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Home , Bobby Veach, Bob Caruthers, Gary Peters (baseball), John Maine, Jorge Sosa, Juan Marichal

Mathematics for the Liberal Arts Exam File Spring 2008

Exam #1

In exercises #1 - 4, an argument or advertisement is given. For each exercise, identify one of our fallacies that is exhibited in that argument or advertisement. GIVE A DETAILED EXPLANATION TO JUSTIFY YOUR CHOICE. 1.) I have never seen a bear in this area so there must not be any bears around here. 2.) I wore a hat during the test and made a high grade so I'm going to start wearing a hat for all of my tests. 3.) Are you going to major in history or are you going to major in mathematics? 4.) Gosh, officer, I know I made an illegal left turn, but please don't give me a ticket. I've had a hard day, and I was just trying to get over to my aged mother's hospital room, and spend a few minutes with her before I report to my second full-time minimum-wage job, which I have to have as the sole support of the seventeen members of my family. 5.) For each of the following, writing "Yes" if it is a proposition (statement) or "No" if it is not. a.) Pick up your sister after school. b.) Arkansas is a nicer place to live than Texas. c.) Iowa is the largest state in the United States. d.) All the dogs on my desk are purple. 6.) Draw a Venn diagram to illustrate the following proposition. All major league players play checkers and some of them cheat. 7.) The following Venn diagram illustrates the makeup of a Henderson State University F M mathematics class. "F" denotes "freshmen," "M" 2 3 11 denotes "mathematics major," and "O" denotes 5 "from of state." "x" and x 6 9 y "y" represent particular students. The numbers 4 8 represent the number of O students who fit the categories.

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

8.) Construct a truth table for the following proposition.

(not p  q)  p 9.) A Canadian company is advertising a jacket for $39.99 (Can.). How much would it cost in Mexican pesos? 10.) Bob weighs 123 kg. In order to participate in a backpacking trip at Philmont Scout Ranch he must weigh no more than 215 pounds. Does he qualify for the hike? If not, how much weight must he lose in order to qualify? 11.) Convert 15 degrees Celsius to degrees Fahrenheit. 12.) Tom was driving 22.3 meters per second in a 50 mile per hour zone. Was Tom speeding? 13.) In your drawer you have 15 identical green socks, 24 identical blue socks and 18 identical brown socks. Without looking, you start pulling socks out of the drawer. a.) How many socks must you pull out so that it is certain you have a matching pair of socks? Explain your answer. b.) How many socks must you pull out so that it is certain you have a matching pair of green socks? Explain your answer. 14.) You are considering buying 13 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.) 15.) There are three paths from Town A to Town B. One of the paths is free from land mines. The North Path has a sign on it that says "There are land mines here." The Central Path has a sign that says "There are mines on the north path." The South Path has a sign that says "The south path is clear." One and only one of the signs is false. Which path is clear of land mines? Explain your answer.

N NORTH PATH  There Are Land Mines Here

CENTRAL PATH Town A There Are Mines On Town B The North Path

SOUTH PATH The South Path Is Clear

Exam #2

1.) 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. 2.) Estimate the total number of hamburgers eaten each year by Americans. Be sure to clearly state all of your assumptions. 3.) You put $3250 in a certificate of deposit account for 5 years. It receives 2.35% interest 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? 4.) You start putting money in your retirement fund at age 26. You put in $300 each month. The interest of 10.25% is compounded quarterly. You retire at age 65. 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? 5.) Maher-Shalal-Hash-Baz started putting money in a college savings account. He wants to have $110,000 in 18 years when his son will be ready for college. The interest rate of 8.75% is compounded monthly. a.) Without inserting any numbers, write out the formula that will figure out the amount of money Maher-Shalal-Hash-Baz 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 he have to pay each month? d.) What is the total of all of his payments? 6.) Billy Bob is borrowing $42,000 to buy a new -wide. The interest rate for his 15 year mortgage is 6.15%. 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 Billy Bob'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? 7.) You are buying a house. After the down payment, you need to borrow $95,000. You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 30 year mortgage is 5.65%. Throughout the problem we will ignore escrow payments that might be added to the payment for insurance and taxes. a.) 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?

9.) The following table shows the number of wins for , 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

10.) Bob made $48,000 in 2004. For 2005, his salary went up 5%. For 2006, his salary went up 5% again. What is his salary in 2006? 11.) The price of a coat was reduced 15%. The price now is $153. What was the original price. 12.) The following chart shows who home runs for the 1915 Tigers and how many they hit.

George Burns, other, 4 5

Ty Cobb, 3

Sam Crawford, 4 Bobby Veach, 3 Marty Kavanagh, 4

Answer the following questions. All questions refer to the 1915 . a.) Who hit the most home runs? b.) How many home runs did ? c.) How many home runs did the Tigers hit? d.) What is the angle for the portion of the chart representing Bobby Veach? e.) How many players hit home runs? f.) Who hit more home runs, Marty Kavanagh or ? g.) Who invented the pie chart?

13.) The following graph shows the number of complete games thrown by Christy "Big Six" Mathewson each year during his career. (source: sabermetric baseball encyclopedia") 40 35 30 25 20 15 10 5

0

1900 1902 1904 1906 1908 1910 1912 1914 1916

a.) How many seasons did Mathewson have at least 25 complete games? b.) What is the most consecutive years Mathewson had at least 25 complete games? c.) What is the most complete games Mathewson had in one season? What season? d.) How many complete games did Joe "Iron Man" McGinnity have in 1904? 14.) 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/) 15.) The following chart shows the number of doubles (denoted by diamonds), triples (denoted by triangles) and home runs (denoted by squares) for (the greatest all-around player in history) in each year of his career. [Note: the quantity is represented by the middle of the shape.]

60

50

40

30

20

10

0

1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1951 a.) How many doubles did Mays hit in 1966? b.) In what year did Mays hit the most triples? c.) How many triples did Mays hit the year he hit the most? d.) How many times did Mays have more doubles than home runs? e.) How many times did Mays exceed 30 in both doubles AND home runs? f.) How many times did Mays have at least 10 triples? g.) What is the most consecutive years Mays hit at least 30 home runs? h.) Did Mays ever have a season when he had at least 20 of each kind of hit? Exam #3

1.) Why is the median often a better measure of a data set's central tendency than the mean? 2.) Explain the difference between a linear model and an exponential model? 3.) The following are the leaders in triples for the 1986 Minnesota Twins. Note that they are not in order. 7 6 5 4 6 4 Without using your calculator, find the following. Be sure to show or explain how you got each answer. a.) mean b.) median c.) mode 4.) The following are the Major League leading totals for 1957. 583 577 644 650 574 594 576 634 611 594 579 615 624 617 609 575 619 648 626 585 Using your calculator, find the following. a.) mean b.) median c.) mode 5.) You roll two dice and take the product of the two numbers. What is the probability the product is greater than 9? 6.) You go to a restaurant. The menu lists five kinds of cold appetizers, seven kinds of warm appetizers, 10 kinds of beverage, 11 kinds of dessert, 28 kinds of entrée, 12 kinds of pasta, nine kinds of salad, and eight kinds of soup. You order one of each kind of item. How many different meals are possible? 7.) The poisonous snakes that can be found in Australia are the Australian Copperhead, Death Adder, Taipan and Tiger Snake. A box contains five Australian Copperheads, seven Death Adders, eight Taipans, and four Tiger Snakes. a.) You reach into the box and randomly choose a snake. You put it back, shake the box and then reach in and take another snake. What is the probability that the first snake was a Death Adder and the second was a Taipan? b.) You reach into the box and randomly choose a snake. You then reach in and take another snake. What is the probability that the first snake was a Taipan and the other was a Tiger Snake? 8.) Ten pieces of paper are in a bag. The papers are numbered as shown below.

1 4 4 4 5

5 7 6 6 6

A piece of paper is pulled out of the box. What is the expected value of the number on the paper? 9.) You flip three coins. a.) Draw a tree diagram to illustrate tossing the three coins. b.) Find the probability that at least two of the coins came up tails.

10.) You are coaching a little league baseball team. You have fourteen players. You choose nine to start the game. a.) Is this a permutations problem, a combinations problem, or neither? b.) How many different groups of nine can you pick? 11.) Consider the eight letters G, H, I, J, K, M, L, and N. For our purposes, a "word" is ANY arrangement of letters. 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? 12.) You are dealt five cards from a standard 52 card deck of cards (four suits - hearts, clubs, diamonds, spades; each suit contains 13 ranks - 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, ace) . What is the probability that you are dealt four of a kind (four cards from one rank and one other card)? 13.) Barium-139 has a half-life of 82.7 minutes. If you have 9 grams of Barium-139, how much will you have left in 12 hours? Be sure to show the formula you use. 14.) In 1901, Bubbaville had a population of 303. In 1912 it had a population of 606. If that exponential growth continued, what would the population have been in 2003? Be sure to show the formula you use. 15.) According to the United States Energy Information Administration's Monthly Energy Review, the average price of a gallon of gasoline in 1949 was $0.27. In 2008, it is $3.29 (at least it was on the day I wrote the test). Adjusting for an average annual inflation rate of 3.9685% (data due to NASA), in which year was gasoline more expensive (2008 or 1949)? Be sure to show all work.

Exam #4

1.) Middle C has a frequency of 260 cycles per second. a.) Find the frequency of the note that is two octaves below middle C. b.) Find the frequency of the note that is one octave above middle C. c.) Find the frequency of the note that is three octaves above middle C. d.) Find the frequency of the note that is two half-steps below middle C. e.) Find the frequency of the note that is five half-steps above middle C. 2.) Consider a country consisting of 5 states with populations given below. If the country's legislature is to have 115 members, find the standard divisor and fill in the table below. Standard Divisor =

State Population Standard # of reps the state # of reps you'll Quota "should" get give state A 1,217,107 B 1,667,819 C 1,217,108 D 1,555 E 1,133,023 Total Population 5,236,612 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.) Consider the following letters.

For each type of symmetry below, list the letters 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 5.) Consider a Fibonacci-like sequence with first term 3 and second term 7. Find the next four terms. 6.) Explain the difference between elections that are determined by majority and plurality voting. 7.) Give examples of two votes that require a super-majority vote. GIVE THE PERCENTAGE OR FRACTION OF VOTES REQUIRED FOR EACH ONE. 8.) Explain how a Borda count works. Give an example of a vote that is done using a Borda count. 9.) A collegiate women's basketball has a diameter of 11 inches. Find the volume and surface area. 10.) A cylinder has a height of 2 feet and a diameter of one yard. Find the volume and surface area. 11.) Find the area and perimeter of the following triangle. Assume all units are in centimeters.

5 6 4

7

12.) Find the area and perimeter of the following shape. Assume all units are in meters.

Area______

Perimeter______

Final Exam

In exercises #1 - 3, an argument is given. For each exercise, identify one of the logical fallacies that is exhibited in that argument. GIVE A DETAILED EXPLANATION TO JUSTIFY YOUR CHOICE. 1.) "I don't know of any great Lithuanian authors so there must not be any great Lithuanian literature." 2.) "If we allow unregulated harvesting of our forests then what are we going to do about the increase in abuse of the food stamp program." 3.) "Dr. Worth, you can't give me an 'F' in this class. After all, I might lose my scholarship." 4.) Your living room is 15 feet by 18 feet. You are going to carpet it with carpet that costs $25 per square yard. How much will it cost to carpet your living room? 5.) Bubba weighs 347 pounds. What is his weight in grams? 6.) You are driving 45 miles per hour. What is your speed in meters per second? 7.) a.) There are 45 socks in a drawer. They are all identical except for color. Ten of them are green, 12 of them are blue, three of them are plaid, 16 of them are brown and four of them are black. i) How many socks must you take from the drawer to be sure you have a matching pair of socks? ii) How many socks must you take from the drawer to be sure you have a matching pair of plaid socks? b.) You have a four minute hourglass and a five minute hourglass. You need to cook something for exactly seven minutes. Give a detailed explanation of how you would use the two hourglasses to time the seven minutes. (Note: You cannot tell by looking if an hourglass is half empty.) 8.) The price of a coat was $800. It was reduced 10% on December 1. It was reduced 15% on December 10. What is the price now? 9.) The price of a coat was reduced 15%. The price now is $153. What was the original price. 10.) Bob Caruthers pitched 445 for the Brooklyn Bridegrooms in 1889. The Bridegrooms' pitching staff had a total of 1212 . What percentage of the total innings were pitched by Caruthers? 11.) 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? 12.) 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? 13.) 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? 14.) The following chart shows the number of times has grounded into double plays over the past ten years. Draw a line graph to illustrate this data. Year GIDP 1998 12 1999 12 2000 10 2001 17 2002 14 2003 16 2004 18 2005 8 2006 22 2007 15

15.) The following chart gives the leaders from 1964.

Name Name Strikeouts 219 Juan Marichal 206 207 Sam McDowell 177 Tony Cloninger 163 Camilo Pascual 213 Al Downing 217 Orlando Pena 184 Don Drysdale 237 Gary Peters 205 172 162 245 Dick Radatz 181 171 181 Sandy Koufax 223 Dick Stigman 159 185 Bob Veale 250 192 Dave Wickersham 164 Jim Maloney 214 166 a.) Find the mean. b.) Find the median. c.) Find the mode. d.) Find the maximum. 16.) Olive Garden's on-line menu lists nine appetizers, three salads, two soups, 163 possible pizza appetizers, 34 types of entrées, 18 non-alcoholic beverages and six types of desserts. If you order one of each kind of item, how many different meals could you order? 17.) In 1969, , Cleon Jones, Ron Swoboda, Art Shamsky, Rod Gaspar, and Amos Otis were the main for the . They needed to have a , a and a . Assuming each player can play each position, we are interested in how many different arrangements of these players they could have had. a.) Is this a permutations problem or a combinations problem? b.) How many different arrangements were possible? 18.) The Angels, Astros, Blue Jays, Devil Rays, Diamondbacks, Expos/Nationals, Mariners, Marlins, Mets, Padres, Pilots/Brewers, Rockies, and Royals are 's expansion teams. The following chart shows the number of games won by each of these teams from 1969 through 2005.

3500

3000

2500

2000

1500

Mets

Astros

Angels Royals

1000 Padres

BlueJays

Mariners Pilots/Brewers

500 Expos/Nationals

Rockies

Diamondbacks Marlins 0 DevilRays

a.) Which of these team has won the most games? b.) How many games have the Mets won? c.) Not all of these teams started play during the same year. Based on what the chart shows, which four teams have probably played the fewest seasons? d.) How many of these teams won more than 2000 games during this time period? 19.) The following chart gives some of 's career statistics.

Team G AB R H 2B 3B HR RBI AVG OBP SLG 1914 Red Sox 5 10 1 2 1 0 0 2 .200 .200 .300 1915 Red Sox 42 92 16 29 10 1 4 21 .315 .376 .576 1916 Red Sox 67 136 18 37 5 3 3 15 .272 .322 .419 1917 Red Sox 52 123 14 40 6 3 2 12 .325 .385 .472 1918 Red Sox 95 317 50 95 26 11 11 66 .300 .411 .555 1919 Red Sox 130 432 103 139 34 12 29 114 .322 .456 .657 1920 Yankees 142 458 158 172 36 9 54 137 .376 .532 .847 1921 Yankees 152 540 177 204 44 16 59 171 .378 .512 .846 1922 Yankees 110 406 94 128 24 8 35 99 .315 .434 .672 1923 Yankees 152 522 151 205 45 13 41 131 .393 .545 .764 1924 Yankees 153 529 143 200 39 7 46 121 .378 .513 .739 1925 Yankees 98 359 61 104 12 2 25 66 .290 .393 .543 1926 Yankees 152 495 139 184 30 5 47 146 .372 .516 .737 1927 Yankees 151 540 158 192 29 8 60 164 .356 .486 .772 1928 Yankees 154 536 163 173 29 8 54 142 .323 .463 .709 1929 Yankees 135 499 121 172 26 6 46 154 .345 .430 .697 1930 Yankees 145 518 150 186 28 9 49 153 .359 .493 .732 1931 Yankees 145 534 149 199 31 3 46 163 .373 .495 .700 1932 Yankees 133 457 120 156 13 5 41 137 .341 .489 .661 1933 Yankees 137 459 97 138 21 3 34 103 .301 .442 .582 1934 Yankees 125 365 78 105 17 4 22 84 .288 .448 .537 1935 Braves 28 72 13 13 0 0 6 12 .181 .359 .431 TOTAL 2,503 8,399 2,174 2,873 506 136 714 2,213 .342 .474 .690 a.) In how many seasons did Ruth hit at least 40 home runs (denoted HR)? b.) What was Ruth's highest batting average (denoted AVG)? c.) How many times did Ruth get MORE than 200 hits (denoted H)? d.) In which seasons did Ruth have more than 160 runs batted in (denoted RBI)? 20.) Draw a tree diagram to illustrate tossing three coins. Find the probability that at least two of the coins came up tails. 21.) 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 , , Kevin Elster, , , Howard Johnson, Kevin McReynolds, 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 hit? d.) Who hit more home runs, Kevin McReynolds or Keith Hernandez? 22.) In 1985, the highest paid major league baseball player made $2,130,300. In 1986, the highest paid player earned $2,800,000. That was an increase of 31.4369%. If salaries continued to grow exponentially at that rate, what would the highest paid player have earned in 2008? 23.) The following chart gives the on the New York Mets' current roster.

Name Height Weight Birth Date 1 Pedro Feliciano 5-10 190 08/25/76 2 6-1 205 05/18/74 3 Aaron Heilman 6-5 225 11/12/78 4 John Maine 6-4 200 05/08/81 5 6-7 230 01/14/84 6 Oliver Perez 6-3 215 08/15/81 7 Duaner Sanchez 6-2 210 10/14/79 8 6-0 210 03/13/79 9 Scott Schoeneweis 6-0 190 10/02/73 10 Joe Smith 6-2 210 03/22/84 11 Jorge Sosa 6-2 220 04/28/77 12 Billy Wagner 5-11 205 07/25/71 Based on this chart, answer the questions below. a.) If a player is chosen at random, what is the probability he is under 6 feet tall? b.) If a player is chosen at random, what is the probability he was born since 1/1/80? c.) If a player is chosen at random, what is the probability that he weighs at least 200 pounds? d.) If a player is chosen at random, what is the probability that he weighs at least 200 pounds or is under 6 feet tall?

24.) 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!!

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