Mathematics for the Liberal Arts Exam File Fall 2015

Exam #1

For each of #1-5, identify one of our logical fallacies that is exhibited. Give a brief explanation for your choice. DO NOT USE THE SAME ANSWER MORE THAN ONCE. 1.) If you aren't sure why you should vote for Senator Kadiddlehopper, then think of the children! 2.) "Buy a Yugo. It is more popular in Lithuania than any other car." 3.) I understand why you think Obama should be president, but what about the corruption charges against Illinois Governor Blagojevich? 4.) "I can't believe you don't support the President's health care plan. You must want all poor people to die." 5.) "Theodore Kaczynski, Georg Cantor and Kurt Godel were all mathematicians and crazy. Dr. Worth is a mathematician so he must be crazy, too." 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.) 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.) 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.) Tom was driving 20.1 meters per second in a 45 mile per hour zone. Was Tom speeding? Be sure to show the use of units. 11.) The part of a baseball diamond inside the base paths is a square that is 90 feet on each side. Find the area inside the base paths and convert it to meters. 12.) Suppose "Gerhard's Combination Motor Oil/Salad Dressing" is on sale at a store in Austria 2.60 shillings per liter. What is the price in dollars per gallon? State your answer to the nearest $0.01 per gallon. 13.) 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 44 Fahrenheit. If you want to tell Maurice the temperature in Celsius, what will you tell him? Show the details of the formula you use. 14.) Methusaleh was 969 years old when he died. How many seconds old was Methusaleh when he died? 15.) You are considering buying 13 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. How can you determine the lightweight coin in a maximum of three weighings on a balance scale? (A balance scale just indicates which of two items is heavier.) 16.) You have a basket with apples in it. There are 13 green apples, 18 red apples and 11 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? 17.) Complete the following Sudoku. Each number 1, 2, 3, 4, 5, 6, 7, 8 and 9 must appear once in each row, once in each column and once in each 3-by-3 subsquare (the ones enclosed by the thicker lines)(a correctly completed example is below)

Exam #2 1.) The price of a coat was $210. Yesterday it was reduced 30%. 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 $210. Last week it was reduced 20%. This week it was reduced another 10%. Sales tax is 8%. With tax included, what is the price 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 people in the United States. 6.) a.) Write 5.3 x 1012 in regular notation. b.) Write 2.2 x 10-6 in regular notation. c.) Write 302,000,000,000 in scientific notation. d.) Write 0.00000000425 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 $2550 in the bank. The account gets an annual percentage rate of interest of 1.4% 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 $5525 in the bank. The account gets an annual percentage rate of interest of 1.25% compounded continuously. The money is left in the account for 6 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 six 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 six years. c.) How much money will you have at the end of six years? 9.) You start putting money in your retirement fund at age 23. You put in $215 each month. The interest of 10.15% 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, -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 $105,000. You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 30 year mortgage is 4.85%. 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. In order to do that, he does a survey by asking the annual income of Arkansas residents in line at the Chenal Valley Country Club in Little Rock. Are his results likely to be representative of Arkansas? Why or why not? 13.) You start putting money in a college savings account. You want to have $135,000 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? 14.) At a doctor's office a piece from a tongue depressor has gotten under the weighing surface of a scale, keeping the surface from being able to go down all the way. Also, there is some demolition work going on nearby that periodically shakes everything in the office. Discuss this situation in how it relates to systematic and random .

Exam #3 1.) In 1988, the New York Mets 152 home runs as a team. The following chart shows the distribution of home runs broken down by home runs hit by Lenny Dykstra, Mookie Wilson, Kevin Elster, Gary Carter, Keith Hernandez, Howard Johnson, Kevin McReynolds, Darryl Strawberry and "other" players. Other

Strawberry Dykstra

Wilson

Elster

Carter

McReynolds Hernandez

Johnson a.) The portion of the pie for Darryl Strawberry has an angle of 92.36842. How many home runs did he hit (fractional home runs are impossible)? b.) Three players hit more than 20 home runs. Who were they? c.) How many home runs did Wally Backman hit? d.) Who hit more home runs, Kevin McReynolds or Keith Hernandez? 2.) The population of Peculiar, Missouri was 205 in 1910. In 1920, the population was 233. That is a growth of 13.6585% over 10 years. If the population of Peculiar continued to grow exponentially at that rate 1910 to 1990, what would the population have been in 1990 (the actual population was 1,777 in 1990). (Data from the Missouri Census Data Center) 3.) The following table gives the number of times Dode Paskert was hit by a pitch in the years from 1907-1913. (data from http://www.baseball-reference.com) Construct a line graph to represent the data in the table. 1907 2 1908 4 1909 2 1910 3 1911 4 1912 7 1913 3 4.) The following table gives some of the career statistics for Carl Yastrzemski, who played 23 years for the . (data from http://www.baseball- reference.com) Year G AB R H 2B 3B HR RBI SB BB BA OBP TB 1961 148 583 71 155 31 6 11 80 6 50 .266 .324 231 1962 160 646 99 191 43 6 19 94 7 66 .296 .363 303 1963 151 570 91 183 40 3 14 68 8 95 .321 .418 271 1964 151 567 77 164 29 9 15 67 6 75 .289 .374 256 1965 133 494 78 154 45 3 20 72 7 70 .312 .395 265 1966 160 594 81 165 39 2 16 80 8 84 .278 .368 256 1967 161 579 112 189 31 4 44 121 10 91 .326 .418 360 1968 157 539 90 162 32 2 23 74 13 119 .301 .426 267 1969 162 603 96 154 28 2 40 111 15 101 .255 .362 306 1970 161 566 125 186 29 0 40 102 23 128 .329 .452 335 1971 148 508 75 129 21 2 15 70 8 106 .254 .381 199 1972 125 455 70 120 18 2 12 68 5 67 .264 .357 178 1973 152 540 82 160 25 4 19 95 9 105 .296 .407 250 1974 148 515 93 155 25 2 15 79 12 104 .301 .414 229 1975 149 543 91 146 30 1 14 60 8 87 .269 .371 220 1976 155 546 71 146 23 2 21 102 5 80 .267 .357 236 1977 150 558 99 165 27 3 28 102 11 73 .296 .372 282 1978 144 523 70 145 21 2 17 81 4 76 .277 .367 221 1979 147 518 69 140 28 1 21 87 3 62 .270 .346 233 1980 105 364 49 100 21 1 15 50 0 44 .275 .350 168 1981 91 338 36 83 14 1 7 53 0 49 .246 .338 120 1982 131 459 53 126 22 1 16 72 0 59 .275 .358 198 1983 119 380 38 101 24 0 10 56 0 54 .266 .359 155 totals 3308 11988 1816 3419 646 59 452 1844 168 1845 .285 .379 5539 a.) In how many seasons did Yastrzemski hit at least 40 home runs (HR)? b.) What was Yastrzemski's highest on base percentage (OBP)? c.) What is the most consecutive years in which Yastrzemski played in more than 150 games (G)? d.) Yastrzemski finished his career with exactly one more walk (BB) than batted in (RBI). In how many seasons did he have more runs batted in than walks? 5.) The following chart shows Tom Seaver's totals for each year of his career. (data from http://www.baseball-reference.com) 400 300 200 100

0

1969 1970 1971 1967 1968 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986

a.) What was the most Seaver had in any year? What year? b.) What is the most consecutive years Seaver struck out at least 200 batters? (This happens to be the all-time major league record.) c.) In 1977, Seaver was traded during the season from the Mets to the Reds (one of the most bone-headed trades in major league history). How many of his strikeouts that year were while he was pitching with the Mets? d.) In how many of his 20 seasons did Seaver strike out fewer than 100 batters? 6.) The following are the number of sacrifice flies for (the best all around ballplayer of all time) from 1960 - 1965. YOU MAY NOT USE YOUR CALCULATOR FOR THIS PROBLEM. YOU MUST SHOW ALL WORK AND GIVE AN EXPLANATION OF HOW YOU GOT YOUR ANSWERS.

9 4 3 7 3 2 Find the following. a.) the mean b.) the median c.) the mode 7.) The following are the top 25 major league totals from 1997. You may use your calculator.

41 40 33 32 31 35 40 43 40 42 56 49 58 32 40 35 31 38 31 36 33 44 31 32 40 Find the following. a.) the mean b.) the median c.) the mode 8.) You roll two dice. What is the probability that the sum of the numbers on the dice is greater than 9? 9.) a.) Draw a tree diagram to illustrate tossing three coins. b.) Use your tree diagram to find the probability of getting exactly one head. 10.) A box contains 8 arthropods, 7 cephalopods and 5 paramecia. You reach into the box and pull out a creature at random. You note the kind of creature, return it to the box, and pull out another creature. What is the probability that you pull out two paramecia? 11.) Consider the function f(x) = x2 - 3x - 5. Find each of the following. a.) f(-2) b.) f(3) c.) f(a+1) 12.) You go to a restaurant where the menu consists of seven types of salads, eight types of hot appetizers, seven types of cold appetizers, 21 types of entrees, nine types of drinks, five types of bread, 12 types of pasta, eight types of soup and seven types of desserts. If you order one of each kind of item, how many different meals could you order? 13.) 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, , , third baseman, left fielder, , ). a.) Is this a permutations problem, a combinations problem, or neither? b.) How many different defensive arrangements can you pick? 14.) Explain the difference between exponential and linear models. 15.) Consider the following table of values. x 11 13 15 16 17 19 22 24 y 8 10 13 14 15 19 21 24 a.) Draw a scatter plot of the data. b.) Write the linear function that best fits the data. c.) Draw the function from b.) on your scatter plot from a.). d.) Tell whether the line fits the data well, based on the correlation coefficient.

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 106 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 give "should" get 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.) 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. 4.) Consider a Fibonacci-like sequence with first term 4 and second term 5. Find the next four terms. 5.) Explain the difference between elections that are determined by majority and plurality voting. 6.) Give examples of two votes that require a super-majority vote. GIVE THE PERCENTAGE OR FRACTION OF VOTES REQUIRED FOR EACH ONE. 7.) Consider the following shapes.

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 8.) Explain how a Borda count works. Give an example of a vote that is done using a Borda count. 9.) A woman's college 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 5 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 exercises #1 - 3, 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.) The charges of police brutality are absolutely untrue, because the police would never do something like that. 2.) "I saw five people on the way to school today who didn't use their turn signals. Folks in Arkansas must not know how to use turn signals." 3.) "Dr. Worth, you can't give me an 'F' in this class. If you give me an F my GPA will drop enough so that I will lose my scholarship." 4.) Aroldis Chapman, of the , was clocked throwing a baseball at a speed of 106.0 miles per hour. What is that speed in feet per second? 5.) a.) In your drawer you have 24 identical blue socks and 18 identical brown socks. Without looking, you start pulling socks out of the drawer. (1) How many socks must you pull out so that it is certain you have a matching pair of socks? (2) How many socks must you pull out so that it is certain you have a matching pair of blue socks?

b.) You have a five minute hour glass and an eight minute hour glass. You are cooking something that must be cooked for exactly nine minutes. How would you use the two hour glasses to time your cooking? It is impossible to tell when an hour glass is exactly half empty. 6.) In 2004, the total payroll for the 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/) 7.) 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/) 8.) In 2004, Bobby Abreu 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/) 9.) You put $2500 in a certificate of deposit account. It receives 4.5% interest compounded quarterly. You neither take out any money nor put in any more money. a.) Write out the formula that will figure out the amount of money you will have after 3 years without any of the numbers inserted. b.) Write out the formula that will figure out the amount of money you will have after 3 years with all of the numbers inserted. c.) How much money will you have after 3 years? 10.) You start putting money in your retirement fund at age 25. You put in $650 each quarter. The interest of 9.5% is compounded quarterly. a.) Without inserting any numbers, write out the formula that will figure out the amount of money you will have if you retire at age 65. b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have at age 65? 11.) You start putting money in an college savings account. You want to have $80,000 in 18 years when your daughter 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 you 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 you have to pay each quarter? d.) What is the total of all of your payments? 12.) Suppose you take out an auto loan for $8200 over a period of 4 years at an APR of 3.25%. a.) Without inserting any numbers, write out the formula that will figure out the amount of your monthly payments. b.) Without doing any simplification, insert all of the 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.) You are borrowing $120,000 to buy a house. The interest rate for your 15 year mortgage is 4.75%. 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 your monthly payments. b.) Without doing any simplification, insert all of the 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? 14.) The following chart shows the point totals of the leaders in the voting for the 2003 Rookie of the Year. (data from http://baseball-reference.com/)

100 80 60 40 20 0

Jody Gerut Angel Berroa Hideki MatsuiRocco Baldelli Mark Teixeira

a.) Who won the voting? b.) How many points did receive? c.) How many players received more than 40 points? d.) Did anyone have a majority of the points? If so, who? 15.) The following chart shows the career leaders (through 2003) in wins among managers who were active during at least part of the 2004 season. (data from http://baseball-reference.com/) Wins Tony LaRussa 2114 2002 1781 1452 1129 1017 Jack McKeon 928 913 910 882 a.) How many of these managers have won more than 1100 games? b.) Which of these won the highest percentage of games he has managed? c.) Which is farthest behind the one immediately preceding him on the chart? d.) How many of these managers have won more than twice as many games as Felipe Alou? 16.) The following chart shows the non-pitchers with the fewest career home runs for players with at least 7000 career at bats. Draw a line graph illustrating the data. HR 15 9 16 14 Stuffy McInnis 20 17 20 17.) The following table shows some of the career statistics for Vada Pinson. (data from Year At Bats Hits Doubles Triples Home Runs 1958 96 26 7 0 1 1959 648 205 47 9 20 1960 652 187 37 12 20 1961 607 208 34 8 16 1962 619 181 31 7 23 1963 652 204 37 14 22 1964 625 166 23 11 23 1965 669 204 34 10 22 1966 618 178 35 6 16 1967 650 187 28 13 18 1968 499 135 29 6 5 1969 495 126 22 6 10 1970 574 164 28 6 24 1971 566 149 23 4 11 1972 484 133 24 2 7 1973 466 121 14 6 8 1974 406 112 18 2 6 1975 319 71 14 5 4 a.) In how many different years did Pinson have more than 20 home runs? b.) In how many different years did Pinson have more than 600 at bats? c.) What is the most of triples Pinson had in one year and what year was it? d.) What is the most consecutive years in which Pinson had at least ten of two of doubles, triples and home runs? 18.) The following chart shows Terrence Long's season-by-season totals. YOU MAY NOT USE YOUR CALCULATOR FOR THIS PROBLEM. SHOW ALL WORK AND GIVE AN EXPLANATION OF HOW YOU GOT YOUR ANSWERS. Find the following. Year Stolen Bases 1999 0 2000 5 2001 9 2002 3 2003 4 2004 3 a.) mean b.) median c.) mode d.) maximum 19.) The following chart shows 's season-by-season home run totals. Year Homers Find the following for his home run totals. 1955 18 1956 26 a.) mean 1957 19 1958 23 b.) median 1959 28 1960 32 c.) mode 1961 24 1962 24 d.) maximum 1963 24 1964 24 1965 13 1966 14 1967 3 1968 2 1969 0

20.) Using a tree diagram, find the probability that, in three flips of a coin, you end up with exactly 1 tail. 21.) You roll two standard six-sided dice and add the numbers. What is the probability the sum is at least five? 22.) You are making license plates consisting of three letters and then three numbers. How many different license plates are possible if numbers may be repeated but letters may not? 23.) The population of Peculiar, Missouri was 205 in 1910. In 1920, the population was 233. If the population of Peculiar grew exponentially from 1910 to 1990, what would the population have been in 1990 (the actual population was 1,777 in 1990). (Data from the Missouri Census Data Center) 24.) If you are doing a survey on income of people in Arkansas, which site would be the best for your survey: Wal-Mart, Waffle House, Wilson's Luxury Car Emporium? Explain your answer. 25.) Find the area and perimeter of the following triangle. Assume all units are in centimeters.