Mathematics for the Liberal Arts Exam File Fall 2011 Exam #1 In exercises #1 - 4, 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. Some of these exercises come from http://www2.sjsu.edu/depts/itl/graphics/main.html. 1.) The charges of police brutality are absolutely untrue, because the police would never do something like that. 2.) I wore a hat during the last test and made the highest grade I've made all semester. I'll wear a hat on the final so I'll get a good grade on the final. 3.) Theodore Kaczynski, Georg Cantor and Kurt Godel were all mathematicians and crazy. Dr. Worth is a mathematician so he must be crazy, too. 4.) I have never seen a bear in this area so there must not be any bears around here. 5.) Construct the truth table for the following. ((p q) q) not p 6.) Draw a Venn diagram to illustrate the following proposition. All fish are dogs and some cats are fish. 7.) For each of the following, write "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.) It's a beautiful day. d.) Bob is 25 years old and Dave's dog is plaid. e.) Donald Duck is the president. f.) 3 + 9 = 10 and the name of this course is advanced underwater basket weaving. 8.) The following Venn diagram illustrates the makeup of a particular group of students. "M" denotes "mathematics major," "P" denotes "plays piano," and "G" denotes "refuses to eat grits." "x" and "y" represent particular students. The numbers represent the number of students who fit the categories. a.) How many students are in the group? b.) How many students are mathematics majors who play the piano? c.) What do we know about student "x?" d.) What do we know about student "y?" 9.) Convert 25 degrees Celsius to degrees Fahrenheit. 10.) A Canadian company is advertising a jacket for $59.99 (Can.). They also list a price of $42.25 (U.S.). Are those prices the same? If not, which one is cheaper? Be sure to show the use of units. 11.) Tom was driving 20.3 meters per second in a 45 mile per hour zone. Was Tom speeding? Be sure to show the use of units. 12.) Bob weighs 110 kg. In order to participate in a backpacking trip at Philmont Scout Ranch he must weigh no more than 215 pounds. Does he qualify for the hike? If not, how much weight must he lose in order to qualify? Be sure to show the use of units. 13.) How many centimeters are there in a mile? Be sure to show the use of units. 14.) There are 14 blue apples, 12 plaid apples and 5 green apples in a basket. a.) What is the smallest number of apples you would have to take out to be sure of getting at least three of one kind? b.) What is the smallest number of apples you would have to take out to be sure of getting at least four plaid apples? 15.) There are 10 rectangular tables in a rectangular room. You must set up the tables so there are 3 tables against each wall. 16.) You have a four minute hourglass and a five minute hourglass. You need to cook something for exactly seven minutes. Give a detailed explanation of how you would use the two hourglasses to time the seven minutes. (Note: You cannot tell by looking if an hourglass is half empty.) Exam #2 1.) 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. 2.) Estimate the total number of hamburgers eaten each year by left-handed Americans. Be sure to clearly state all of your assumptions. 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 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.) 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? 7.) Billy Bob is borrowing $34,000 to buy a new double-wide. The interest rate for his 10 year mortgage is 6.45%. 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 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? 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 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? 9.) Jay Leno told the following joke on "The Tonight Show." (I've made a slight change in the numbers.) "When they closed Denver's old Stapleton Airport, the gift shop had a big clearance sale - everything was 94 percent off. This was great! You could get a bottle of aspirin for $18!" Assuming he is giving correct data, how much did the aspirin cost before the sale? 10.) 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? 11.) 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.) Bob bought a house worth $120,000. Now, after five years he was told the house's value had gone up 26%. What is the house worth now? 13.) 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? 14.) 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? Exam #3 1.) 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. 2.) A person is interested in finding out the average income of people in Arkadelphia. In order to do that, he does a survey by asking the annual income of Arkadelphia residents who are shopping at the local Wal-Mart. Are his results likely to be representative of Arkadelphia? Why or why not? 3.) The following chart gives historic population data for Russellville, Arkansas. 25000 20000 15000 10000 5000 0 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 a.) What was the population of Russellville in 1950? b.) Which decade saw the greatest population change? c.) How many decades saw the population decrease? d.) What was the population of Russellville in 1963? 4.) Draw a tree diagram to illustrate flipping three coins.