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 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 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 -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, of the 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 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 on the 1916 Philadelphia Athletics. The team won a total of 36 games.

a.) Who won the most games for the 1916 Athletics? b.) How many games did Elmer Myers win? c.) How many games did Socks Seibold lose for the 1916 Athletics? d.) What is the angle for Joe Bush's piece of the pie? 3.) The following chart gives the career statistics for Dode Paskert. Year Team Lg G AB R H 2B 3B HR RBI BA OBP SLG 1907 CIN NL 16 50 10 14 4 0 1 8 .280 .333 .420 1908 CIN NL 118 395 40 96 14 4 1 36 .243 .298 .306 1909 CIN NL 104 322 49 81 7 4 0 33 .252 .327 .298 1910 CIN NL 144 506 63 152 21 5 2 46 .300 .389 .374 1911 PHI NL 153 560 96 153 18 5 4 47 .273 .358 .345 1912 PHI NL 145 540 102 170 37 5 2 43 .315 .420 .413 1913 PHI NL 124 454 83 119 21 9 4 29 .262 .358 .374 1914 PHI NL 132 451 59 119 25 6 3 44 .264 .349 .366 1915 PHI NL 109 328 51 80 17 4 3 39 .244 .319 .348 1916 PHI NL 149 555 82 155 30 7 8 46 .279 .346 .402 1917 PHI NL 141 546 78 137 27 11 4 43 .251 .331 .363 1918 CHC NL 127 461 69 132 24 3 3 59 .286 .362 .371 1919 CHC NL 88 270 21 53 11 3 2 29 .196 .274 .281 1920 CHC NL 139 487 57 136 22 10 5 71 .279 .366 .396 1921 CIN NL 27 92 8 16 1 1 0 4 .174 .208 .207 totals 1716 6017 868 1613 279 77 42 577 .268 .350 .361 a.) "Doubles" is denoted by "2B." In how many years did Paskert have more than 25 doubles? b.) "Batting average" is denoted by "BA." What was Paskert's highest batting average? c.) "Runs scored" is denoted by "R" and "Runs batted in" is denoted by "RBI." In how many seasons did Paskert have more runs batted in than runs scored? d.) "" is denoted by "SLG." In how many seasons did Paskert have a slugging percentage higher than .380? e.) "Stolen Bases" is denoted by "SB." How many stolen bases did Paskert have in 1920? 4.) Explain the difference between an exponential model and a linear model.

5.) The following chart gives the career home runs for nine different players.

a.) Of these players, how many have over 500 career home runs? b.) Who hit more career home runs, Mickey Morandini or Ray Oyler? c.) How many career home runs did Willie Mays (the greatest all-around ball player ever) hit? d.) Who hit more career home runs, Mickey Mantle or ? e.) How many career home runs did hit? 6.) Mineral Springs, Arkansas had a population of 546 in 1880. By 1900, it had lost half of its population. Assuming the population continued to decline exponentially at the same rate, what would the population be in 2005? (Note: the actual 2000 population was 1,264.) 7.) The following are the players who had the most triples for the 1979 Cubs. Find the following WITHOUT USING YOUR CALCULATOR AT ALL AND YOU MUST GIVE SOME INDICATION OF HOW YOU FOUND THE NUMBER. Bill Buckner 7 Ivan DeJesus 10 Jerry Martin 3 Dave Kingman 5 Scot Thompson 5 Larry Biittner 3 a.) Find the mean. b.) Find the median. c.) Find the mode. d.) Find the maximum. 8.) Ruby Tuesday's on-line menu lists 13 appetizers, three salads, two soups, ten side dishes, 51 types of entrées, 22 non-alcoholic beverages and six types of desserts. If you order one of each kind of item, how many different meals could you order? 9.) The following chart tells how many games were won by the American and champions each year from 1940 through 1949. 110

105

100 American 95 League

90 National League 85

80

75

1941 1947 1940 1942 1943 1944 1945 1946 1948 1949

a.) In how many of these years did the National League champion win more games than the champion? b.) How many games did the National League champion win in 1942? c.) How many games did the Yankees win in 1944? d.) How many more games did the 1946 American League champion win than the 1945 American League champion won? e.) How many times during these years did both league champions win at least 100 games? 10.) You roll two dice. What is the probability that the sum of the numbers on the dice is greater than 9? 11.) This chart lists the pitchers (in alphabetical order) from 1972-1974 who had the most in a season. (source: sabermetric baseball encyclopedia) Use your calculator to answer the following questions. Player Year Strikeouts a.) For these players, what is Bert Blyleven 1972 228 the mean number of Bert Blyleven 1973 258 strikeouts? Bert Blyleven 1974 249 Tom Bradley 1972 209 1972 310 Steve Carlton 1973 223 b.) For these players, what is Steve Carlton 1974 240 the median number of Joe Coleman 1972 222 strikeouts? 1972 208 1974 225 Mickey Lolich 1972 250 c.) For these players, what is Mickey Lolich 1973 214 the mode number of 1974 221 strikeouts? 1972 234 Gaylord Perry 1973 238 Gaylord Perry 1974 216 1972 329 Nolan Ryan 1973 383 Nolan Ryan 1974 367 1972 249 Tom Seaver 1973 251

12.) a.) Draw a tree diagram to illustrate tossing three coins. b.) Use your chart to find the probability that exactly two of the coins came up heads. 13.) A box contains five regular tacos, seven soft tacos, eight bean burritos, and four tostadas. You reach into the box and randomly choose an item. You then reach in and take another item. a.) What is the probability that the first item was a regular taco and the second was a tostada? b.) What is the probability one item was a regular taco and the other a tostada? 14.) You are coaching a little league baseball team. You have fifteen players. You are choosing a defensive arrangement involving the nine positions (pitcher, catcher, first baseman, second baseman, shortstop, third baseman, left fielder, center fielder, right fielder). a.) Is this a permutations problem, a combinations problem, or neither? b.) How many different defensive arrangements can you pick?

Exam #4 1.) Middle C has a frequency of 260 cycles per second. a.) Find the frequency of the note that is two octaves below middle C. b.) Find the frequency of the note that is one octave above middle C. c.) Find the frequency of the note that is three octaves above middle C. d.) Find the frequency of the note that is two half-steps below middle C. e.) Find the frequency of the note that is five half-steps above middle C. 2.) Consider a country consisting of 5 states with populations given below. If the country's legislature is to have 115 members, find the standard divisor and fill in the table below. Standard Divisor =

State Population Standard Quota # of reps the state # of reps you'll "should" get give state A 1,217,107 B 1,667,819 C 1,217,108 D 1,555 E 1,133,023 Total Population 5,236,612

3.) Consider a Fibonacci-like sequence with first term 3 and second term 7. Find the next four terms. 3, 7, _____, _____, _____, _____ 4.) Explain the difference between elections that are determined by majority and plurality voting. 5.) Draw a section of tile floor, with four rows of four tiles each, that illustrates the idea of vanishing points. Also draw walls. Identify the principal vanishing point and two other vanishing points. 6.) Consider the following shapes.

A B C D E

F G H I J For each type of symmetry below, list the letters that have that kind of symmetry. Some may fit more than one symmetry. a.) symmetry around a horizontal line through the middle of the shape b.) symmetry around a vertical line through the middle of the shape c.) rotational symmetry d.) none of the above symmetries 7.) Give examples of two votes that require a super-majority vote. GIVE THE PERCENTAGE OR FRACTION OF VOTES REQUIRED FOR EACH ONE. 8.) Explain how a Borda count works. Give an example of a vote that is done using a Borda count. 9.) A collegiate women's basketball has a diameter of 11 inches. Find the volume and surface area. Show at least four decimal places. 10.) A cylinder has a height of 2 feet and a diameter of one yard. Find the volume and surface area. Show at least four decimal places. 11.) Find the area and perimeter of the following triangle. Assume all units are in centimeters.

12.) Find the area and perimeter of the following shape. Show at least four decimal places.

Final Exam In each of the following three statements, a logical fallacy is exhibited. In each problem, identify one of our fallacies that is exhibited. Give a good explanation justifying your answer. DO NOT USE THE SAME FALLACY FOR MORE THAN ONE EXAMPLE. 1.) "Show your concern for your children's future by buying a good life insurance policy now!" 2.) "That guy didn't use his turn signal. I guess NO ONE in Arkansas knows how to use a turn signal." 3.) "Hair growth precedes the growth of teeth in babies so hair must cause teeth growth." 4.) You are planning to carpet your living room which is a rectangle that measures 14 feet x 18 feet. How much will it cost if the carpet you want is $17.99 per square yard. Be sure to show all of your work. 5.) How many centimeters are in one mile? Be sure to show all of your work. 6.) Billy Bob wants to go on a trail ride but they won't let him go unless he weighs less than 215 pounds. Right now Billy Bob weighs 127 kg. How many pounds does he need to lose? 7.) Bubba's salary was $400 per week. Last month he received a 6% pay raise. This month he received another 4% pay raise. What is Bubba's salary now? Be sure to show all of your work. 8.) Bubba's friend, Billy Bob, got an 8% pay raise. He is now making $270 per week. What was Billy Bob's salary before the pay raise? Be sure to show all of your work. 9.) Bubba and Billy Bob collect used oil filters. Bubba has 225. Billy Bob only has 84% of what Bubba has. How many used oil filters does Billy Bob have? 10.) The price for Bubba's new jacket is $74.99. Sales tax is 8.43% What will the total cost be for the jacket? 11.) You are buying a house. After the down payment, you need to borrow $85,000. You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 15 year mortgage is 3.275% compounded monthly. 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.) How much interest will you pay over the life of the loan? 12.) You put $3250 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? d.) How much interest did you earn? 13.) You start putting money in your retirement fund at age 23. You put in $400 each month. The interest of 10.375% 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? 14.) The following data are the number of wins for Mets pitcher Craig Swan from 1976 through 1981. 6 9 9 14 5 0 YOU MAY NOT USE YOUR CALCULATOR FOR THIS PROBLEM. YOU MUST SHOW ALL WORK AND GIVE AN EXPLANATION OF HOW YOU GOT YOUR ANSWERS. Find the following for this data. a.) the mean b.) the median c.) the mode d.) the minimum 15.) You roll two dice. What is the probability that the sum of the numbers on the dice is greater than 3? 16.) The following chart, downloaded from http://www.bis.doc.gov/, shows U.S. raw steel production and iron ore consumption from 1991-2000. Use the chart to answer the questions that appear below the chart. Be sure to use correct units in all of your answers.

a.) How much raw steel was produced in the United States in 1991? b.) In what year (from 1991-2000) was U. S. iron ore consumption the highest? How much was it? c.) In how many years (from 1991-2000) did raw steel production decrease from the previous year? List any year(s) when this occurred. d.) Which year (from 1991-2000) showed the lowest level of iron ore consumption in the U. S.? How much was it? 17.) The following chart shows the major league leaders in pitching wins from 1964. Find the quantities listed below the chart. Jim Bouton 18 15 Bob Bruce 15 21 Bob Buhl 15 15 Wally Bunker 19 Jim O'Toole 17 19 Milt Pappas 16 20 Camilo Pascual 15 Tony Cloninger 19 Gary Peters 20 18 Juan Pizarro 19 17 Dick Radatz 16 Bob Gibson 19 20 24 17 Jim Kaat 17 18 19 Bob Veale 18 Denny Lemaster 17 Dave Wickersham 19 Mickey Lolich 18 a.) mean b.) median c.) mode d.) maximum 18.) Draw a tree diagram to illustrate tossing three coins. Find the probability that exactly two of the coins came up heads. 19.) The following chart shows the breakdown of number of games won by the pitchers on the 1916 Philadelphia Athletics. The team won a total of 36 games.

a.) Who won the most games for the 1916 Athletics? b.) How many games did Elmer Myers win? c.) Add up the seven percentages. Explain why they don't add up to 100%. d.) How many games did Socks Seibold lose for the 1916 Athletics?

20.) From 1914 to 2012, the United States has seen an average annual inflation rate of 3.2332009%. If a loaf of bread cost five cents in 1914, and inflation was the only thing that affected the price of bread, what would a loaf of bread cost in 2012? Show all of your work. 21.) Ruby Tuesday's on-line menu lists 13 appetizers, three salads, two soups, ten side dishes, 51 types of entrées, 22 non-alcoholic beverages and six types of desserts. If you order one of each kind of item, how many different meals could you order? 22.) You are coaching a little league baseball team. You have fifteen players. You are choosing a defensive arrangement involving the nine positions (pitcher, catcher, first baseman, second baseman, shortstop, third baseman, left fielder, center fielder, right fielder). a.) Is this a permutations problem, a combinations problem, or neither? b.) How many different defensive arrangements can you pick? 23.) Find the perimeter and area of the triangle below.

24.) A cylindrical storage drum has a height of 4 feet and a diameter of one yard. Find the volume and surface area. GIVE AT LEAST 4 PLACES TO THE RIGHT OF THE DECIMAL POINT!! 25.) Do the following. Be sure to circle the letter for the one you want me to grade. A.) 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.] B.) In your drawer you have 15 identical green socks, 24 identical blue socks and 18 identical plaid socks. Without looking, you start pulling socks out of the drawer. (i) How many socks must you pull out so that it is certain you have a matching pair of socks? (ii) How many socks must you pull out so that it is certain you have a matching pair of green socks?