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 pitcher 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 catcher 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 New York Mets' 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 baseball 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 major league baseball 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 New York Yankees 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 error. 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 double-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 Bobo Newsom 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 pitchers 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.) "Slugging Percentage" 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.