Mathematics for the Liberal Arts Exam File Summer 2010

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.

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

14.) 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?

15.) 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.

16.) 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.) In 1996, the total payroll for the was $63,000,000. Their total operating expenses were $95,000,000. What percentage of their operating expenses went to payroll? (data from http://www.businessofbaseball.com/)

2.) The price of a sofa was $800. Two weeks ago the price was dropped 15%. This week it was dropped 10%. What is the price now?

3.) The price of the car was discounted 10%. If the sale price was $8361, what was the original price?

4.) Mrs. McGinty is riding in the back of the RV while Mr. McGinty drives along a very bumpy road. Mrs. McGinty is measuring some material for a sewing project. Unbeknownst to her, her cat chewed off the first two inches of her tape measure. She is also having trouble measuring because of the bumpiness of the ride. Discuss this situation regarding sources of systematic and random .

5.) a.) Calculate (5 x 10-8) x (4.2 x 1012) without using your calculator. Be careful to show all of your work and express your final answer in scientific notation. b.) Write 0.0000034 in scientific notation. c.) Write 450,000,000 in scientific notation.

6.) Mephibosheth started putting money in a college savings account. He wants to have $125,000 in 18 years when his son will be ready for college. The interest rate of 7.95% is compounded quarterly. a.) Without inserting any numbers, write out the formula that will figure out the amount of money Mephibosheth will have to put in the account each quarter. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will he have to pay each quarter? d.) What is the total of all of his payments? 7.) You start putting money in your retirement fund at age 25. You put in $800 each quarter. The interest of 10.56% is compounded quarterly. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have if you retire at age 63. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have at age 63? d.) What is the total of all of your payments? e.) How much interest did you earn?

8.) You put $3500 in a certificate of deposit account. It receives 2.25% interest compounded quarterly. You neither take out any money nor put in any more money. a.) Write out the formula that will figure out the amount of money you will have after 3 years without any of the numbers inserted. b.) Write out the formula that will figure out the amount of money you will have after 3 years with all of the numbers inserted. c.) How much money will you have after 3 years?

9.) Bubba is borrowing $32,500 to buy a new -wide. The interest rate for his 15 year mortgage is 7.05%. Throughout the problem 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 Bubba's monthly payments. b.) Without doing any simplification, insert all of the numbers into the formula. c.) What will be his monthly payment? d.) What will be the total of all of his monthly payments? e.) How much interest will he pay over the life of the loan?

10.) CNN is doing a poll on their web site. Explain why this poll is biased.

11.) The listed price was $14.95. Tax was 8.25%. What was the total cost?

12.) You are buying a house. After the down payment, you need to borrow $115,000. 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?

Exam #3

1.) The following chart shows the players from the 1956 who were most frequently hit by pitches. Draw a line graph to illustrate the data.

Larry Doby 4 Walt Dropo 3 Sammy Esposito 2 Nellie Fox 10 Fred Hatfield 8 Sherm Lollar 16 Minnie Minoso 23 Jim Rivera 3

2.) Explain the difference between a linear model and an exponential model. 3.) The following data are the number of wins for Mets Craig Swan from 1976 through 1981. 6 9 9 14 5 0

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 this data. a.) the mean b.) the median c.) the mode d.) the maximum e.) the minimum

4.) In 1956, the hit 221 home runs as a team. The following chart shows the distribution of home runs broken down by home runs hit by , Gus Bell, , , Ray Jablonski, , , and "other" players.

a.) Who hit the most home runs? How many home runs did he hit? b.) Three players hit more than 30 home runs. Who were they? c.) How many home runs did Roy McMillan hit? d.) What is the angle for Ted Kluszewski's portion of the pie?

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

6.) The following table gives some career statistics for .

Year Team G W L PCT ERA CG SHO IP H ER HR BB SO

1955 Dodgers 12 2 2 .500 3.02 2 2 41-2/3 33 14 2 28 30

1956 Dodgers 16 2 4 .333 4.91 0 0 58-2/3 66 32 10 29 30

1957 Dodgers 34 5 4 .556 3.88 2 0 104-1/3 83 45 14 51 122

1958 Dodgers 40 11 11 .500 4.48 5 0 158-2/3 132 79 19 105 131

1959 Dodgers 35 8 6 .571 4.05 6 1 153-1/3 136 69 23 92 173

1960 Dodgers 37 8 13 .381 3.91 7 2 175 133 76 20 100 197

1961 Dodgers 42 18 13 .581 3.52 15 2 255-2/3 212 100 27 96 269

1962 Dodgers 28 14 7 .667 2.54 11 2 184-1/3 134 52 13 57 216

1963 Dodgers 40 25 5 .833 1.88 20 11 311 214 65 18 58 306

1964 Dodgers 29 19 5 .792 1.74 15 7 223 154 43 13 53 223

1965 Dodgers 43 26 8 .765 2.04 27 8 335-2/3 216 76 26 71 382

1966 Dodgers 41 27 9 .750 1.73 27 5 323 241 62 19 77 317 12 Years 397 165 87 .655 2.76 137 40 2,324-1/3 1,754 713 204 817 2,396

a.) What is the most (SO) he had in one season? What year? b.) In how many seasons did he have an earned average (ERA) below 2.00? c.) In how many seasons did Koufax allow fewer hits (H) than pitched (IP)? d.) In how many seasons did he have more than twice as many strikeouts (SO) as walks (BB)?

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

8.) The following chart shows the players who hit the most home runs from 1950- 1959.

a.) Who hit the most home runs from 1950-1959? b.) How many home runs did Mickey Mantle hit from 1950-1959? c.) How many home runs did hit from 1950-1959? d.) How many players hit more than 300 home runs from 1950-1959?

9.) The following are the leading totals for at bats from in 1948. 560 644 648 594 589 588 585 558 577 584 617 590 567 608 560 611 565 560 566 574 641 635 558 562 Use your calculator to find the following. a.) the mean b.) the median c.) the mode d.) the maximum e.) the minimum

10.) 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.

11.) 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 tacos? 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 tamale?

12.) 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 it continued to drop exponentially at that rate, what would the population of Searcy be in 2008? 13.) You go to a restaurant. The menu contains eight hot appetizers, seven cold appetizers, five soups, 10 vegetables, 12 side dishes, nine breads, 12 salads, 54 entrées, 18 beverages and 14 desserts. If you order one item from each category, how many different meals could you order?

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.

3.) Draw a section of tile floor, with four rows of four tiles each, that illustrates the idea of vanishing points. Also draw the walls. 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?

10.) Give two examples of votes that are decided by super-majority votes. Give the percentage required in each case.

11.) 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, an argument or advertisement is given. For each exercise, identify one and only one of our fallacies that is exhibited in that argument or advertisement. GIVE A DETAILED EXPLANATION TO JUSTIFY YOUR CHOICE.

1.) The charges of police brutality are absolutely untrue, because the police would never do something like that. 2.) "I saw five people on the way to school today who didn't use their turn signals. Folks in Arkansas must not know how to use turn signals." 3.) "Dr. Worth, you can't give me an 'F' in this class. If you give me an F my GPA will drop enough so that I will lose my scholarship."

4.) During spring training in 1995, , then of the , was clocked throwing a baseball at a speed of 103.0 miles per hour. What is that speed in feet per second? (data from http://baseball-almanac.com/) 5.) a.) In your drawer you have 24 identical blue socks and 18 identical brown socks. Without looking, you start pulling socks out of the drawer. (1) How many socks must you pull out so that it is certain you have a matching pair of socks? (2) How many socks must you pull out so that it is certain you have a matching pair of blue socks? b.) You have a five minute hour glass and an eight minute hour glass. You are cooking something that must be cooked for exactly nine minutes. How would you use the two hour glasses to time your cooking? It is impossible to tell when an hour glass is exactly half empty. 6.) In 2004, the total payroll for the New York Yankees was $182,835,513. They paid Alex Rodriguez $21,726,881. What was Rodriguez' salary as a percentage of the total team payroll? (data from http://www.businessofbaseball.com/)

7.) of the Florida Marlins was paid $600,000 in 2002. For 2003, his salary went up 66.6667%. For 2004, his salary went up 140%. What was his 2004 salary? (data from http://www.businessofbaseball.com/)

8.) In 2004, Bobby Abreu of the made a salary of $10,600,000. That was an increase of 16.4835% from his 2003 salary. What was Abreu's 2003 salary? (data from http://www.businessofbaseball.com/)

9.) You put $2500 in a certificate of deposit account. It receives 4.5% interest compounded quarterly. You neither take out any money nor put in any more money. a.) Write out the formula that will figure out the amount of money you will have after 3 years without any of the numbers inserted. b.) Write out the formula that will figure out the amount of money you will have after 3 years with all of the numbers inserted. c.) How much money will you have after 3 years?

10.) You start putting money in your retirement fund at age 25. You put in $650 each quarter. The interest of 9.5% is compounded quarterly. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have if you retire at age 65. 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?

11.) You start putting money in an college savings account. You want to have $80,000 in 18 years when your daughter will be ready for college. The interest rate of 9.5% is compounded quarterly. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have to put in the account each quarter. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have to pay each quarter? d.) What is the total of all of your payments? 12.) Suppose you take out an auto loan for $8200 over a period of 4 years at an APR of 7.25%. a.) Without inserting any numbers, write out the formula that will figure out the amount of your monthly payments. b.) Without doing any simplification, insert all of the 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?

13.) You are borrowing $90,000 to buy a house. The interest rate for your 15 year mortgage is 5.75%. Throughout the problem 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 your monthly payments. b.) Without doing any simplification, insert all of the 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?

14.) The following chart shows the point totals in the voting for the 2003 Rookie of the Year. (data from http://baseball-reference.com/)

100 80 60 40 20 0

Jody Gerut Angel Berroa Hideki MatsuiRocco Baldelli Mark Teixeira

a.) Who won the voting? b.) How many points did receive? c.) How many players received more than 40 points? 15.) The following chart shows the career leaders (through 2003) in wins among managers who were active during at least part of the 2004 season. (data from http://baseball-reference.com/) Wins Tony LaRussa 2114 2002 1781 1452 1129 1017 Jack McKeon 928 Frank Robinson 913 910 882 a.) How many of these managers have won more than 1100 games? b.) Which of these won the highest percentage of games he has managed? c.) Which is farthest behind the one immediately preceding him on the chart? 16.) The following table shows some of the career statistics for . (data from http://baseball-reference.com/) Year At Bats Hits Doubles Triples Home Runs 1958 96 26 7 0 1 1959 648 205 47 9 20 1960 652 187 37 12 20 1961 607 208 34 8 16 1962 619 181 31 7 23 1963 652 204 37 14 22 1964 625 166 23 11 23 1965 669 204 34 10 22 1966 618 178 35 6 16 1967 650 187 28 13 18 1968 499 135 29 6 5 1969 495 126 22 6 10 1970 574 164 28 6 24 1971 566 149 23 4 11 1972 484 133 24 2 7 1973 466 121 14 6 8 1974 406 112 18 2 6 1975 319 71 14 5 4 a.) In how many different years did Pinson have more than 20 home runs? b.) In how many different years did Pinson have more than 600 at bats? c.) What is the most of triples Pinson had in one year and what year was it? 17.) The following chart shows the non- with the fewest career home runs for players with at least 7000 career at bats. Draw a line graph illustrating the data. (data from Lee Sinins' "Sabermetric Baseball Encyclopedia) HR 15 9 16 14 Stuffy McInnis 20 17 20 18.) The following chart shows Terrence Long's season-by-season totals. YOU MAY NOT USE YOUR CALCULATOR FOR THIS PROBLEM. YOU MUST SHOW ALL WORK AND GIVE AN EXPLANATION OF HOW YOU GOT YOUR ANSWERS. (data from http://baseball-reference.com/) Find the following. Year Stolen Bases 1999 0 2000 5 2001 9 2002 3 2003 4 2004 3

a.) mean b.) median c.) mode

19.) The following chart shows 's season-by-season totals. (data from http://baseball-reference.com/)

Year Homers Find the following for his home run totals. 1955 18 1956 26 a.) mean 1957 19 1958 23 b.) median 1959 28 1960 32 c.) mode 1961 24 1962 24 1963 24 1964 24 1965 13 1966 14 1967 3 1968 2 1969 0

20.) Using a tree diagram, find the probability that, in three flips of a coin, you end up with exactly 1 tail.

21.) You roll a standard six-sided die five times. What is the probability you will roll a 4 at least once? 22.) You are making license plates consisting of three letters and then three numbers. How many different license plates are possible if numbers may be repeated but letters may not? 23.) The population of Peculiar, Missouri was 205 in 1910. In 1920, the population was 233. If the population of Peculiar grew linearly from 1910 to 1990, what would the population have been in 1990 (the actual population was 1,777 in 1990). (Data from the Missouri Census Data Center) 24.) Explain the difference between votes that are decided by majority vote and those decided by plurality vote. 25.) Find the area and perimeter of the following triangle. Assume all units are in centimeters.