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 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 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 -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 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. Use your tree diagram to determine the probability that, when flipping three coins, you end up with exactly 2 tails. 5.) The following table gives some career statistics for Willie Mays, the best all- around player in baseball history. (source www.baseball-almanac.com/) Year Team G AB R H 2B 3B HR RBI BB SO AVG 1951 Giants 121 464 59 127 22 5 20 68 57 60 .274 1952 Giants 34 127 17 30 2 4 4 23 16 17 .236 1954 Giants 151 565 119 195 33 13 41 110 66 57 .345 1955 Giants 152 580 123 185 18 13 51 127 79 60 .319 1956 Giants 152 578 101 171 27 8 36 84 68 65 .296 1957 Giants 152 585 112 195 26 20 35 97 76 62 .333 1958 Giants 152 600 121 208 33 11 29 96 78 56 .347 1959 Giants 151 575 125 180 43 5 34 104 65 58 .313 1960 Giants 153 595 107 190 29 12 29 103 61 70 .319 1961 Giants 154 572 129 176 32 3 40 123 81 77 .308 1962 Giants 162 621 130 189 36 5 49 141 78 85 .304 1963 Giants 157 596 115 187 32 7 38 103 66 83 .314 1964 Giants 157 578 121 171 21 9 47 111 82 72 .296 1965 Giants 157 558 118 177 21 3 52 112 76 71 .317 1966 Giants 152 552 99 159 29 4 37 103 70 81 .288 1967 Giants 141 486 83 128 22 2 22 70 51 92 .263 1968 Giants 148 498 84 144 20 5 23 79 67 81 .289 1969 Giants 117 403 64 114 17 3 13 58 49 71 .283 1970 Giants 139 478 94 139 15 2 28 83 79 90 .291 1971 Giants 136 417 82 113 24 5 18 61 112 123 .271 1972 Giants 19 49 8 9 2 0 0 3 17 5 .184 1972 Mets 69 195 27 52 9 1 8 19 43 43 .267 1973 Mets 66 209 24 44 10 0 6 25 27 47 .211 a.) What is the most home runs (HR) he in one year? What year? b.) In how many years did he have a batting average (AVG) above .300? c.) What is the most consecutive year in which he hit at least 30 home runs (HR)? d.) In how many years did he exceed both 100 runs scored (denoted R) AND runs batted in (denoted RBI) in the same year? 6.) You are making a license plate. It has 3 letters followed by 4 numbers. How many different license plates can be made? 7.) The only major league players, prior to the year 2000, to have at least 20 doubles, 20 triples, 20 homeruns and 10 stolen bases in a season are Willie Mays (1957), Wildfire Schulte (1911), Jeff Heath (1941), George Brett (1979) and Jim Bottomley (1928). This chart shows the data for those players in those years. (source Sabermetric Encyclopedia).

45

40

35

30 Mays

25 Schulte Heath 20 Brett

15 Bottomley

10

5

0 SB 2B 3B HR

a.) Which player(s) had exactly 20 triples (denoted 3B)? b.) Which player hit the most home runs (denoted HR)? c.) Which player had the fewest stolen bases (denoted SB)? d.) How many stolen bases did Willie Mays have? 8.) Explain the difference between a linear model and an exponential model. 9.) The following chart shows the number of wins each year from 1961 to 1970 for the Champion and the Champion. (source www.baseball-reference.com)

a.) How many games did the National League champion win in 1969? b.) How many times did the National League champion win more games than the American League champion? c.) How many times did BOTH league champions finish with fewer than 100 wins? d.) Who won more games in 1961, and by how many? 10.) In their lunch menu, the Olive Garden restaurant in Fort Smith, offers nine appetizers, three soups, two salads, thirty-four entrees, forty-two beverages and eight desserts. If you order one appetizer, one soup, one salad, one entrée, one beverage and one dessert, how many different meals could you order? 11.) The table below gives the number of base hits had in his first six full seasons in the major leagues. YEAR HITS 1968 7 1969 4 1970 6 1971 8 1972 4 1973 8 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 the numbers of hits in those seasons. a.) the mean b.) the median c.) the mode 12.) The following are the number of at bats for each of the 1969 . 365 353 362 400 395 565 483 327 303 247 215 211 202 177 169 93 74 40 15 10 1 91 84 74 47 37 29 24 17 12 4 1 Find the following for this data set. a.) the mean b.) the median c.) the mode 13.) 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 one paramecium and one cephalopod? 14.) Fifteen people have formed a baseball team. We are interested in the number of nine player batting orders that can be created from the fifteen players. a.) Is this a combination problem or a permutation problem? b.) How many different lineups are possible? 15.) According to microbiologist, Dr. Chuck Gerba, one of three chickens is contaminated with salmonella. The vast majority of contaminated chickens have fewer than 300 salmonella, all killed in the cooking. Even if they survived, it usually takes several thousand to cause illness. However, if the salmonella gets transferred during food preparation to the potato salad, the warm, moist environment allows them to double in population every 20 minutes. Suppose 100 salmonella got into the potato salad. How many would there be 6 hours later? (source - "Reader's Digest," February 1995) 16.) In 1870, Searcy, Arkansas had a population of 874. By 1880 the population had dropped to 840 (that's a drop of 3.8902% over the 10 year period). If that rate had remained the same, what would the population of Searcy be in 2005?

Exam #4 1.) Our note has a frequency of 320 cycles per second. Find the frequency of the note that is 5 half-steps above our note. 2.) Our note has a frequency of 320 cycles per second. Find the frequency of the note that is 7 half-steps below our note. 3.) Our note has a frequency of 320 cycles per second. Find the frequency of the note that is one octave above our note. 4.) Our note has a frequency of 320 cycles per second. Find the frequency of the note that is one octave below our note. 5.) Our note has a frequency of 320 cycles per second. Find the frequency of the note that is two octaves above our note. 6.) Draw a section of tile hallway (include the walls), with four rows of four tiles each, that illustrates the idea of vanishing points. Identify the principal vanishing point and two others. 7.) Consider the following shapes.

1 2 3 4

5 6 7 8

= For each type of symmetry below, list the shapes 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 (when rotated through SOME angle less than 360 degrees) d.) none of the above symmetries 8.) A Fibonacci-like sequence has a first term of 5 and a second term of 2. Find the: a.) third term b.) fourth term c.) fifth term d.) sixth term 9.) Explain the difference between votes that are decided by majority vote and those decided by plurality vote. 10.) Give examples of two elections that require a super-majority vote. Be sure to give the percentage required in each vote. 11.) Explain how a Borda Count works. Give an example of something that is done with a Borda Count. 12.) 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 # of representatives # of representatives you Quota the state "should" get will give the state using normal rounding A 280,000 B 8,300,000 C 10,100,000 D 24,966,000 E 24,967,000 Total 68,613,000 Population 13.) Find the area and perimeter of the following triangle. Assume all units are in centimeters.

5 6 4

7

14.) A cylindrical storage drum has a height of 2 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!! 15.) Find the area and perimeter of the following trapezoid. Assume all units are in centimeters.

16.) The window below is shaped like a rectangle with a semi-circle on top. What are the area and perimeter of the window? GIVE AT LEAST 4 PLACES TO THE RIGHT OF THE DECIMAL POINT!!

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. DO NOT USE THE SAME FALLACY FOR MORE THAN ONE EXERCISE. 1.) Senator Harry Reid, speaking about opposition to health care legislation: "Instead of joining us on the right side of history, all [they] can come up with is, 'Slow down, stop everything, let's start over.' If you think you've heard these same excuses before, you're right. When this country belatedly recognized the wrongs of slavery, there were those who dug in their heels and said, 'Slow down, it's too early, things aren't bad enough.'" 2.) "Do you support the death penalty, or do you think criminals should be free to terrorize the nation?" 3.) "They always win when they wear their blue uniforms." 4.) Union City, New Jersey has a population of 56,000 people in 1.3 square miles. This gives a population density of 43,077 people per square mile. What is the population density in people per square kilometer? 5.) A Canadian company is advertising a jacket for $47.53 (Can.). How much would it cost in U.S. dollars? 6.) Billy Bob weighs 350 lbs. You must show the use of units. What is his weight in kilograms? 7.) 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? 8.) The listed price was $14.95. Tax was 8.25%. What was the total cost? 9.) In 2000, the New York Mets won 94 games and lost 68 games. What percentage of their games did they win? 10.) Draw a line graph representing the given data. Keep the people in the order given. Person Books Read Allan 35 Bob 3 Carol 31 Debbie 28 11.) You start putting money in your retirement fund at age 24. You put in $250 each month. The interest of 12% is compounded monthly. a.) Write out the formula that will figure out the amount of money you will have if you retire at age 65 with none of the numbers inserted. b.) Write out the formula that will figure out the amount of money you will have if you retire at age 65 with all of the numbers inserted. c.) How much money will you have at age 65? 12.) You put $1000 in a savings account. It receives 5.4% interest compounded quarterly. You don't take out any money or put any more money in. 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? 13.) You are borrowing $130,000 to buy a house. The interest rate for your 30 year mortgage is 6.7%. 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.) In 1988, the New York Mets hit 152 home runs as a team. The following chart shows the distribution of home runs broken down by home runs hit by Lenny Dykstra, , Kevin Elster, , , Howard Johnson, Kevin McReynolds, and "other" players.

Other Strawberr Dykstra y Wilson Elster

Carter

McReynol Hernandez ds Johnson

a.) The portion of the pie for Darryl Strawberry has an angle of 92.36842. How many home runs did he hit? 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? 15.) The following are the National League's leading home totals from 1876 to 1881. Note that they are unordered. 8 6 9 4 4 5 Without using your calculator, find the following. Be sure to show or explain how you got each answer. a.) mean b.) median c.) mode 16.) The following are the American and National League leading totals from 1976 to 1985. 268 206 276 204 275 232 286 209 180 127 286 187 313 223 303 260 262 341 235 327 Using your calculator, find the following. a.) mean b.) median c.) mode 17.) a.) Draw a tree diagram to illustrate tossing three coins. b.) Find the probability that at least two of the coins came up tails. 18.) A box contains 8 cats, 7 squid and 5 cobras. 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 cobras? 19.) For the purposes of this problem, a "word" is any sequence of letters. a.) How many five letter words can be created from the letters A, B, C, D, E, F and G? b.) How many five letter words can be created from the letters A, B, C, D, E, F and G, if no letters may be repeated? 20.) This chart gives some of the batting statistics for the 1969 World Champion New York Mets. It lists ALL of the Mets' players who went to bat at least once during the season. Answer the questions below based on the information in the chart.

Player G AB R H 2B 3B HR RBI BA OBP SLG SB 113 365 38 92 12 3 6 40 .252 .313 .351 2 112 353 36 84 9 2 11 49 .238 .307 .368 3 102 362 48 101 14 7 3 32 .279 .347 .381 7 124 400 38 87 11 3 1 39 .218 .290 .268 4 123 395 42 98 11 6 0 24 .248 .341 .306 1 149 565 97 153 23 4 26 76 .271 .342 .464 12 137 483 92 164 25 4 12 75 .340 .422 .482 16 109 327 38 77 10 2 9 52 .235 .326 .361 1 100 303 42 91 9 3 14 47 .300 .375 .488 1 103 247 20 53 9 2 2 23 .215 .259 .291 3 118 215 26 49 6 1 1 14 .228 .313 .279 7 Bobby Pfeil 62 211 20 49 9 0 0 10 .232 .260 .275 0 72 202 31 51 5 0 12 37 .252 .321 .455 3 J.C. Martin 66 177 12 37 5 1 4 21 .209 .257 .316 0 61 169 21 35 8 1 3 18 .207 .286 .320 4 48 93 6 14 3 1 0 4 .151 .202 .204 1 29 74 5 19 3 1 3 12 .257 .295 .446 0 16 40 1 6 3 0 1 2 .150 .209 .300 0 10 15 0 2 2 0 0 1 .133 .188 .267 0 Bob Heise 4 10 1 3 1 0 0 0 .300 .462 .400 0 39 91 7 11 3 0 0 6 .121 .200 .154 1 Jerry Koosman 32 84 1 4 0 0 0 1 .048 .059 .048 0 35 74 2 6 1 0 0 1 .081 .104 .095 0 30 47 3 8 0 0 1 5 .170 .184 .234 0 Jim McAndrew 27 37 0 5 1 0 0 3 .135 .200 .162 0 25 29 3 3 0 0 0 2 .103 .103 .103 0 Tug McGraw 43 24 1 4 1 0 0 3 .167 .200 .208 0 40 17 1 4 0 0 0 1 .235 .235 .235 0 Jack Dilauro 23 12 0 0 0 0 0 0 .000 .000 .000 0 59 4 0 1 0 0 0 0 .250 .250 .250 0 3 1 0 0 0 0 0 0 .000 .000 .000 0 Al Jackson 9 1 0 0 0 0 0 0 .000 .000 .000 0 TOTAL 162 5427 632 1311 184 41 109 598 .242 .309 .351 66

a.) Which Mets' player hit the most home runs (HR) this season? b.) How many Mets' players had at least 300 at bats (AB) this season? c.) Of the (those who played 1st base, 2nd base, 3rd base or ), which hit the most triples (3B) during this season? d.) All players listed below Bob Heise were . Of the pitchers, how many had at least one hit (H) during this season? 21.) You are a second grade teacher. Your class is going to be doing a short play. The roles in the play are "sales clerk," "customer one," "customer two," and "supervisor." You have 23 students in your class. a.) How many different casts could you choose for the play? b.) Is this a permutation problem or a combination problem? 22.) 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 2007? (Note: the actual 2000 population was 1,264.) 23.) Convert 25 degrees Celsius to degrees Fahrenheit. 24.) Find the volume and surface area of the box shown below. Assume all measurements are in feet.

25.) A.) You are considering buying 15 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.) B.) Three kinds of apples are mixed in a basket. There are 14 Red Delicious apples, 12 Golden Delicious apples and 9 Granny Smith apples. (1) What is the smallest number of apples you would have to take out to be sure of getting at least three of one kind? (2) What is the smallest number of apples you would have to take out to be sure of getting at least 2 Granny Smith apples?