Mathematics for the Liberal Arts Exam File Fall 2005 Exam #1 In exercises #1 - 5, 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.) Are you going to major in history or are you going to major in mathematics? 2.) 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 my thirty-seven children and the nineteen members of my extended family who depend on me for food and shelter. 3.) I asked one of my friends what he thought of the new spending restraints and he agreed it is a good idea. The new restraints are therefore generally popular. (example taken from http://www.datanation.com/fallacies/) 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.) Sandy Koufax is the best left-handed pitcher of all-time. d.) Bob is 25 years old and Dave's dog is plaid. e.) George Bush is the president. f.) 3 + 9 = 10 and the name of this course is advanced underwater basket weaving. 8.) Draw a Venn diagram to illustrate the following proposition. All fish ride bicycles and some dogs ride bicycles. 9.) The following Venn diagram gives information about players currently on the New York Mets' roster. The circle labeled "A" denotes players who are 30 years old or older. The circle labeled "T" denotes players who are 6 feet tall or taller. The circle labeled "H" denotes players who are 200 pounds or heavier. (data from www.mlb.com) A T 1 5 9 14 x 1 14 H 0 y 2 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 under 200 pounds? d.) What can you say about the player denoted by the "y?" 10.) C.C. Sabathia, a pitcher for the Cleveland Indians, is 6'7" tall and weighs 290 pounds. Convert his weight to kilograms and his height to centimeters. Put your final answers in the blanks provided. (source: www.majorleaguebaseball.com) 11.) Tom threw a baseball 45.4 meters per second. Dave threw a ball 98 miles per hour. Who threw the ball faster, Tom or Dave? 12.) The carpet you want to buy costs $18.95 per square yard. If you are going to be carpeting a room that is 18 feet long and 15 feet wide, how much will it cost to carpet the room? 13.) An Australian company is advertising a jacket for $127.53 (Aust.). How much would it cost in U.S. dollars? 14.) Bob weighs 120 KILOGRAMS. He wants to lose weight to get down to 185 POUNDS. How many SCRUPLES does he need to lose? 15.) 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. How many socks must you pull out so that it is certain you have a matching pair of either green or blue socks? Explain your answer. 16.) There are 10 rectangular tables in a rectangular room. You must set up the tables so there are exactly 3 tables against each wall. Show or explain how this can be done. 17.) You have a seven minute hour glass and a nine minute hour glass. You are cooking something that must be cooked for exactly three minutes. How would you use the two hour glasses to time your cooking? [Note: It is impossible to tell when an hour glass is exactly half empty, or has just one minute left, etc.] Exam #2 1.) 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/) 2.) Juan Pierre 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/) 3.) In 2004, Bobby Abreu of the Philadelphia Phillies 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/) 4.) The price of a sofa was $930. Two weeks ago the price was dropped 15%. This week it was dropped 10%. What is the price now? 5.) In 2001, the Seattle Mariners won 71.6% of the 162 games the played. Keeping in mind that it is not possible to win a fractional game, how many games did the Mariners win in 2001? (source: www.baseball-reference.com) 6.) a.) Write 5.3 x 1011 in regular notation. b.) Write 2.2 x 10-8 in regular notation. c.) Write 32,000,000,000 in scientific notation. d.) Write 0.000000000425 in scientific notation. e.) Use the scientific notation in part a.) and b.). Multiply the two numbers together, SHOWING ALL NECESSARY WORK AND WITHOUT USING YOUR CALCULATOR, and write your final answer in scientific notation. 7.) Estimate the total number of hamburgers eaten each year by left-handed Americans. Be sure to clearly state all of your assumptions. 8.) You put $3500 in the bank. The account gets an annual percentage rate of interest of 2.1% compounded monthly. The money is left in the account for 4 years. Throughout the problem, we assume no other money is added or removed from the accounts. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the amount of money you will have at the end of four years. b.) WITHOUT SIMPLIFYING ANYTHING, insert the numbers into the formula you will use to find the amount of money you will have at the end of four years. c.) How much money will you have at the end of four years? 9.) You put $5100 in the bank. The account gets an annual percentage rate of interest of 3.45% compounded continuously. The money is left in the account for 3 years. Throughout the problem, we assume no other money is added or removed from the accounts. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the amount of money you will have at the end of three years. b.) WITHOUT SIMPLIFYING ANYTHING, insert the numbers into the formula you will use to find the amount of money you will have at the end of three years. c.) How much money will you have at the end of three years? 10.) You start putting money in your retirement fund at age 23. You put in $225 each month. The interest of 10.185% is compounded quarterly. You will retire when you turn 65. a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find the amount of money in your fund when you retire. b.) WITHOUT SIMPLIFYING ANYTHING, insert the correct 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.) Find the amount of interest you will receive. 11.) You start putting money in a college savings account. You want to have $115,000 in 18 years when your daughter will be ready for college. The interest rate of 8.35% is compounded monthly. a.) WITHOUT INSERTING ANY NUMBERS, write 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? 12.) You are buying a house. After the down payment, you need to borrow $105,000. You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 15 year mortgage is 5.275%. 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? 13.) Consider the following question. How do doctors' salaries compare to lawyers' salaries? Which type of study (experimental, observational, double-blind) would best answer the question? Give a reason for your answer.