Mathematics for the Liberal Arts Exam File Fall 2008

Exam #1

For each of #1-5, identify one AND ONLY ONE of our logical fallacies that is exhibited. Give a brief explanation for your choice.

Appeal to emotion Appeal to ignorance Appeal to popularity Circular reasoning Diversion False cause Hasty generalization Limited choice Personal attack Straw man

1.) "If you care about your grandchildren's future you will support the efforts to stop global warming." 2.) "Bubba Sue is from Alabama. All girls from Alabama have two word first names." 3.) "Are you going to major in history or are you going to major in mathematics?" 4.) "The last time I wore this hat during a test, I got an 'A'. It must be a lucky hat." 5.) "I can't believe you're supporting Ted Kennedy's tax hike proposal. After all, he was the one who drove the car off the bridge when Mary Jo Kopechne died."

6.) Construct the truth table for the following proposition.

((not p  q )  p) → q

7.) For each of the following, tell whether or not it is a proposition. a.) "John Dodge died after being in the head by a pitch during a minor league ballgame." b.) "Take your feet off of the coffee table!" c.) ♪♫♪♫"It's a beautiful day in the neighborhood."♪♫♪♫ d.) "Arkansas is north of Missouri." e.) "Millard Fillmore was the first president of the United States." f.) 5570 = 258,763,175,164,940,474,024,358,370,140,027,266,101,972,731,000, 849,487,432,696,691,594,165,238,662,840,430,349,527,071,435,270,918,32 5,962,916,208,543,427,488,052,599,275,665,011,888,825,298,326,160,809, 388,572,824,784,890,926,606,058,775,413,600,010,597,522,294,247,623,16 2,729,939,249,253,929,160,355,766,626,578,037,058,304,627,367,809,464, 646,477,784,187,980,841,016,392,280,101,929,404,993,990,389,555,433,58 5,024,261,204,937,436,050,131,287,877,419,867,645,500,009,913,951,677, 820,165,286,902,920,342,981,815,338,134,765,625.

8.) Draw a Venn Diagram to illustrate the following categorical proposition. All dogs eat acorns and some dogs ride skateboards.

9.) The following Venn diagram represents how a college class is broken down in the categories of female students (denoted "F"), students from Arkansas (denoted "A") and mathematics majors (denoted "M"). Answer the questions below the diagram. [Note that "x" and "y" represent students. Those students are already included in the numbers given in the diagram and should not be counted in addition to the numbers.]

a.) How many students are in the class? b.) How many of the students are mathematics majors from Arkansas? c.) How many female students are in the class? d.) How many psychology majors are in the class? e.) What do we know about student "x?" f.) What do we know about student "y?"

10.) Your living room is 15 feet wide and 18 feet long. What is the area of your living room in square meters? You must show the use of units and conversion factors.

11.) Your French friend Maurice is coming to visit. You want to tell him the temperatures he should expect. The high temperatures are expected to be around 84 Fahrenheit. If you want to tell Maurice the temperature in Celsius, what will you tell him? Show the details of the formula you use.

12.) Billy Bob's combination motor oil/salad dressing/kitty litter sells for $5.49 (U.S.) per gallon. Billy Bob wants to start selling his product in Mexico. What will the price be in pesos per liter? You must show the use of units and conversion factors.

13.) You are driving 100 feet per second. The speed limit is 70 miles per hour. Are you speeding? You must show the use of units and conversion factors.

14.) Methusaleh was 969 years old when he died. How many seconds old was Methusaleh when he died?

15.) You have a basket with apples in it. There are 23 green apples, 14 red apples and 8 plaid apples. You are going to take some apples out of the basket. a.) How many apples must you take out of the basket to be absolutely certain you have removed a matching pair of apples? b.) How many apples must you take out of the basket to be absolutely certain you have removed a matching pair of plaid apples? c.) How many apples must you take out of the basket to be absolutely certain you have removed four apples of the same color?

16.) You have ten rectangular tables in a rectangular room. You must arrange the tables so that there are three tables along each wall. Draw a picture to show how you could do this.

17.) Seventy-five people ate dinner at "Billy Bob's All You Can Stomach Exotic Animal Eatery" last night. Sixty-five of them ate squid. Fifty-three of them ate platypus. Forty-eight of them ate earthworm cookies. What is the fewest number of people who must have eaten all three of squid, platypus and earthworm cookies?

Exam #2

1.) The price of a coat was $140. Yesterday it was reduced 35%. What is the price now?

2.) In 2004, Jose Reyes of the New York Mets earned a salary of $307,500. For 2005, he received a raise of 7.967479675%. For 2006, he received a raise of 20.93373494%. WITHOUT ROUNDING OFF EITHER PERCENTAGE, determine his 2006 salary. (source: www.baseball-reference.com)

3.) The price of a coat was $140. Last week it was reduced 15%. This week it was reduced another 10%. Sales tax is 8%. With tax included, what is the cost of the coat now?

4.) David Wright of the New York Mets earned a salary in 2006 of $374,000. That was a 15.968992248% raise from his 2005 salary. What was his 2005 salary? (source: www.baseball-reference.com)

5.) Use reasonable estimations to approximate the total number of slices of bread eaten each year by all left-handed people in the United States.

6.) a.) Write 5.3 x 1011 in regular notation. b.) Write 2.2 x 10-8 in regular notation. c.) Write 32,000,000,000 in scientific notation. d.) Write 0.000000000425 in scientific notation. e.) Use the scientific notation from parts a.) and b.). Multiply the two numbers together, SHOWING ALL NECESSARY WORK AND WITHOUT USING YOUR CALCULATOR, and write your final answer in scientific notation.

7.) You put $2750 in the bank. The account gets an annual percentage rate of interest of 1.1% compounded monthly. The money is left in the account for 4 years. Throughout the problem, we assume no other money is added or removed from the account. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the amount of money you will have at the end of four years. b.) WITHOUT SIMPLIFYING ANYTHING, insert the numbers into the formula you will use to find the amount of money you will have at the end of four years. c.) How much money will you have at the end of four years?

8.) You put $6125 in the bank. The account gets an annual percentage rate of interest of 1.45% compounded continuously. The money is left in the account for 5 years. Throughout the problem, we assume no other money is added or removed from the accounts. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the amount of money you will have at the end of three years. b.) WITHOUT SIMPLIFYING ANYTHING, insert the numbers into the formula you will use to find the amount of money you will have at the end of five years. c.) How much money will you have at the end of three years?

9.) You start putting money in your retirement fund at age 23. You put in $225 each month. The interest of 10.185% is compounded quarterly. You will retire when you turn 65. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the amount of money in your fund when you retire. b.) WITHOUT SIMPLIFYING ANYTHING, insert the correct numbers into the formula. c.) How much money will you have at age 65? d.) What is the total of all of your payments? e.) Find the amount of interest you will receive.

10.) Consider the following question.

How do doctors' salaries compare to lawyers' salaries?

Which type of study (experimental, observational, -blind) would best answer the question? Give a reason for your answer.

11.) You are buying a house. After the down payment, you need to borrow $120,000. You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 30 year mortgage is 5.85%. Throughout the problem we will ignore escrow payments that might be added to the payment for insurance and taxes. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the monthly payment on this loan. b.) WITHOUT SIMPLIFYING ANYTHING, insert the correct numbers into the formula. c.) What will be your monthly payment? d.) What will be the total of all of your monthly payments? e.) How much interest will you pay over the life of the loan?

12.) A person is interested in finding out the average income of people in Arkansas. In order to do that, he does a survey by asking the annual income of Arkansas residents in line at the Reddie Café in the Garrison Center. Are his results likely to be representative of Arkansas? Why or why not?

13.) You start putting money in a college savings account. You want to have $125,000 in 18 years when your daughter will be ready for college. The interest rate of 10.35% is compounded monthly. a.) WITHOUT INSERTING ANY NUMBERS, write the formula that will figure out the amount of money you will have to put in the account each month. b.) WITHOUT DOING ANY SIMPLIFICATION, insert all of the numbers into the formula. c.) How much money will you have to pay each month? d.) What is the total of all of your payments?

14.) At a doctor's office a piece from a tongue depressor has gotten under the weighing surface of a scale, keeping the surface from being able to go down all the way. Also, there is some demolition work going on nearby that periodically shakes everything in the office. Discuss this situation in how it relates to systematic and random .

Exam #3

1.) The following chart shows the number of times four managers were ejected from games from 2002 through 2007. Draw a time series plot to illustrate the data.

Manager 2002 2003 2004 2005 2006 2007 Bobby Cox 7 9 5 2 9 5 Lou Piniella 3 4 2 2 0 1 Joe Torre 2 1 2 2 2 2 Charlie Manuel 2 0 0 5 6 3

2.) Explain the difference between a linear model and an exponential model.

3.) The following data is the number of times Bobby Cox was ejected from 2002 through 2007. 7 9 5 2 9 5 YOU MAY NOT USE YOUR CALCULATOR FOR THIS PROBLEM. YOU MUST SHOW ALL WORK AND GIVE AN EXPLANATION OF HOW YOU GOT YOUR ANSWERS. Find the following for the numbers of ejections in those seasons. a.) the mean b.) the median c.) the mode

4.) In 1988, the New York Mets hit 152 home runs as a team. The following chart shows the distribution of home runs broken down by home runs hit by Lenny Dykstra, Mookie Wilson, Kevin Elster, Gary Carter, Keith Hernandez, Howard Johnson, Kevin McReynolds, Darryl Strawberry and "other" players.

Other

Strawberry Dykstra

Wilson

Elster

Carter

McReynolds Hernandez

Johnson

a.) The portion of the pie for Darryl Strawberry has an angle of 92.36842. How many home runs did he hit? b.) Three players hit more than 20 home runs. Who were they? c.) How many home runs did Wally Backman hit? d.) Who hit more home runs, Kevin McReynolds or Keith Hernandez? e.) Who invented the pie chart?

5.) The following table gives some career statistics for Willie Mays, the best all- around player in baseball history.

Year Team G AB R H 2B 3B HR RBI BB SO AVG 1951 Giants 121 464 59 127 22 5 20 68 57 60 .274 1952 Giants 34 127 17 30 2 4 4 23 16 17 .236 1954 Giants 151 565 119 195 33 13 41 110 66 57 .345 1955 Giants 152 580 123 185 18 13 51 127 79 60 .319 1956 Giants 152 578 101 171 27 8 36 84 68 65 .296 1957 Giants 152 585 112 195 26 20 35 97 76 62 .333 1958 Giants 152 600 121 208 33 11 29 96 78 56 .347 1959 Giants 151 575 125 180 43 5 34 104 65 58 .313 1960 Giants 153 595 107 190 29 12 29 103 61 70 .319 1961 Giants 154 572 129 176 32 3 40 123 81 77 .308 1962 Giants 162 621 130 189 36 5 49 141 78 85 .304 1963 Giants 157 596 115 187 32 7 38 103 66 83 .314 1964 Giants 157 578 121 171 21 9 47 111 82 72 .296 1965 Giants 157 558 118 177 21 3 52 112 76 71 .317 1966 Giants 152 552 99 159 29 4 37 103 70 81 .288 1967 Giants 141 486 83 128 22 2 22 70 51 92 .263 1968 Giants 148 498 84 144 20 5 23 79 67 81 .289 1969 Giants 117 403 64 114 17 3 13 58 49 71 .283 1970 Giants 139 478 94 139 15 2 28 83 79 90 .291 1971 Giants 136 417 82 113 24 5 18 61 112 123 .271 1972 Giants 19 49 8 9 2 0 0 3 17 5 .184 1972 Mets 69 195 27 52 9 1 8 19 43 43 .267 1973 Mets 66 209 24 44 10 0 6 25 27 47 .211

a.) What is the most home runs (HR) he hit in one season? What year? b.) In how many seasons did he have a batting average (AVG) above .300? c.) What is the most consecutive seasons in which he hit at least 30 home runs (HR)? d.) In how many seasons did he exceed both 100 runs scored (denoted R) AND runs batted in (denoted RBI)?

6.) The following chart shows the number of all-time wins for the expansion teams from .

4000 3500 3000 2500 2000 1500 1000 500

0

Rays

Mets

Astros

Royals

Angels

Padres

Marlins

Rockies

Rangers

Brewers

BlueJays

Mariners Nationals

Diamondbacks

a.) How many games have the Mets won? b.) Which of these teams has won the most games? Fewest? c.) How many of these teams have won more than 3500 games? d.) How many games did the Mets win in 1969?

7.) The following are the leading totals for at bats from major league baseball in 2008.

616 627 635 611 625 612 626 623 653 611 634 686 628 644 688 624 623 624 645 616 632 661 635 611 611

Use your calculator to find the following. a.) the mean b.) the median c.) the mode 8.) Draw a tree diagram to illustrate flipping three coins. Then use the diagram to find the probability of getting two tails and one head on the three flips.

9.) A box contains eight tostadas, six quesadillas and four tacos. a.) You reach into the box, grab an item, reach into the box again and grab another item. What is the probability that you got two quesadillas? b.) Everything is back in the box. You reach into the box, grab an item, note what it is, put it back, reach into the box again and grab another item. What is the probability that you got a tostada first and a taco second? c.) Everything is back in the box. You reach into the box, grab an item. What is the probability that it is an enchilada?

10.) You roll a die 4 times. What is the probability that you roll a two at least once?

11.) In 1870, Searcy, Arkansas had a population of 874. By 1880 the population had dropped to 840 (that's a drop of 3.8902% over the 10 year period). If that rate had remained the same, what would the population of Searcy be in 2008?

12.) According to microbiologist, Dr. Chuck Gerba, one of three chickens is contaminated with salmonella. The vast majority of contaminated chickens have fewer than 300 salmonella, all killed in the cooking. Even if they survived, it usually takes several thousand to cause illness. However, if the salmonella gets transferred during food preparation to the potato salad, the warm, moist environment allows them to double in population every 20 minutes. Suppose 100 salmonella got into the potato salad. How many would there be 6 hours later? (source - "Reader's Digest," February 1995)

13.) You are making a license plate. It has 3 letters followed by 4 numbers. How many different license plates can be made if letters may not be repeated?

14.) Fifteen people have formed a baseball team. We are interested in the number of nine player batting orders that can be created from the fifteen players. a.) Is this a combination problem or a permutation problem? b.) How many different lineups are possible?

15.) Consider the nine letters G, H, I, J, K, M, L, N, and O. For our purposes, a "word" is ANY arrangement of letters (for example, GGKKJ is a "word"). a.) How many four letter "words" can be made from these letters if repetitions are allowed? b.) How many four letter "words" can be made from these letters if no repetitions are allowed?

Exam #4

1.) Find the area and perimeter of the following triangle. Assume all units are in centimeters.

2.) A cylindrical storage drum has a height of 2 feet and a diameter of 18 inches. Find the volume and surface area. GIVE AT LEAST 4 PLACES TO THE RIGHT OF THE DECIMAL POINT!!

3.) Draw a section of tile floor, with four rows of four tiles each, that illustrates the idea of vanishing points. Identify the principal vanishing point and two others.

4.) A Fibonacci-like sequence has a first term of 1and a second term of 8. Find the next four terms.

5.) Consider the following shapes.

1 2 3 4

5 6 7 8

For each type of symmetry below, list the shapes that have that kind of symmetry. Some may fit more than one symmetry. a.) symmetry around a horizontal line through the middle of the shape b.) symmetry around a vertical line through the middle of the shape c.) rotational symmetry when rotated 180 degrees d.) none of the above symmetries

6.) Explain the difference between votes that are decided by majority vote and those decided by plurality vote.

7.) Middle C has a frequency of 260 cycles per second. Find the frequency of the note that is: a.) 5 half-steps above Middle C. b.) 3 half-steps below Middle C. c.) one octave above Middle C. d.) two octaves below Middle C. e.) three octaves above Middle C.

8.) Explain what a Borda count is and give an example.

9.) The window below is shaped like a rectangle with a semi-circle on top. What are the area and perimeter of the window? GIVE AT LEAST 4 PLACES TO THE RIGHT OF THE DECIMAL POINT!!

10.) Consider a country consisting of 5 states with populations given below. If the country's legislature is to have 100 members, find the standard divisor and fill in the table below. Explain why you allot the representatives the way you did.

Standard Divisor =

State Population Standard with normal # of representatives Quota rounding, # of you will give state representatives state "should" get A 6,205,331 B 6,205,332 C 1,815 D 19,886,060 E 10,234,549 Total Population 42,533,087

Final Exam

In exercises #1 - 3, identify one and only one of our fallacies that is exhibited. GIVE A DETAILED EXPLANATION TO JUSTIFY YOUR CHOICE. 1.) "If you aren't sure why you should vote for Senator Kadiddlehopper, then think of the children!" 2.) "That is the third time this week some guy in a pickup truck has cut me off on the interstate. Obviously rednecks don't know how to drive." 3.) "I understand why you think Obama should be president, but what about the corruption charges against Illinois Governor Blagojevich?"

4.) CC Sabathia, the 311 pound , recently signed a contract with the New York Yankees for $161 million. Convert his weight to centigrams and the contract amount to Mexican pesos.

5.) The part of a baseball diamond inside the bases is a square that is 90 feet on each side. Find the area inside the basepaths and convert it to meters.

6.) You are driving 75 feet per second in a 45 mile per hour section of the highway. Are you speeding? Be sure to show all work.

7.) a.) In a basket, you have 24 green apples, 14 red apples and 18 yellow apples. Without looking, you start pulling apples out of the basket. i.) How many apples must you pull out so that it is certain you have three matching apples? Explain your answer. ii.) How many apples must you pull out so that it is certain you have three green apples? Explain your answer. b.) You are considering buying 15 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. How can you determine the lightweight coin in a maximum of three weighings on a balance scale? (A balance scale just indicates which of two items is heavier.)

8.) Bubba saw a combination chain saw/tooth flossing machine for $400. He couldn't afford it. The next week it was on sale for 10% off. He still couldn't afford it. The next week it was on sale for another 15% off. He bought it. How much did it cost?

9.) Billy Bob bought a new four wheeler. It was on sale for $13,090. That was 15% off of the original price. How much did it cost before the sale?

10.) Mephibosheth bought a jacket for $149, a hat for $25 and a pair of shoes for $45. Sales tax is 8.4%. What was the total cost for the jacket, hat and shoes with tax included?

11.) Wilma Sue is buying Billy Bob a new double-wide for Christmas. She is borrowing $27,000 to buy it. The interest rate for his 10 year mortgage is 5.95%. We will ignore the escrow payments that would normally be added to the mortgage payment to cover insurance and taxes. a.) Without inserting any numbers, write out the formula that will figure out the amount of Wilma Sue's monthly payments. b.) Without doing any simplification, insert all of the numbers into the formula. c.) What will be her monthly payment? d.) What will be the total of all of her monthly payments? e.) How much interest will she pay over the life of the loan?

12.) You put $4000 in a 5 year CD paying an annual percentage rate of 3.2% compounded quarterly. You neither take out any money nor put in any more money. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have after 5 years. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have after 5 years?

13.) You are 23 years old and plan to retire at age 65. You start putting $150 per month in a retirement fund that pays 7.653% interest compounded quarterly. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have when you retire. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have at age 65? d.) What is the total of all of your payments? e.) How much interest did your money earn?

14.) The following is the number of sacrifice flies hit Leon "Daddy Wags" Wagner hit each year from 1960 to 1965. (data from www.baseball-reference.com) 1 7 4 7 5 3 Find the following WITHOUT USING YOUR CALCULATOR AT ALL AND YOU MUST GIVE SOME INDICATION OF HOW YOU FOUND THE NUMBER. a.) Find the mean. b.) Find the median. c.) Find the mode.

15.) The following table gives the all-time top 24 totals for . (data from www.baseball-reference.com) Player Year Mark Baldwin 368 1889 a.) For these players, what is the Charlie Buffinton 417 1884 mean number of strikeouts? 483 1884 Bob Feller 348 1946 369 1884 385 1884 Hardie Henderson 346 1884 Randy Johnson 364 1999 b.) For these players, what is the Randy Johnson 347 2000 median number of Randy Johnson 372 2001 strikeouts? Tim Keefe 361 1883 513 1886 Sandy Koufax 382 1965 Jim McCormick 343 1884 Charley Radbourn 441 1884 499 1886 c.) For these players, what is the Toad Ramsey 355 1887 mode number of strikeouts? Nolan Ryan 383 1973 Nolan Ryan 367 1974 Dupee Shaw 451 1884 Bill Sweeney 374 1884 Rube Waddell 349 1904 Mickey Welch 345 1884 Jim Whitney 345 1883

16.) The following table shows the number of wins for Sandy Koufax, Don Drysdale and Juan Marichal from 1961 through 1966. Draw a time series plot that represents this data. Be sure to label your graph so I can determine who is represented by each part of the graph. (data from www.baseball-reference.com)

Koufax Drysdale Marichal 1961 18 13 13 1962 14 25 18 1963 25 19 25 1964 19 18 21 1965 26 23 22 1966 27 13 25

17.) The following graph shows the number of runs batted in (RBI) by Pinky Hargraves had in every year of his major league career.

70 60 50 40 30 20 10 0

1923 1924 1925 1926 1928 1929 1930 1931 1932 1933

a.) In what year did Hargraves have the most RBI? How many did he have that year? b.) In how many years did Hargraves have more than 30 RBI? c.) In what year did Hargraves exceed his previous year's RBI total by the largest amount? d.) How many home runs did Hargaves hit in 1928?

18.) List two things that must be considered when trying to decide whether or not to believe a poll or statistical study.

19.) You are in prison making license plates. How many three letter-three number license plates are possible if numbers may not be repeated?

20.) Draw a tree diagram to illustrate the possible outcomes of flipping a coin three times. Then, use the tree diagram to determine the probability of getting an odd number of heads in the three flips.

21.) You have a box. In the box are 8 red marbles, 5 blue marbles, and 11 plaid marbles. a.) If you reach into the box and pull out a marble, what is the probability the marble is plaid? b.) If you pull out a marble, note its color, put it back and pull out another marble, what is the probability both marbles are blue? c.) If you pull out a marble, note its color and pull out another marble, what is the probability both marbles are blue?

22.) One of the items on Olive Garden's on-line menu is the Sampler Italiano. From calamari, stuffed mushrooms, fried zucchini, chicken fingers, fried mozzarella or toasted meat ravioli you can choose any three for $8.25. How many different Sampler Italianos are possible?

23.) In 1880, Mountain Home, Arkansas had a population of 137. By 1890 it had doubled. Assuming the population continued to grow exponentially at the same rate, what would the population be in 2005? (Note: the actual 2000 population was 11,012.)

24.) A large door has the shape of a rectangle with a triangle on top (see picture). If all measurements are in feet, find the area and perimeter.

25.) Draw a section of tile floor, with four rows of four tiles each, that illustrates the idea of vanishing points. Identify the principal vanishing point and two others. Also draw the walls around the area of floor.