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Mathematics for the Liberal Arts Exam File Fall 2008 Exam #1 for Each Of

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Mathematics for the Liberal Arts Exam File Fall 2008 Exam #1 for Each Of Mathematics for the Liberal Arts Exam File Fall 2008 Exam #1 For each of #1-5, identify one AND ONLY ONE of our logical fallacies that is exhibited. Give a brief explanation for your choice. Appeal to emotion Appeal to ignorance Appeal to popularity Circular reasoning Diversion False cause Hasty generalization Limited choice Personal attack Straw man 1.) "If you care about your grandchildren's future you will support the efforts to stop global warming." 2.) "Bubba Sue is from Alabama. All girls from Alabama have two word first names." 3.) "Are you going to major in history or are you going to major in mathematics?" 4.) "The last time I wore this hat during a test, I got an 'A'. It must be a lucky hat." 5.) "I can't believe you're supporting Ted Kennedy's tax hike proposal. After all, he was the one who drove the car off the bridge when Mary Jo Kopechne died." 6.) Construct the truth table for the following proposition. ((not p q ) p) → q 7.) For each of the following, tell whether or not it is a proposition. a.) "John Dodge died after being hit in the head by a pitch during a minor league ballgame." b.) "Take your feet off of the coffee table!" c.) ♪♫♪♫"It's a beautiful day in the neighborhood."♪♫♪♫ d.) "Arkansas is north of Missouri." e.) "Millard Fillmore was the first president of the United States." f.) 5570 = 258,763,175,164,940,474,024,358,370,140,027,266,101,972,731,000, 849,487,432,696,691,594,165,238,662,840,430,349,527,071,435,270,918,32 5,962,916,208,543,427,488,052,599,275,665,011,888,825,298,326,160,809, 388,572,824,784,890,926,606,058,775,413,600,010,597,522,294,247,623,16 2,729,939,249,253,929,160,355,766,626,578,037,058,304,627,367,809,464, 646,477,784,187,980,841,016,392,280,101,929,404,993,990,389,555,433,58 5,024,261,204,937,436,050,131,287,877,419,867,645,500,009,913,951,677, 820,165,286,902,920,342,981,815,338,134,765,625. 8.) Draw a Venn Diagram to illustrate the following categorical proposition. All dogs eat acorns and some dogs ride skateboards. 9.) The following Venn diagram represents how a college class is broken down in the categories of female students (denoted "F"), students from Arkansas (denoted "A") and mathematics majors (denoted "M"). Answer the questions below the diagram. [Note that "x" and "y" represent students. Those students are already included in the numbers given in the diagram and should not be counted in addition to the numbers.] a.) How many students are in the class? b.) How many of the students are mathematics majors from Arkansas? c.) How many female students are in the class? d.) How many psychology majors are in the class? e.) What do we know about student "x?" f.) What do we know about student "y?" 10.) Your living room is 15 feet wide and 18 feet long. What is the area of your living room in square meters? You must show the use of units and conversion factors. 11.) Your French friend Maurice is coming to visit. You want to tell him the temperatures he should expect. The high temperatures are expected to be around 84 Fahrenheit. If you want to tell Maurice the temperature in Celsius, what will you tell him? Show the details of the formula you use. 12.) Billy Bob's combination motor oil/salad dressing/kitty litter sells for $5.49 (U.S.) per gallon. Billy Bob wants to start selling his product in Mexico. What will the price be in pesos per liter? You must show the use of units and conversion factors. 13.) You are driving 100 feet per second. The speed limit is 70 miles per hour. Are you speeding? You must show the use of units and conversion factors. 14.) Methusaleh was 969 years old when he died. How many seconds old was Methusaleh when he died? 15.) You have a basket with apples in it. There are 23 green apples, 14 red apples and 8 plaid apples. You are going to take some apples out of the basket. a.) How many apples must you take out of the basket to be absolutely certain you have removed a matching pair of apples? b.) How many apples must you take out of the basket to be absolutely certain you have removed a matching pair of plaid apples? c.) How many apples must you take out of the basket to be absolutely certain you have removed four apples of the same color? 16.) You have ten rectangular tables in a rectangular room. You must arrange the tables so that there are three tables along each wall. Draw a picture to show how you could do this. 17.) 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? Exam #2 1.) The price of a coat was $140. Yesterday it was reduced 35%. What is the price now? 2.) In 2004, Jose Reyes of the New York Mets earned a salary of $307,500. For 2005, he received a raise of 7.967479675%. For 2006, he received a raise of 20.93373494%. WITHOUT ROUNDING OFF EITHER PERCENTAGE, determine his 2006 salary. (source: www.baseball-reference.com) 3.) The price of a coat was $140. Last week it was reduced 15%. This week it was reduced another 10%. Sales tax is 8%. With tax included, what is the cost of the coat now? 4.) David Wright of the New York Mets earned a salary in 2006 of $374,000. That was a 15.968992248% raise from his 2005 salary. What was his 2005 salary? (source: www.baseball-reference.com) 5.) Use reasonable estimations to approximate the total number of slices of bread eaten each year by all left-handed people in the United States. 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 from parts 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.) You put $2750 in the bank. The account gets an annual percentage rate of interest of 1.1% 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 account. 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? 8.) You put $6125 in the bank. The account gets an annual percentage rate of interest of 1.45% compounded continuously. The money is left in the account for 5 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 five years. c.) How much money will you have at the end of three years? 9.) 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. 10.) 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. 11.) You are buying a house. After the down payment, you need to borrow $120,000. You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 30 year mortgage is 5.85%. 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? 12.) A person is interested in finding out the average income of people in Arkansas.
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