Mathematics for the Liberal Arts Exam File Spring 2014 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 ) p) → 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,

849,487,432,696,691,594,165,238,662,840,430,349,527,071,435,270,918,325,962,916,208,543,427,488,052,599,275,665,011,888,825,298,326,160,809,388,572,824,784,890,926,606,058,775,413,600,010,597,522,294,247,623,162,729,939,249,253,929,160,355,766,626,578,037,058,304,627,367,809,464,646,477,784,187,980,841,016,392,280,101,929,404,993,990,389,555,433,585,024,261,204,937,436,050,131,287,877,419,867,645,500,009,913,951,677,820,165,286,902,920,342,981,815,338,134,765,625.

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.

17.) Seventy-five people ate dinner at "Billy Bob's All You Can Stomach Exotic Animal Eatery" last night. Sixty-five of them ate squid. Fifty-three of them ate platypus. Forty-eight of them ate earthworm cookies. What is the fewest number of people who MUST have eaten all three of squid, platypus and earthworm cookies?

Exam #2 1.) In 2007, Albert Pujols of the St. Louis Cardinals was paid $12,937,813. For 2008,

his salary went up 7.2%. For 2009, his salary went up 4%. What was his 2009 salary?

2.) A car was on sale for $11,745. That was 13% off the original price. What was the original price?

3.) Through 2009, Lance Berkman had earned $79,505,000 in his major league baseball career. In 2005, he earned $10,500,000. What percentage of his career earnings did he earn in 2005?

4.) In Bubbaville, 19.4% of the 2500 people own at least two hound dogs. How many of the people in Bubbaville own at least two hound dogs?

5.) 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 Reddie Café in the Garrison Center. Are his results likely to be representative of Arkansas? Why or why not?

6.) a.) 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.

b.) Write 0.0000034 in scientific notation. c.) Write 450,000,000 in scientific notation.

7.) Use reasonable estimations to approximate the total number of slices of bread eaten each year by people in Arkansas.

8.) You start putting money in your retirement fund at age 27. You put in $300 each month. The interest of 10.16% 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 62. b.) Without doing any simplification, insert all of the numbers into the formula.

c.) How much money will you have at age 62? d.) What is the total of all of your payments? 9.) You put $3200 in a certificate of deposit account. It receives 3.25% 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 are borrowing $120,000 to buy a house. The interest rate for your 30 year mortgage is 6.15%. 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? 11.) Bubba is borrowing $14,000 to buy a new four wheeler. The interest rate for his 5

year loan is 4.85%. a.) Without inserting any numbers, write out the formula that will figure out the

amount of Bubba'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?

12.) Mephibosheth 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 6.95% is compounded quarterly. a.) Without inserting any numbers, write out the formula that will figure out the

amount of money Mephibosheth 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? 13.) Mrs. McGinty is riding in the back of the RV while Mr. McGinty drives along a

very bumpy road. Mrs. McGinty is measuring some material for a sewing project. Unbeknownst to her, her cat chewed off the first two inches of her tape measure. She is also having trouble measuring because of the bumpiness of the ride. Discuss this situation regarding sources of systematic and random error.

Exam #3 1.) The following table gives the leaders in triples for the 1913 Detroit Tigers. Draw

a bar graph that illustrates the data. Baldy Louden 5

Bobby Veach 10

Del Gainer 8

Donie Bush 10

Paddy Baumann 4

Red McKee 4

Sam Crawford 23

Ty Cobb 16

2.) This chart shows some of the career statistics for Jimmie Foxx. Year Team G AB R H 2B 3B HR RBI AVG OBP SLG 1925 Athletics 10 9 2 6 1 0 0 0 .667 .667 .778 1926 Athletics 26 32 8 10 2 1 0 5 .313 .333 .438 1927 Athletics 61 130 23 42 6 5 3 20 .323 .393 .515 1928 Athletics 118 400 85 131 29 10 13 79 .328 .416 .548 1929 Athletics 149 517 123 183 23 9 33 118 .354 .463 .625 1930 Athletics 153 562 127 188 33 13 37 156 .335 .429 .637 1931 Athletics 139 515 93 150 32 10 30 120 .291 .380 .567 1932 Athletics 154 585 151 213 33 9 58 169 .364 .469 .749 1933 Athletics 149 573 125 204 37 9 48 163 .356 .449 .703 1934 Athletics 150 539 120 180 28 6 44 130 .334 .449 .653 1935 Athletics 147 535 118 185 33 7 36 115 .346 .461 .636 1936 Red Sox 155 585 130 198 32 8 41 143 .338 .440 .631 1937 Red Sox 150 569 111 162 24 6 36 127 .285 .392 .538 1938 Red Sox 149 565 139 197 33 9 50 175 .349 .462 .704 1939 Red Sox 124 467 130 168 31 10 35 105 .360 .464 .694 1940 Red Sox 144 515 106 153 30 4 36 119 .297 .412 .581 1941 Red Sox 135 487 87 146 27 8 19 105 .300 .412 .505 1942 Red Sox/Cubs 100 305 43 69 12 0 8 33 .226 .320 .344 1944 Cubs 15 20 0 1 1 0 0 2 .050 .136 .100 1945 Phillies 89 224 30 60 11 1 7 38 .268 .336 .420 20 Years 2,317 8,134 1,751 2,646 458 125 534 1,922 .325 .428 .609

a.) What was Foxx's highest batting average (denoted AVG)?

b.) How many times did Foxx hit more than 50 homers (denoted HR)? In what year(s)?

c.) What is the most consecutive years Foxx slugging percentage (denoted SLG) was at least .600?

d.) How many home runs did Babe Ruth hit in 1931? 3.) The following chart shows the doubles, triples and home runs for all National

Leaguers with at least 10 triples in 1937. Answer the questions below.

a.) Of these players, which one had the most doubles in 1937? How many

did he have? b.) Who led the National League in home runs in 1937? c.) Who led the National League in triples in 1937? d.) How many of these players had at least 10 home runs in 1937?

4.) The following table shows the leaders in triples for the 1962 New York Mets.

Charlie Neal 9 Without using your calculator, find the following. Be sure to show or explain how you got each answer. a.) mean b.) median c.) mode

Elio Chacon 3

Felix Mantilla 4

Frank Thomas 3

Marv Throneberry 3

Richie Ashburn 3

5.) The following pie chart shows the home run production for the 1962 Giants.

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a.) Who hit the most home runs for the 1962 Giants? b.) How many players hit home runs for the 1962 Giants? c.) The angle for the portion representing Willie Mays (the greatest all around

player in baseball history) is 86.47058824. If the team hit 204 home runs, how many did Mays hit?

d.) Three players hit more than 20 home runs. Who were they? 6.) Explain the difference between a linear model and an exponential model. 7.) Bubbaville had a population of 2400 in 1910. In 1925, its population had fallen to

1200. Assuming that exponential rate of decline continued, what would the population of Bubbaville be in 2006?

8.) The following are the major league leaders in total bases from 1932.

Al Simmons 367 Jack Burns 270 Find the following: a.) mean b.) median c.) mode

Babe Herman 312 Jimmie Foxx 438

Babe Ruth 302 Joe Cronin 274

Ben Chapman 275 Joe Vosmik 287

Bill Terry 373 John Stone 283

Bruce Campbell 273 Lefty O'Doul 330

Charlie Gehringer 307 Lou Gehrig 370

Chuck Klein 420 Mel Ott 340

Don Hurst 317 Paul Waner 321

Earl Averill 359 Pinky Whitney 280

Earle Combs 269 Smead Jolley 273

Hal Lee 296 Wally Berger 282

Heinie Manush 325

9.) You flip three coins. a.) Draw a tree diagram to illustrate tossing the three coins. b.) Find the probability that at least two of the coins came up tails.

10.) A box contains eight jelly beans, five peeps, and three Tasmanian Devils. a.) You reach into the box and remove an item. You reach into the box again

and remove another item. What is the probability you got two jelly beans?

b.) You reach into the box and remove an item. You note what it is and put it back. Then you reach into the box again and remove another item. What is the probability you got a peep first, then a Tasmanian Devil?

11.) You go to a restaurant. The menu lists five kinds of cold appetizers, seven kinds of warm appetizers, four kinds of bread, 10 kinds of beverage, 11 kinds of dessert, 28 kinds of entrée, 12 kinds of pasta, 12 kinds of vegetables, nine kinds of salad, and eight kinds of soup. You order one of each kind of item. How many different meals are possible?

12.) You have a class of 25 second graders. Fifteen are boys, ten are girls. You are going to have them form a committee consisting of three boys and two girls. How many different committees can you form?

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, 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?

14.) You roll a two standard six-sided dice and add the numbers. What is the probability you get a sum of at least five?

15.) For each of the scatter plots below, answer the following questions. Put your answers in the table below the graph.

a.) Is there a correlation in the data? Write "Yes" or "No." b.) Give a reason for your answer in a.).

c.) If you said "yes" in a.), is the correlation strong or weak? Write "strong" or "weak." If your answer to a.) was "no" then write N/A.

d.) Give a reason for your answer in c.). If your answer to a.) was "no" then write N/A.

e.) If you said "yes" in a.), is the correlation positive or negative? Write "positive" or "negative." If your answer to a.) was "no" then write N/A.

f.) Give a reason for your answer in e.). If your answer to a.) was "no" then write N/A.

Exam #3 1.) A note has a frequency of 360 cycles per second. Find the frequency of the note

that is 3 half-steps above our note. 2.) A note has a frequency of 360 cycles per second. Find the frequency of the note

that is 4 half-steps below our note. 3.) A note has a frequency of 360 cycles per second. Find the frequency of the note

that is one octave above our note. 4.) A note has a frequency of 360 cycles per second. Find the frequency of the note

that is one octave below our note.

5.) A note has a frequency of 360 cycles per second. Find the frequency of the note that is three 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 other vanishing points.

7.) Consider the following shapes.

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 d.) none of the above symmetries

8.) A Fibonacci-like sequence has a first term of 1 and a second term of 8. 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 104 members, find the standard divisor and fill in the table below.

Standard Divisor =

State Population Standard Quota

# of reps. state "should" get with normal rounding

# of reps. you will give

A 526,175

B 526,176

C 1,115,207

D 6,875

E 379,102

Total Population 2,553,535

13.) Find the area and perimeter of the following triangle. Assume all units are in centimeters.

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 a rectangle with a semi-circle on each end. Find the

following. What are the area and perimeter of the window? GIVE AT LEAST 4 PLACES TO THE RIGHT OF THE DECIMAL POINT!!

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.) "The government policies changed the housing market so now I'm going to lose my house."

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.) Bubba's new jacket costs $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.) A poll is being conducted on MSNBC's web site. Discuss any sources of bias or

any other problems associated with this poll. 15.) You roll two dice. What is the probability that the sum of the numbers on the

dice is greater than 9? 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 Jim Maloney 15

Bob Bruce 15 Juan Marichal 21

Bob Buhl 15 Claude Osteen 15

Wally Bunker 19 Jim O'Toole 17

Jim Bunning 19 Milt Pappas 16

Dean Chance 20 Camilo Pascual 15

Tony Cloninger 19 Gary Peters 20

Don Drysdale 18 Juan Pizarro 19

Whitey Ford 17 Dick Radatz 16

Bob Gibson 19 Ray Sadecki 20

Larry Jackson 24 Chris Short 17

Jim Kaat 17 Curt Simmons 18

Sandy Koufax 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.) 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?