. A) B) C) D) E) 6) Celita takes out a conventional installment loan for five years at 6.% compounded monthly. What are her monthly payments if she borrows $,? A) $66.67 B) $2.23 C) $9. D) $93.79 E) $88.2 7) Given the histogram, which statement is true? A) Graph is skewed to the left. B) Graph is skewed to the right. C) Graph is bimodal. D) Graph is approximately symmetric. E) The mean is equal to the median. 8) Which of the following graphs have an Euler circuit? A) G only B) G 2 only C) G 3 only D) G and G 3 only E) All of the graphs. 9) The number of edges in a tree with 8 vertices is A) 8! B) 2 8 C) 8 D) 7 E) 2 7 Math 3 Final Exam Blue Spring 23 page 2

3 ) Whitney borrows $ at 5.5% simple interest for 4 years. What is the total amount due at the end of 4 years? A) $22 B) $9.2 C) $22 D) $ E) $8.33 ) The nearest-neighbor tour starting with vertex A is given by: A) A,C,B,D,E,A B) A,C,B,E,D,A C) A,C,E,B,D,A D) A,C,E,D,B,A E) A,B,C,D,E,A 2) Find the median of the following: 6, 4, 48, 95, 6, 3 A) 7.5 B) 6 C) 35 D) 4.83 E) 48 3) The first nine digits of an ISBN are What is the correct check digit? A) B) 2 C) 5 D) 7 E) 4 4) Determine the number of Hamiltonion circuits in a complete graph with 6 vertices. A) 5 B) 6 C) 72 D) 24 E) 2 5) The table shows the number of college students (out of 29) who prefer a given pizza topping. Find the probability that a randomly selected student prefers veggie pizza, given that the student is a junior. A) B) 23/69 C) 23 D) 23/58 E) 23/29 Math 3 Final Exam Blue Spring 23 page 3

4 6) Perform the indicated calculation in Z 9 : [8] + [6] A) [] B) [6] C) [3] D) [4] E) [5] 7) An optimal Eulerization of this graph can be obtained by duplicating how many edges? A) B) None, it has an Euler circuit. C) 2 D) 3 E) 4 8) Find the standard deviation of 9, 2, 5, 4, 2, 7. A) 6.5 B) 3.3 C) 2.45 D).98 E) ) Determine the effective annual yield for 6.% compounded semi-annually. Round to the nearest tenth of a percent. A) 6.% B) 6.3% C) 6.4% D) 6.% E) 6.2% 2) The numbers on the edges represent distances in miles between locations A, B, C, D, and E. Find the total distance for the Hamilton circuit found using the cheapest-link algorithm. A) 2 B) 6 C) 4 D) 8 E) 7 Math 3 Final Exam Blue Spring 23 page 4

5 2) Find the value of the 3 rd quartile (upper quartile): 2, 4, 5, 5, 8, 9,,, 2, 4, 4, 6, 7, 9, 22 A) 5 B) 6 C) 22 D) 7 E) 4 22) Add the given codewords using addition over Z 2 in each place for c = and c 2 =. A) B) C) D) E) 23) How much money should be deposited today into an account that earns 3% compounded monthly so that it will accumulate to $6, in years? (Round to the nearest dollar.) A) $ B) $ C) $ D) $ E) $ ) A bag contains 5 red marbles, 7 blue marbles, 3 yellow marbles and 2 green marbles. What is the probability that a randomly selected marble is not blue? A) 3/7 B) 7/ C) /7 D) 7/7 E) 25) Find the remainder if 87 is divided by 7. A) 2 B) C) 2 D) E) 3 26) Suppose that a fifteen-person committee needs to select one of the alternatives A, B, or C. Their votes are summarized in the following preference table. Number of Votes First Choice A C B C Second Choice B A C B Third Choice C B A A Which choice is the winner using the Borda count method? A) A B) B C) C D) Tie between A and B E) Tie between C and A Math 3 Final Exam Blue Spring 23 page 5

6 27) In a poll of a 2456 adults, 56% said they planned to vote yes on a school bond referendum. Find the 95% confidence interval for the proportion of adults who plan to vote yes. A) 53% to 59% B) 54.43% to 54.57% C) 55.98% to 65.2% D) 54.5% to 57.5% E) 53.98% to 58.2% 28) What is the Hamming distance between the codewords: and A) B) 5 C) 2 D) 3 E) 4 29) A sociologist surveyed the households in a small town. The random variable x represents the number of dependent children in the households. Find the mean number of dependent children. Do not round. A).38 B) 2.56 C) D) 2.4 E) 2 X P(x) ) Suppose that an eleven-person committee needs to select one of the alternatives A, B, or C. Their votes are summarized in the following preference table. Which choice is the head to head Winner? Number of Votes First Choice A B C Second Choice C C B Third Choice B A A A) A B) B C) C D) There is no head-to-head winner E) No answer listed. 3) In order to monitor the quality of the three-way switches it produces, a manufacturer randomly selects 5 three-way switches to test. Twelve of the switches tested were defective. The sample in this study is: A) All three-way switches in the U.S. B) The three-way switches produced by the manufacturer. C) The 5 three-way switches it tested. D) The three-way switches produced by the manufacturer. E) The 2 defective switches. 32) The principal P is borrowed and the loan's future value, A, at time t is given. Determine the loan's simple interest rate, r, to the nearest tenth of a percent. P = $ 55; A = $ 57; t = year A) 3.6% B) 5.% C) 4.2% D) 3.5% E) 5.%. Math 3 Final Exam Blue Spring 23 page 6

7 33) What are the odds of spinning a number less than 6? A) 5:8 B) 5:3 C) 3:5 D) 8:5 E) 6:2 34) Dan deposits $ at the end of each month for four years into an account that pays 3.9% compounded monthly. How much will Max have accumulated in the account at the end of four years? (Round to the nearest dollar.) A) $623.2 B) $ C) $48 D) $ E) $ ) What type of study would be most appropriate? Suppose we want to study the effect of smoking on lung capacity in women. A) Experiment without blinding B) Observational study C) Experiment with double blinding D) Experiment with single blinding E) Case-control study 36) Suppose the check matrix for a (2,6) matrix code is as follows. Decode the word if it is a codeword or if it differs from a codeword in a single digit. The decoded message is: A) Cannot be determined. B) C) D) E) 37) The distribution of heights of young men is approximately normal with a mean of 7 inches and a standard deviation of 2.5 inches. Approximately what percent of men are between 65 and 75 inches tall? A) 68% B) 95% C) 99.7% D) 5% E) 34% Math 3 Final Exam Blue Spring 23 page 7

8 Use the following table for problem ) The distribution of heights of young men is approximately normal with a mean of 7 inches and a standard deviation of 2.5 inches. Approximately what percent of men are less than 7.5 inches tall? A) 47.5% B) 72.57% C) 69.5% D) 27.43% E) 98.57% 39) A savings account pays 5.5% compounded monthly. If you make a deposit of $4 into this account, how much will you have after seven years? Round to the nearest dollar. A) $ B) $ C) $62.34 D) $ E) $6.34 4) Nineteen voters must choose between alternatives A, B, C, or D. Their votes are summarized in the following preference table. Number of Votes First Choice A B C D Second Choice B C B C Third Choice C A A B Fourth Choice D D D A Which candidate is eliminated second using the plurality with elimination method? A) A B) B C) C D) D E) None of the candidates. Math 3 Final Exam Blue Spring 23 page 8

9 PLEASE TEAR THIS OFF TO USE AS YOU ARE TAKING YOUR FINAL Simple Interest: Effective Annual Yield (EAY): Future Value (with Simple Interest): n number of compounding periods in year *Note: Effective Annual Yield is the same as Annual Percentage Yield (APY) Savings Formula Compound Interest -finite # of compound periods: n number of compounding periods in year d deposit made at the end of each period n number of compounding periods in year Loan Formula (Amortization Formula): Compound Interest continuous d deposit made at the end of each period n number of compounding periods in year Math 3 Final Exam Blue Spring 23 page 9

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