Mathematics for the Liberal Arts Exam File Fall 2005

Exam #1

In exercises #1 - 5, 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.) Are you going to major in history or are you going to major in mathematics?

2.) Gosh, officer, I know I made an illegal left turn, but please don't give me a ticket. I've had a hard day, and I was just trying to get over to my aged mother's hospital room, and spend a few minutes with her before I report to my second full-time minimum-wage job, which I have to have as the sole support of my thirty-seven children and the nineteen members of my extended family who depend on me for food and shelter.

3.) I asked one of my friends what he thought of the new spending restraints and he agreed it is a good idea. The new restraints are therefore generally popular. (example taken from http://www.datanation.com/fallacies/)

4.) I have never seen a bear in this area so there must not be any bears around here.

5.) If we allow unregulated harvesting of our forests then what are we going to do about the increase in abuse of the food stamp program.

6.) Construct a truth table for the following proposition. (not p  q)  (not q)

7.) For each of the following, writing "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.) is the best left-handed of all-time.

d.) Bob is 25 years old and Dave's dog is plaid.

e.) George Bush 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 proposition. All fish ride bicycles and some dogs ride bicycles.

9.) The following Venn diagram gives information about players currently on the ' roster. The circle labeled "A" denotes players who are 30 years old or older. The circle labeled "T" denotes players who are 6 feet tall or taller. The circle labeled "H" denotes players who are 200 pounds or heavier. (data from www.mlb.com)

A T

1 5 9

14 x 1 14

H 0 y 2

a.) How many players are under 6 feet tall?

b.) What can you say about the player denoted by the "x?"

c.) How many players are under 30 years old and under 200 pounds?

d.) What can you say about the player denoted by the "y?"

10.) C.C. Sabathia, a pitcher for the , is 6'7" tall and weighs 290 pounds. Convert his weight to kilograms and his height to centimeters. Put your final answers in the blanks provided. (source: www.majorleaguebaseball.com)

11.) Tom threw a 45.4 meters per second. Dave threw a ball 98 miles per hour. Who threw the ball faster, Tom or Dave?

12.) The carpet you want to buy costs $18.95 per square yard. If you are going to be carpeting a room that is 18 feet long and 15 feet wide, how much will it cost to carpet the room?

13.) An Australian company is advertising a jacket for $127.53 (Aust.). How much would it cost in U.S. dollars?

14.) Bob weighs 120 KILOGRAMS. He wants to lose weight to get down to 185 POUNDS. How many SCRUPLES does he need to lose?

15.) In your drawer you have 15 identical green socks, 24 identical blue socks and 18 identical brown socks. Without looking, you start pulling socks out of the drawer. How many socks must you pull out so that it is certain you have a matching pair of either green or blue socks? Explain your answer.

16.) There are 10 rectangular tables in a rectangular room. You must set up the tables so there are exactly 3 tables against each wall. Show or explain how this can be done.

17.) 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.]

Exam #2

1.) In 2004, the total payroll for the was $182,835,513. They paid $21,726,881. What was Rodriguez' salary as a percentage of the total team payroll? (data from http://www.businessofbaseball.com/)

2.) Juan Pierre 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/)

3.) In 2004, 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/)

4.) The price of a sofa was $930. Two weeks ago the price was dropped 15%. This week it was dropped 10%. What is the price now?

5.) In 2001, the won 71.6% of the 162 games the played. Keeping in mind that it is not possible to win a fractional game, how many games did the Mariners win in 2001? (source: www.baseball-reference.com)

6.) a.) Write 5.3 x 1011 in regular notation.

b.) Write 2.2 x 10-8 in regular notation.

c.) Write 32,000,000,000 in scientific notation.

d.) Write 0.000000000425 in scientific notation.

e.) Use the scientific notation in part 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.) Estimate the total number of hamburgers eaten each year by left-handed Americans. Be sure to clearly state all of your assumptions.

8.) You put $3500 in the bank. The account gets an annual percentage rate of interest of 2.1% 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 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 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?

9.) You put $5100 in the bank. The account gets an annual percentage rate of interest of 3.45% compounded continuously. The money is left in the account for 3 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 three 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 three years.

c.) How much money will you have at the end of three years?

10.) You start putting money in your retirement fund at age 23. You put in $225 each month. The interest of 10.185% 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.

11.) You start putting money in a college savings account. You want to have $115,000 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?

12.) 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 15 year mortgage is 5.275%. 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?

13.) 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.

14.) You are buying a car. You are going to borrow $24,500 to pay off the car. The interest rate for your 6 year loan is 2.25%.

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?

15.) 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 who are shopping for a car at the local Mercedes dealership. Are his results likely to be representative of Arkansas? Why or why not?

Exam #3

1.) 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?

2.) 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.

3.) The following table gives some career statistics for , 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 season? What year?

b.) In how many seasons did he have a average (AVG) above .300?

c.) What is the most consecutive seasons in which he hit at least 30 home runs (HR)?

d.) In how many seasons did he exceed both 100 runs scored (denoted R) AND runs batted in (denoted RBI)?

4.) You are making a license plate. It has 3 letters followed by 4 numbers. How many different license plates can be made?

5.) The only major league players 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?

6.) Explain the difference between a linear model and an exponential model.

7.) 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?

8.) 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?

9.) The table below gives the number of base hits pitcher 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

10.) The following are the number of at bats for each of the 1969 New York Mets.

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

11.) 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?

12.) 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?

13.) The following chart gives a breakdown of some people in a class. Answer the following questions based on the chart.

Male Female Totals Freshmen 12 10 22 Sophomores 13 12 25 Juniors 5 9 14 Seniors 1 4 5 Totals 31 35 66

a.) If a student is chosen at random, what is the probability that the student is male?

b.) If a student is chosen at random, what is the probability that the student is a male junior?

c.) If a female is chosen at random, what is the probability that she is a sophomore?

d.) If a student is chosen at random, what is the probability that the student is a male or a junior?

14.) 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)

15.) 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.) A note has a frequency of 260 cycles per second. Find the frequency of the note that is:

a.) 5 half-steps above our note.

b.) 7 half-steps below our note.

c.) one octave above our note.

d.) one octave below our note.

e.) two octaves above our note.

2.) Draw a section of tile floor, with four rows of four tiles each, that illustrates the idea of vanishing points. Identify the principal vanishing point and two others.

3.) 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!!

4.) 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 180 degrees

d.) none of the above symmetries

5.) Consider a Fibonacci-like sequence with first term 3 and second term 2. Find the next four terms.

6.) Explain the difference between elections that are determined by majority and plurality voting.

7.) Give examples of two elections that require a super-majority vote. Be sure to give the percentage or fraction required in each vote.

8.) Consider a country consisting of 5 states with populations given below. If the country's legislature is to have 110 members, find the standard divisor and fill in the table below. Explain why you allot the representatives the way you did.

Standard Divisor =

State Population Standard # of representatives # of representatives Quota state "should" get you will give state A 9,000 B 3,025,751 C 4,266,000 D 8,664,974 E 8,664,975 Total Population 24,630,700

9.) Find the area and perimeter of the following trapezoid. Assume all units are in centimeters.

14

15 12 13

28

10.) 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!!

11.) Explain how a Borda Count works.

Final Exam

In exercises #1 - 3, an argument is given. For each exercise, identify one of the logical fallacies that is exhibited in that argument. GIVE A DETAILED EXPLANATION TO JUSTIFY YOUR CHOICE.

1.) "I don't know of any great Lithuanian authors so there must not be any great Lithuanian literature."

2.) "If we allow unregulated harvesting of our forests then what are we going to do about the increase in abuse of the food stamp program."

3.) "Dr. Worth, you can't give me an 'F' in this class. After all, I might lose my scholarship."

4.) Your living room is 15 feet by 18 feet. You are going to carpet it with carpet that costs $25 per square yard. How much will it cost to carpet your living room?

5.) Bubba weighs 347 pounds. What is his weight in scruples?

6.) You are driving 45 miles per hour. What is your speed in meters per second?

7.) a.) There are 45 socks in a drawer. They are all identical except for color. Ten of them are green, 12 of them are blue, three of them are plaid, 16 of them are brown and four of them are black. How many socks must you take from the drawer to be sure you have a matching pair of socks?

b.) 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.)

8.) The price of a coat was $800. It was reduced 10% on December 1. It was reduced 15% on December 10. What is the price now?

9.) The price of a coat was reduced 15%. The price now is $153. What was the original price.

10.) Bob Caruthers pitched 445 for the Brooklyn Bridegrooms in 1889. The Bridegrooms' pitching staff had a total of 1212 . What percentage of the total innings were pitched by Caruthers?

11.) You are borrowing $90,000 to buy a house. The interest rate for your 15 year mortgage is 5.75%. 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?

12.) 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?

13.) 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?

14.) The following chart shows the number of times Alex Rodriguez has grounded into double plays over the past ten years. Draw a line graph to illustrate this data.

Year GIDP 1996 15 1997 14 1998 12 1999 12 2000 10 2001 17 2002 14 2003 16 2004 18 2005 8

15.) The following chart gives the leaders from 1964.

Name 219 207 Tony Cloninger 163 217 237 172 245 171 Sandy Koufax 223 Denny Lemaster 185 192 Jim Maloney 214 206 Sam McDowell 177 213 Orlando Pena 184 205 162 Dick Radatz 181 Chris Short 181 Dick Stigman 159 Bob Veale 250 Dave Wickersham 164 166

a.) Find the mean.

b.) Find the median.

c.) Find the mode.

d.) Find the maximum.

16.) The Angels, Astros, Blue Jays, Devil Rays, Diamondbacks, Expos/Nationals, Mariners, Marlins, Mets, Padres, Pilots/Brewers, Rockies, and Royals are 's expansion teams. The following chart shows the number of games won by each of these teams from 1969 through 2005. 17.) 17. )

1925 Yankees 1925 Yankees 1924 Yankees 1923 Yankees 1922 Yankees 1921 Yankees 1920 Red Sox 1919 Red Sox 1918 Red Sox 1917 Red Sox 1916 Red Sox 1915 Red Sox 1914 Team The gives statistics.The some Babe following of Ruth's chart career couldmeals y desserts. you order oneofeach kindtypes If of ofitem, how many different possible pizza appetizers, 34 types of entrées, 18 non Olive Garden's on d.) c.) b.) a.)

2000 2500 3000 3500 1000 1500

500 period? teamsthese wonHow than more of 2000 many games duringthis time seasons? chart shows,teamsthe have four which probablyfewest the played teams of all these Not playstarted duringthe year. Based same on what How games many theseof Which team hasgames? won themost 0

153 152 110 152 142 130 98 95 52 67 42 G 5 ou order? ou

-

line menu lists nine appetizers, three salads, two soups, 163 Angels 359 529 522 406 540 458 432 317 123 136 AB 92 10

Astros

have won? theMets 143 151 177 158 103 61 94 50 14 18 16 R 1

Blue Jays

104 200 205 128 204 172 139

95 40 37 29 Devil Rays H 2

Diamondbacks 2B 12 39 45 24 44 36 34 26 10 6 5 1

Expos/Nationals 3B 13 16 12 11 2 7 8 9 3 3 1 0

Mariners HR 25 46 41 35 59 54 29 11 2 3 4 0

- Marlins alcoholic beverages and six

RBI 121 131 171 137 114 66 99 66 12 15 21 2

Mets

AVG .290 .378 .393 .315 .378 .376 .322 .300 .325 .272 .315 .200 Padres

OBP Pilots/Brewers .393 .513 .545 .434 .512 .532 .456 .411 .385 .322 .376 .200

Rockies SLG .543 .739 .764 .672 .846 .847 .657 .555 .472 .419 .576 .300

Royals

1926 Yankees 152 495 139 184 30 5 47 146 .372 .516 .737 1927 Yankees 151 540 158 192 29 8 60 164 .356 .486 .772 1928 Yankees 154 536 163 173 29 8 54 142 .323 .463 .709 1929 Yankees 135 499 121 172 26 6 46 154 .345 .430 .697 1930 Yankees 145 518 150 186 28 9 49 153 .359 .493 .732 1931 Yankees 145 534 149 199 31 3 46 163 .373 .495 .700 1932 Yankees 133 457 120 156 13 5 41 137 .341 .489 .661 1933 Yankees 137 459 97 138 21 3 34 103 .301 .442 .582 1934 Yankees 125 365 78 105 17 4 22 84 .288 .448 .537 1935 Braves 28 72 13 13 0 0 6 12 .181 .359 .431 TOTAL 2,503 8,399 2,174 2,873 506 136 714 2,213 .342 .474 .690

a.) In how many seasons did Ruth hit at least 40 home runs (denoted HR)?

b.) What was Ruth's highest batting average (denoted AVG)?

c.) How many times did Ruth get MORE than 200 hits (denoted H)?

d.) In which seasons did Ruth have more than 160 runs batted in (denoted RBI)?

18.) In 1969, , , , , , and were the main for the New York Mets. They needed to have a , a and a . Assuming each player can play each position, we are interested in how many different arrangements of these players they could have had.

a.) Is this a permutations problem or a combinations problem?

b.) How many different arrangements were possible?

19.) 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 , , Kevin Elster, , , Howard Johnson, Kevin McReynolds, 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?

b.) Three players hit more than 20 home runs. Who were they?

c.) How many home runs did hit?

d.) Who hit more home runs, Kevin McReynolds or Keith Hernandez?

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

22.) The following chart gives the on the New York Mets' current roster.

Name Height Weight Birth Date 1 Brian Bannister 6-2 200 02/28/81 2 6-3 225 09/29/77 3 Kris Benson 6-4 205 11/07/74 4 Bartolome Fortunato 6-1 195 08/24/74 5 Anderson Garcia 6-2 170 03/23/81 6 6-0 185 03/25/66 7 Tim Hamulack 6-4 220 11/14/76 8 6-5 220 11/12/78 9 Philip Humber 6-4 210 12/21/82 10 Matt Lindstrom 6-4 210 02/11/80 11 Pedro Martinez 5-11 180 10/25/71 12 Henry Owens 6-3 230 04/23/79 13 Juan Padilla 6-0 200 02/17/77 14 Juan Perez 6-1 170 09/03/78 15 Royce Ring 6-0 220 12/21/80 16 Jae Seo 6-1 215 05/24/77 17 6-4 205 10/31/70 18 Billy Wagner 5-11 200 07/25/71 19 Mitch Wylie 6-3 190 01/14/77 20 Tyler Yates 6-4 240 08/07/77 21 Victor Zambrano 6-0 205 08/06/75

Based on this chart, answer the questions below. a.) If a player is chosen at random, what is the probability he is under 6 feet tall?

b.) If a player is chosen at random, what is the probability he was born since 1/1/80?

c.) If a player is chosen at random, what is the probability that he weighs at least 200 pounds?

d.) If a player is chosen at random, what is the probability that he weighs at least 200 pounds or is under 6 feet tall?

23.) In 1985, the highest paid major league baseball player made $2,130,300. In 1986, the highest paid player earned $2,800,000. That was an increase of 31.4369%. If salaries continued to grow exponentially at that rate, what would the highest paid player have earned in 2005? (The highest paid player in 2005 made $26,000,000.)

24.) 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!!

25.) 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!!