Test File - Summer 2018

Exam #1

In exercises #1 - 5, an argument is given. For each exercise, identify one of the logical fallacies that is exhibited in that argument. Explain how the fallacy is involved. 1.) "Show your concern for your children's future by buying a good life insurance policy now!" 2.) "Hair growth precedes the growth of teeth in babies so hair must cause teeth growth." 3.) "'Avatar' must be the best movie of all time since it has the highest box office receipts of all time." 4.) "Only a fool would support the proposed legislation about forest management." 5.) "Do you live in Texas or do you live in Arkansas?" 6.) For each of the following, writing "Yes" if it is a proposition (statement) or "No" if it is not. a.) 3 + 8 = 7 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.) Grab that fish! f.) Charlie Brown is the president. 7.) 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. 8.) You need to put carpet in a rectangular room that measures 12 feet by 17 feet. At a price of $27.50 per square yard, and assuming that you can buy precisely the amount of carpet you need, how much will the carpet for the room cost? Show the use of units in your work. 9.) Bob is 6 feet tall. What is his height in millimeters? Show the use of units in your work. 10.) Draw a Venn Diagram to illustrate the statement "All players are athletes and some baseball players throw left-handed." 11.) The following Venn diagram illustrates the makeup of a psychology class. "S" denotes "sophomore," "P" denotes "psychology major," and "A" denotes "from Arkansas." "x" and "y" represent particular students. The numbers represent the number of students who fit the categories. a.) How many students are in the class? b.) How many students are psychology majors from Arkansas? c.) What do we know about student "x?" d.) What do we know about student "y?" 12.) What year was it 1,000,000,000 seconds ago? 13.) 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.) 14.) 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.) 15.) In your drawer you have 24 blue socks, 5 plaid socks and 18 brown socks. Without looking, you start pulling socks out of the drawer. a.) How many socks must you pull out so that it is certain you have a pair of brown socks? b.) How many socks must you pull out so that it is certain that you have a matching pair of socks? c.) How many socks must you pull out so that it is certain that you have a matching pair of blue or plaid socks?

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 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 .

Exam #3 1.) The following table gives the leaders in triples for the 1913 . 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 16 2.) This chart shows some of the career statistics for . 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 more than 50 homers (denoted HR)? In what year(s)? c.) What is the most consecutive years Foxx (denoted SLG) was at least .600? d.) How many home runs did 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.

60

50

40

30 2B 20 3B 10 HR

0

Al Todd Al

GusSuhr

Billy Jurges Billy

AugieGalan

LeeHandley

Jo-Jo MooreJo-Jo

GeneMoore

Billy Herman Billy

JoeMedwick

ArkyVaughan Ival Goodman DonGutteridge

a.) Of these players, which one had the most doubles in 1937? How many did he have? b.) Who led the 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 . Charlie Neal 9 Without using your calculator, find the following. Be Elio Chacon 3 sure to show or explain how you got each answer. Felix Mantilla 4 a.) mean Frank Thomas 3 Marv Throneberry 3 b.) median 3 c.) mode 5.) The following pie chart shows the home production for the 1962 Giants.

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. 367 Jack Burns 270 Babe Herman 312 Jimmie Foxx 438 Find the following: Babe Ruth 302 Joe Cronin 274 Ben Chapman 275 Joe Vosmik 287 Bill Terry 373 John Stone 283 a.) mean Bruce Campbell 273 Lefty O'Doul 330 307 370 420 Mel Ott 340 Don Hurst 317 Paul Waner 321 b.) median Earl Averill 359 Pinky Whitney 280 269 Smead Jolley 273 Hal Lee 296 Wally Berger 282 Heinie Manush 325 c.) mode 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. You are going to have them form a committee consisting of five students. How many different committees can you form? a.) Is this a permutations problem, a combinations problem, or neither? b.) How many different defensive committees can you pick? 13.) You are coaching a little league baseball team. You have thirteen players. You are choosing a defensive arrangement involving the nine positions (, catcher, , , shortstop, , 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?

Exam #4 1.) Middle C has a frequency of 260 cycles per second. Find the frequency of the note that is a.) two octaves below middle C. b.) one octave above middle C. c.) three octaves above middle C. d.) two half-steps below middle C. e.) 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 "should" get # of reps you'll give 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.) A Fibonacci-like sequence has 1st term 5, 2nd term 2. Find the next four terms. 4.) Explain the difference between 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.) Give examples of two votes that require a super-majority vote. GIVE THE PERCENTAGE OR FRACTION OF VOTES REQUIRED FOR EACH ONE. 7.) Explain how a Borda count works. Give an example of a vote done with a Borda count. 8.) A basketball has a diameter of 12 inches. Find the volume and surface area. Show at least four places to the right of the decimal. 9.) A cylinder has a height of 4 feet and a diameter of one yard. Find the volume and surface area. Show at least four places to the right of the decimal. 10.) 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 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 inches 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 less than 4? 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 21 Bob Buhl 15 Claude Osteen 15 Wally Bunker 19 Jim O'Toole 17 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 19 20 24 17 Jim Kaat 17 Curt Simmons 18 19 Bob Veale 18 Denny Lemaster 17 Dave Wickersham 19 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 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?