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Home , Andy Messersmith, Bobo Newsom, Bob Ojeda, Bruce Berenyi, Camilo Pascual, Chris Short

Mathematics for the Liberal Arts Exam File Fall 2007

Exam #1

In exercises #1 - 5, a logical fallacy is exhibited. For each one, identify one of our fallacies that is exhibited in that argument or advertisement. 1.) Former major league Ross Grimsley, nicknamed "Scuzz," would not wash or change any part of his uniform as long as the team was winning, believing that washing or changing anything would jinx the team. 2.) "Buy new and improved CRUST™ toothpaste, the toothpaste used by more people than any toothpaste in the country!" 3.) "Eighty year old people don't need to go into nursing homes. After all my mother is 85 and she power-walks two miles each day, drives her car (safely), climbs stairs, does crosswords, and reads the daily paper." (adapted from http://www.fallacyfiles.org) 4.) "I have never seen a bear in this area so there must not be any bears around here." 5.) "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." 6.) Construct a truth table for the following proposition. (not p ∧ q) → (not q) 7.) For each of the following, writing "Yes" if it is a proposition (statement) or "No" if it is not. a.) Grab that fish! b.) Arkansas is larger than Rhode Island. c.) Bob Uecker is the best of all-time. d.) Bob is 25 years old and Dave's dog is plaid. e.) Mickey Mouse was president of the United States in 1998. 8.) Draw a Venn diagram to illustrate the following proposition. All fish eat pizza and no fish ride bicycles. 9.) The part of a major league infield that is inside the bases is a square that is 90 feet on each side. What is its area in square centimeters? 10.) The following Venn diagram gives information about players on the ' roster as of September 15, 2007. The circle labeled "O" denotes players who are 30 years old or older. The circle labeled "H" denotes players who are 6 feet tall or taller. The circle labeled "R" denotes players who throw right-handed. (data from www.mlb.com)

a.) How many players are under 6 feet tall? b.) What can you say about the player denoted by the "x?" c.) How many players are under 30 years old and throw right-handed? d.) What can you say about the player denoted by the "y?" 11.) Billy Bob's combination motor oil/salad dressing is on sale for $3.50 per gallon. He is now beginning to sell it in Mexico. What would the price be in pesos per liter? SHOW ALL NECESSARY WORK!! 12.) Tom threw a 44.7 meters per second. Dave threw a ball 92 miles per hour. Who threw the ball faster, Tom or Dave? Be sure to show all necessary work. 13.) Walter Young, at 6-foot-5, 322-pounds, is believed to be the heaviest player ever. Convert his height to centimeters and his weight to kilograms. 14.) At 4:32 p.m. on September 15, 2007, www.weather.com listed the temperature in Arkadelphia as being 78 degrees Fahrenheit. What is that in Celsius? 15.) In your drawer you have 15 identical green socks, 24 identical blue socks and 18 identical plaid 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? b.) How many socks must you pull out so that it is certain you have a matching pair of green socks? c.) How many socks must you pull out so that it is certain you have a matching pair of either plaid or blue socks? 16.) In a particular scout troop, 70% of the scouts have a compass, 75% have matches, 85% have a knife and 85% have a watch. What is the least percentage of the scouts that must have all four items? 17.) You have a seven minute hour glass and a four minute hour glass. You are cooking something that must be cooked for an exact amount of time. [Note: It is impossible to tell when an hour glass is exactly half empty, or has just one minute left, etc.] a.) How would you use the two hour glasses to time your cooking if you must cook for exactly three minutes? b.) How would you use the two hour glasses to time your cooking if you must cook for exactly five minutes?

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 $135,000 in 18 years when his son will be ready for college. The interest rate of 8.75% 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 27. You put in $900 each quarter. The interest of 10.16% 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 62. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have at age 62? d.) What is the total of all of your payments? 8.) You put $3200 in a certificate of deposit account. It receives 3.25% 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 $34,000 to buy a new -wide. The interest rate for his 15 year mortgage is 7.85%. 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 following chart shows the number of runs scored by pitcher in his first six full seasons in the major leagues. Draw a bar graph to illustrate this data. Year Runs 1934 6 1935 6 1936 11 1937 11 1938 9 1939 6 1940 9 12.) The following chart shows the breakdown of number of games won by the on the 1916 Philadelphia Athletics. The team won a total of 36 games.

a.) Who won the most games for the 1916 Athletics? b.) How many games did Elmer Myers win? c.) Add up the seven percentages. Explain why they don't add up to 100%. d.) How many games did Socks Seibold lose for the 1916 Athletics? e.) Who invented the pie chart? 13.) The following chart gives the career statistics for Dode Paskert. Year Team Lg G AB R H 2B 3B HR RBI BA OBP SLG 1907 CIN NL 16 50 10 14 4 0 1 8 .280 .333 .420 1908 CIN NL 118 395 40 96 14 4 1 36 .243 .298 .306 1909 CIN NL 104 322 49 81 7 4 0 33 .252 .327 .298 1910 CIN NL 144 506 63 152 21 5 2 46 .300 .389 .374 1911 PHI NL 153 560 96 153 18 5 4 47 .273 .358 .345 1912 PHI NL 145 540 102 170 37 5 2 43 .315 .420 .413 1913 PHI NL 124 454 83 119 21 9 4 29 .262 .358 .374 1914 PHI NL 132 451 59 119 25 6 3 44 .264 .349 .366 1915 PHI NL 109 328 51 80 17 4 3 39 .244 .319 .348 1916 PHI NL 149 555 82 155 30 7 8 46 .279 .346 .402 1917 PHI NL 141 546 78 137 27 11 4 43 .251 .331 .363 1918 CHC NL 127 461 69 132 24 3 3 59 .286 .362 .371 1919 CHC NL 88 270 21 53 11 3 2 29 .196 .274 .281 1920 CHC NL 139 487 57 136 22 10 5 71 .279 .366 .396 1921 CIN NL 27 92 8 16 1 1 0 4 .174 .208 .207 totals 1716 6017 868 1613 279 77 42 577 .268 .350 .361 a.) "Doubles" is denoted by "2B." In how many years did Paskert have more than 25 doubles? b.) "Batting average" is denoted by "BA." What was Paskert's highest batting average? c.) "Runs scored" is denoted by "R" and "Runs batted in" is denoted by "RBI." In how many seasons did Paskert have more runs batted in than runs scored? d.) "" is denoted by "SLG." In how many seasons did Pakert have a slugging percentage higher than .380? e.) "Stolen Bases" is denoted by "SB." How many stolen bases did Paskert have in 1920? 14.) The following chart gives the career home runs for nine different players.

700 600 500 400 300 200 100 0 Willie Bobby Bonilla Bobby Willie McCovey Willie Mickey Morandini Roberto

a.) Of these players, how many have over 500 career home runs? b.) Who more career home runs, Mickey Morandini or Ray Oyler? c.) How many career home runs did Willie Mays (the greatest all-around ball player ever) hit? d.) Who hit more career home runs, Mickey Mantle or Jimmie Foxx? e.) How many career home runs did Gavvy Cravath hit? 15.) The following chart tells how many games were won by the American and champions each year from 1940 through 1949. 110 105 100 American 95 League 90 National League 85 80 75 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949

a.) In how many of these years did the National League champion win more games than the champion? b.) How many games did the National League champion win in 1942? c.) How many games did the Yankees win in 1944? d.) How many more games did the 1946 American League champion win than the 1945 American League champion won? e.) How many times during these years did both league champions win at least 100 games?

Exam #3

1.) For each of the scatter plots below, answer the following questions. Put your answers in the table below the graph. a.) Is there a correlation in the data? Write "Yes" or "No." b.) Give a reason for your answer in a.). c.) If you said "yes" in a.), is the correlation strong or weak? Write "strong" or "weak." If your answer to a.) was "no" then write N/A. d.) Give a reason for your answer in c.). If your answer to a.) was "no" then write N/A. e.) If you said "yes" in a.), is the correlation positive or negative? Write "positive" or "negative." If your answer to a.) was "no" then write N/A. f.) Give a reason for your answer in e.). If your answer to a.) was "no" then write N/A.

a.) a.) a.) b.) b.) b.) c.) c.) c.) d.) d.) d.) e.) e.) e.) f.) f.) f.) 2.) When two events are correlated, there are three possible explanations. One is that one event caused the other. One is that some third event caused both events. What is the other possibility? 3.) The following are the players who had the most triples for the 1979 Cubs. Find the following WITHOUT USING YOUR CALCULATOR AT ALL AND YOU MUST GIVE SOME INDICATION OF HOW YOU FOUND THE NUMBER. 7 Ivan DeJesus 10 Jerry Martin 3 5 Scot Thompson 5 Larry Biittner 3

a.) Find the mean. b.) Find the median. c.) Find the mode. 4.) This chart lists the major league baseball pitchers (in alphabetical order) from 1972-1974 who had the most in a season. (source: sabermetric baseball encyclopedia) Use your calculator to answer the following questions. Player Year Strikeouts a.) For these players, what is 1972 228 the mean number of Bert Blyleven 1973 258 strikeouts? Bert Blyleven 1974 249 Tom Bradley 1972 209 b.) For these players, what is 1972 310 the median number of Steve Carlton 1973 223 strikeouts? Steve Carlton 1974 240 Joe Coleman 1972 222 c.) For these players, what is 1972 208 the mode number of 1974 225 strikeouts? 1972 250 Mickey Lolich 1973 214 1974 221 1972 234 Gaylord Perry 1973 238 Gaylord Perry 1974 216 1972 329 Nolan Ryan 1973 383 Nolan Ryan 1974 367 1972 249 Tom Seaver 1973 251 5.) Why is the median often a better measure of central tendency than the mean? 6.) You roll a single standard six-sided die once. What is the probability that you roll: a.) an odd number less than four b.) a seven c.) a number less than seven 7.) You roll two dice. What is the probability that the sum of the numbers on the dice is greater than 9? 8.) A box contains five regular tacos, seven soft tacos, eight bean burritos, and four tostadas. You reach into the box and randomly choose an item. You then reach in and take another item. a.) What is the probability that the first item was a regular taco and the second was a tostada? b.) What is the probability one item was a regular taco and the other a tostada? 9.) You are dealt five cards from a standard 52 card deck. What is the probability that you will have four cards from one rank? 10.) 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 if repetitions are allowed? b.) How many four letter "words" can be made if no repetitions are allowed? 11.) Explain how the change of the quantity per unit time differs between an exponential model and a linear model. 12.) Mineral Springs, Arkansas had a population of 546 in 1880. By 1900, it had lost half of its population. Assuming the population continued to decline exponentially at the same rate, what would the population be in 2005? (Note: the actual 2000 population was 1,264.) 13.) You are coaching a little league baseball team. You have fifteen players. You are choosing a defensive arrangement involving the nine positions (pitcher, catcher, , second baseman, , third baseman, , center fielder, right fielder). a.) Is this a permutations problem, a combinations problem, or neither? b.) How many different defensive arrangements can you pick? 14.) The population of Little Rock 45,941 in 1910. For a while, the population grew at a rate of 3.5538% annually. Assuming that rate continued, what would the population of Little Rock be in 2007? (The actual 2000 population was 183,133.) (Data from UALR's Institute for Economic Advancement) 15.) 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 2 heads and one tail in the three flips. 16.) The following chart gives a breakdown of some people in a class. Answer the following questions based on the chart. Male Female Totals Freshmen 8 10 18 Sophomores 6 7 13 Juniors 9 7 16 Seniors 12 13 25 Totals 35 37 72 a.) If a student is chosen at random, what is the probability that the student is male? b.) If a female student is chosen at random, what is the probability that the student is a sophomore? c.) If a student is chosen at random, what is the probability that the student is a male or a sophomore?

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 4 feet and a diameter of two yards. 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.) 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 5.) A Fibonacci-like sequence has a first term of 5 and a second term of 11. Find the: a.) third term b.) fourth term c.) fifth term d.) sixth term 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.) 3 half-steps above Middle C. b.) 9 half-steps below Middle C. c.) one octave above Middle C. d.) one octave below Middle C. e.) two octaves below 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 121 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 # of representatives # of representatives Quota state "should" get you will give state 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 is given. For each exercise, identify one of the logical fallacies that is exhibited in that argument. 1.) "Bubba gets really mad when he hears about illegal immigrants. He must hate Mexicans." 2.) A former Miss Alabama - "I would not live forever, because we should not live forever, because if we were supposed to live forever, then we would live forever, but we cannot live forever, which is why I would not live forever." 3.) "Before women got the vote, there were no nuclear weapons." (from http://www.don-lindsay-archive.org/skeptic/arguments.html) 4.) Your living room is 14 feet by 18 feet. You are going to carpet it with carpet that costs $23 per square yard. How much will it cost to carpet your living room? 5.) Bubba weighs 347 pounds. What is his weight in milligrams? 6.) You are driving 54 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. How many socks must you take from the drawer to be sure you have a matching pair of green socks? b.) You have a four minute hourglass and a five minute hourglass. You need to cook something for exactly six minutes. Give a detailed explanation of how you would use the two hourglasses to time the six minutes. (Note: You cannot tell by looking if an hourglass is half empty.) 8.) The price of a coat was $640. 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.) For the 1986 Mets, had 283 of the team's 1067 outfield . What percentage of the teams outfield putouts did Dykstra have? 11.) You are borrowing $120,000 to buy a house. The interest rate for your 30 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 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 $100,000 in 18 years when your daughter will be ready for college. The interest rate of 8.5% is compounded monthly. 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 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? 13.) You put $3500 in a certificate of deposit account. It receives 3.5% 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 pitching wins for Charlie Getzein each year from 1885 to 1890. Draw a line graph to illustrate this data. year wins 1885 12 1886 30 1887 29 1888 19 1889 18 1890 23 15.) The following chart gives the major league leaders from 1964. Name Strikeouts Name Strikeouts 219 206 207 Sam McDowell 177 163 213 217 Orlando Pena 184 237 205 172 Juan Pizarro 162 Bob Gibson 245 Dick Radatz 181 171 181 223 Dick Stigman 159 185 250 Mickey Lolich 192 164 Jim Maloney 214 166 a.) Find the mean. b.) Find the median. c.) Find the mode. d.) Find the maximum. 16.) 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? 17.) Ruby Tuesday's on-line menu lists 13 appetizers, three salads, two soups, ten side dishes, 51 types of entrées, 22 non-alcoholic beverages and six types of desserts. If you order one of each kind of item, how many different meals could you order? 18.) The following table gives the wins, losses and saves for all of the pitchers for the 1986 Mets. Player Wins Losses Saves 15 6 0 17 6 0 16 6 1 18 5 0 10 7 0 Roger McDowell 14 9 22 8 6 21 4 2 1 2 3 0 Rick Anderson 2 1 1 2 2 0 0 0 0 0 1 0 0 0 0 Ed Lynch 0 0 0 a.) How many pitchers had more than 10 wins? b.) How many pitchers lost more games than they won? c.) Which pitcher pitched the most ? d.) Which pitcher had the most wins? 19.) In 1986, Lenny Dykstra, , , Kevin Mitchell, George Foster and were the main outfielders for the New York Mets. They needed to have a right fielder, a left fielder and a center fielder. 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? 20.) The following pie chart shows the home distribution on the 1974 Pirates. The percentage given shows the percentage of the team's home runs hit by the given player.

a.) How many players hit home runs for the 1974 Pirates? b.) Who hit the most home runs for the 1974 Pirates? c.) As a team, the 1974 Pirates hit 114 home runs. How many did Richie Hebner hit? (Note: the percentages are rounded off, also, it is not possible to hit a fractional number of home runs) d.) How many of the 1974 Pirates hit more than 10 home runs? 21.) Draw a tree diagram to illustrate tossing three coins. Find the probability that exactly two of the coins came up heads. 22.) You roll two dice and add the numbers. What is the probability you will get a sum greater than 9? 23.) In 1860, the population of Fort Smith, Arkansas was 1,532. By 1880, it had doubled. If the exponential rate of growth had continued, what would Fort Smith's population be in 2007? 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 right circular cylinder has a diameter of 4 feet and a height of 2 yards. Find the following.