Mathematics for the Liberal Arts Test File Spring 2010 Exam #1 In exercises #1 - 8, identify one and only one of our fallacies that is exhibited. GIVE A DETAILED EXPLANATION TO JUSTIFY YOUR CHOICE. 1.) "Dr. Worth, you can't give me an 'F' in this class. If you give me an F my GPA will drop to 2.9 and I have to have a 3.0 to keep my scholarship." 2.) "I have never seen a bear in this area so there must not be any bears around here." 3.) "Titanic must be the best movie of all time since it has the highest box office receipts of all time." 4.) "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." 5.) "I don't know of any great Lithuanian authors so there must not be any great Lithuanian literature." 6.) "I read the other day that most people really like the new gun control laws. I was sort of suspicious of them, but I guess if most people like them, then they must be okay." (from http://www.nizkor.org/features/fallacies/) 7.) "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." 8.) "Smith, who is from England, decides to attend graduate school at Ohio State University. He has never been to the US before. The day after he arrives, he is walking back from an orientation session and sees two white (albino) squirrels chasing each other around a tree. In his next letter home, he tells his family that American squirrels are white." (from http://www.nizkor.org/features/fallacies/) 9.) What year was it 2,000,000,000 seconds ago? 10.) Convert 45 miles per hour to meters per second. 11.) Convert 45 degrees Celsius to Fahrenheit. 12.) The part of a major league infield that is inside the bases is a square that is 90 feet on each side. What is the area in square centimeters? You must show the use of units and conversion factors. 13.) Bubba saw a combination chain saw/tooth flossing machine for 2400 pesos. How much would it cost in $ (US)? 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 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. a.) How many socks must you take from the drawer to be sure you have a matching pair of socks? b.) How many socks must you take from the drawer to be sure you have a matching pair of plaid socks? 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? 17.) For each of the following, write "Yes" if it is a proposition (statement) or "No" if it is not. a.) Eating grits causes cancer. b.) "Pick up that book." c.) Snow is no fun. d.) Arkansas is the largest state in the United States. e.) 2827 = 1,183,768,682,616,191,959,377,597,437,620,164,493,312. 18.) Construct a truth table for the following proposition. not((p q) (not q)) 19.) Draw a Venn diagram to illustrate the following proposition. All cats are dogs and some dogs are fish. 20.) The following Venn Diagram gives a breakdown of the New York Mets' current roster. "Y" denotes a player who is under 30 years old. "L" denotes a player who throws left-handed. "H" denotes a player who is at least 200 pounds. a.) How many players are at least 200 pounds and do not throw left-handed? b.) How many players are under 30 years old? c.) What do we know about the player represented by "x?" d.) What do we know about the player represented by "y?" Exam #2 1.) In 2007, Albert Pujols of the St. Louis Cardinals was paid $12,937,813. For 2008, his salary went up 7.21247092%. For 2009, his salary went up 4.01109542%. What was his 2009 salary? 2.) A car was on sale for $11,745. That was 13% off the original price. What was the original price? 3.) Through 2009, Lance Berkman had earned $79,505,000 in his major league baseball career. In 2005, he earned $10,500,000. What percentage of his career earnings did he earn in 2005? 4.) In Bubbaville, 19.4% of the 2500 people own at least two hound dogs. How many of the people in Bubbaville own at least two hound dogs? 5.) In 1890, the population of Alma, Arkansas was 486. By 1900 the population had dropped 9.46502%. From 1900 to 1910, the population went up 28.40909%. What was the population in 1910? 6.) 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. 7.) Mephibosheth started putting money in a college savings account. He wants to have $120,000 in 18 years when his son will be ready for college. The interest rate of 6.95% 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? 8.) You start putting money in your retirement fund at age 27. You put in $300 each month. 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? 9.) 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? 10.) 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? 11.) Bubba is borrowing $14,000 to buy a new four wheeler. The interest rate for his 5 year loan is 4.85%. 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? 12.) Use reasonable estimations to approximate the total number of slices of bread eaten each year by people in Arkansas. 13.) 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. 14.) 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? Exam #3 1.) The following table gives the leaders in triples for the 1913 Detroit Tigers. Draw a bar graph that illustrates the data. Baldy Louden 5 Bobby Veach 10 Del Gainer 8 Donie Bush 10 Paddy Baumann 4 Red McKee 4 Sam Crawford 23 Ty Cobb 16 2.) This chart shows some of the career statistics for Jimmie Foxx.