Mathematics for the Liberal Arts Exam File Spring 2017 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. 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.) "If there really were a large and unusual type of animal in Loch Ness, then we would have undeniable evidence of it by now. Therefore, there is no such animal." 6.) Construct the truth table for the following proposition. (not p q ) → 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 ,325,962,916,208,543,427,488,052,599,275,665,011,888,825,298,326,16 0,809,388,572,824,784,890,926,606,058,775,413,600,010,597,522,294,2 47,623,162,729,939,249,253,929,160,355,766,626,578,037,058,304,627, 367,809,464,646,477,784,187,980,841,016,392,280,101,929,404,993,990 ,389,555,433,585,024,261,204,937,436,050,131,287,877,419,867,645,50 0,009,913,951,677,820,165,286,902,920,342,981,815,338,134,765,625. 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. 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.) Bubba weighs 348 pounds. What is his weight in scruples. You must show the use of units and conversion factors. 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? You must show the use of units and conversion factors. 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. Exam #2 1.) Calculate (6.2 x 10-3) x (4 x 107) without using your calculator. Be careful to show ALL of your work and express your final answer in scientific notation. 2.) Bob made $40,000 in 2004. For 2005, his salary went up 5%. For 2006, his salary went up 5% again. What is his salary in 2006? 3.) Bob has a bad cold. He is trying to take some cough syrup. He is pouring the cough syrup into a measuring spoon while coughing. The spoon is chipped so that it can't hole as much as it is supposed to hold. Discuss sources of random error and systematic error in this situation. 4.) Do the following. a.) Write 0.00000034 in scientific notation. b.) Write 45,000,000,000 in scientific notation. c.) Write 6.2 x 10-5 in standard notation. d.) Write 4.7 x 10 6 in standard notation. 5.) You start putting money in your retirement fund at age 23. You put in $500 each month. The interest of 10.25% is compounded quarterly. You retire at age 65. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have when you retire. b.) Without doing any simplification, insert all of the 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.) How much interest did your money earn? 6.) Billy Bob is borrowing $34,000 to buy a new double-wide. The interest rate for his 10 year mortgage is 6.45%. 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 Billy Bob'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? 7.) Maher-Shalal-Hash-Baz 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 9.5% is compounded quarterly. a.) Without inserting any numbers, write out the formula that will figure out the amount of money Maher-Shalal-Hash-Baz 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 are buying a house. After the down payment, you need to borrow $115,000. You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 30 year mortgage is 6.15%. 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, 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? 9.) The price of a sofa was $780. Two weeks ago the price was dropped 15%. This week it was dropped 10%. What is the price now? 10.) 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/) 12.) Estimate the number of eggs eaten in the United States each year. Show all work. 12.) You put $2500 in a certificate of deposit account for 3 years. It receives 4.5% interest compounded quarterly. You neither take out any money nor put in any more money. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have after 3 years. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have after 3 years? 13.) I want to do a study on the average income of people in Arkansas. I am considering doing the study at Walmart, Waffle House, or a Mercedes dealership. Which would be the best choice? Why? Exam #3 1.) The following chart shows the number of runs scored by pitcher Bobo Newsom in his first seven full seasons in the major leagues. Draw a bar graph to illustrate this data. Year 1934 1935 1936 1937 1938 1939 1940 Runs 6 6 11 11 9 6 9 2.) The following chart shows the breakdown of number of games won by the pitchers on the 1916 Philadelphia Athletics.