Mathematics for the Liberal Arts Test File Summer 2006 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. 1.) "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."

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.) "I saw five people on the way to school today who didn't use their turn signals.

Folks in Arkansas must not know how to use turn signals." 4.) "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." 5.) In October 2005, a man won $1,000,000 (Can.) by kicking a 50 yard field goal

during halftime of a Canadian Football League. How much money did he win in $ (U.S.)? ALL NECESSARY WORK MUST BE SHOWN!! YOU MUST SHOW THE USE OF UNITS!!

6.) On September 10, 1960, Mickey Mantle hit a home run against Paul Foytack that

cleared the right-field roof at Tiger Stadium. Based on where it was found, it was later estimated to have traveled 643 feet. How many millimeters did the ball travel? ALL NECESSARY WORK MUST BE SHOWN!! YOU MUST SHOW THE USE OF UNITS!! (source: en.wikipedia.org)

7.) Construct a truth table for the following proposition. (not p ∧ q) → (not q) 8.) Construct a Venn Diagram to illustrate the proposition that "All dogs have fleas."

9.) 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.

M P 12 8 14 11 x 9 7 y 8 10 G

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?"

10.) Tom threw a baseball 45.4 meters per second. Dave threw a ball 98 miles per hour. Who threw the ball faster, Tom or Dave? ALL NECESSARY WORK MUST BE SHOWN!! YOU MUST SHOW THE USE OF UNITS!!

11.) Bob weighs 120 KILOGRAMS. He wants to lose weight to get down to 185

POUNDS. How many OUNCES does he need to lose? ALL NECESSARY WORK MUST BE SHOWN!! YOU MUST SHOW THE USE OF UNITS!!

12.) 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.) Sandy Koufax is the best left-handed pitcher 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. 13.) 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? ALL NECESSARY WORK MUST BE SHOWN!! YOU MUST SHOW THE USE OF UNITS!!

14.) 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. a.) How many socks must you take from the drawer to be sure you have a

matching pair of socks? b.) How many socks must you take from the drawer to be sure you have a

matching pair of plaid socks?

15.) 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.)

16.) 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.)

Exam #2

1.) In 1996, the total payroll for the New York Yankees was $63,000,000. Their total

operating expenses were $95,000,000. What percentage of their operating expenses went to payroll? (data from http://www.businessofbaseball.com/)

2.) In 2000, as a franchise, the New York Mets had a value of $314, 000,000. In

2001, their value went up 44.585987%. From 2001 to 2002, the value went up another 6.1674% What was the 2002 value? (data from http://www.businessofbaseball.com/)

3.) In 2003, Moises Alou of the Chicago Cubs made a salary of $9,500,000. That

was an increase of 58.3333333% from his 2002 salary. What was Alou's 2002 salary? (data from http://www.businessofbaseball.com/)

4.) The price of a recliner was $650. Two weeks ago the price was dropped 10%. This week it was dropped 15%. What is the price now?

5.) a.) Write 5.3 x 108 in regular notation.

b.) Write 2.2 x 10-5 in regular notation. c.) Write 41,200,000,000 in scientific notation. d.) Write 0.0000000545 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.

6.) You put $4500 in a savings account in the bank. The account gets an annual

percentage rate of interest of 2.35% 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?

7.) You put $3100 in the bank. The account gets an annual percentage rate of interest of 2.87% 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?

8.) You start putting money in your retirement fund at age 23. You put in $575 each quarter. 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.

9.) You start putting money in a college savings account. You want to have $125,000 in 18 years when your daughter will be ready for college. The interest rate of 7.95% 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? 10.) You are buying a house. After the down payment, you need to borrow $121,000.

You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 30 year mortgage is 6.375%. 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? 11.) You are buying a car. You are going to borrow $19,500 to pay off the car. The

interest rate for your 5 year loan is 2.55%.

a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will

use to find the monthly payment on this loan. b.) WITHOUT SIMPLIFYING ANYTHING, insert the correct numbers into the

formula. c.) What will be your monthly payment?

d.) What will be the total of all of your monthly payments? e.) How much interest will you pay over the life of the loan? 12.) A person is interested in finding out the average income of people in Arkansas.

In order to do that, he does a survey by asking the annual income of Arkansas residents who shopping for a car at the local Mercedes dealership. Are his results likely to be representative of Arkansas? Why or why not?

13.) CNN is doing a poll on their web site. Explain why this poll is biased. 14.) Estimate the total number of hot dogs eaten each year by female Americans. Be

sure to clearly state all of your assumptions. Exam #3 1.) 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 hit in one season? What year? b.) In how many seasons did he have a batting 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)?

2.) Explain the difference between a linear model and an exponential model. 3.) Barium-139 has a half-life of 82.7 minutes. If you have 9 grams of Barium-139,

how much will you have left in 12 hours? Be sure to show the formula you use. 4.) The following chart shows the innings pitched (IP) and strikeouts (SO) for Sandy

Koufax during his career. (source: www.baseball-reference.com)

050

100150200250300350400

1955

1956

1957

1958

1959

1960

1961

1962

1963

1964

1965

1966

IPSO

a.) In what year did Koufax have the most strikeouts? How many did he

have? b.) How many times did Koufax strike out more than 300 batters? c.) How many times did Koufax have more strikeouts than innings pitched?

5.) In 1860, the population of Fort Smith, Arkansas was 1,532. By 1880, it had doubled. If the exponential rate of growth had continued, what would Fort Smith's population be in 2006?

6.) The table below gives the number of base hits pitcher Jerry Koosman had in his

first six full seasons in the major leagues.

YEAR HITS1968 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

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

Male Female Totals

Freshmen 8 10 18 Sophomores 6 7 13

Juniors 9 7 16 Seniors 12 13 25 Totals 35 37 72

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

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

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

a male or a sophomore?

8.) The following chart gives the strikeout leaders from 1964.

Name Strikeouts

Jim Bunning 219 Dean Chance 207 Tony Cloninger 163 Al Downing 217 Don Drysdale 237 Whitey Ford 172 Bob Gibson 245 Jim Kaat 171 Sandy Koufax 223 Denny Lemaster 185 Mickey Lolich 192 Jim Maloney 214 Juan Marichal 206 Sam McDowell 177 Camilo Pascual 213 Orlando Pena 184 Gary Peters 205 Juan Pizarro 162 Dick Radatz 181 Chris Short 181 Dick Stigman 159 Bob Veale 250 Dave Wickersham 164 Earl Wilson 166

a.) Find the mean.

b.) Find the median. c.) Find the mode. 9.) 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 heads.

10.) 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? 11.) 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

12.) You have a box. In the box are 8 red marbles, 5 blue marbles, and 11 plaid

marbles.

a.) If you reach into the box and pull out a marble, what is the probability the marble is plaid?

b.) If you pull out a marble, note its color, put it back and pull out another

marble, what is the probability both marbles are blue?? c.) If you pull out a marble, note its color and pull out another marble, what is

the probability both marbles are blue?

13.) The only major league players to have at least 20 doubles (denoted 2B), 20 triples (denoted 3B), 20 homeruns (denoted HR) and 10 stolen bases (denoted SB) in a single 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).

0

5

10

15

20

25

30

35

40

45

SB 2B 3B HR

MaysSchulteHeathBrettBottomley

a.) Which player(s) had exactly 20 triples? b.) Which player hit the most home runs? c.) Which player had the fewest stolen bases? d.) How many stolen bases did Willie Mays have?

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

Ang

els

Ast

ros

Blu

e Ja

ys

Expo

s/N

atio

nals

Mar

iner

s

Met

s

Padr

es

Pilo

ts/B

rew

ers

Roy

als

Dev

il R

ays

Dia

mon

dbac

ks

Mar

lins

Roc

kies

0

500

1000

1500

2000

2500

3000

3500

a.) Which of these team has won the most games? b.) How many games have the Mets won? c.) Not all of these teams started play during the same year. Based on what

the chart shows, which four teams have probably played the fewest seasons?

d.) How many of these teams won more than 2000 games during this time

period?

15.) 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?

Exam #4 1.) Find the area and perimeter of the following triangle. Assume all units are in

centimeters.

Area______________________

Perimeter__________________ 2.) 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!!

Volume_______________________

Surface Area__________________

3.) A Fibonacci-like sequence has a first term of 2 and a second term of 8. Find the: a.) third term b.) fourth term c.) fifth term d.) sixth term 4.) 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. 5.) 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

6.) Explain the difference between votes that are decided by majority vote and those decided by plurality vote.

7.) Middle C has a frequency of 260 cycles per second. Find the frequency of the

note that is: a.) 5 half-steps above Middle C. b.) 7 half-steps below Middle C. c.) one octave above Middle C. d.) one octave below Middle C. e.) two octaves above Middle C.

8.) Explain what a Borda count is and give an example. 9.) 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!!

Area______________________

Perimeter__________________

10.) Consider a country consisting of 5 states with populations given below. If the

country's legislature is to have 100 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

Quota with normal

rounding, # of representatives

state "should" get

# of representatives you will give state

A 6,205,331 B 6,205,332 C 1,815 D 19,886,060 E 10,234,549

Total Population 42,533,087 Final Exam In exercises #1 - 3, an argument or advertisement is given. For each exercise, identify one and only one of our fallacies that is exhibited in that argument or advertisement. GIVE A DETAILED EXPLANATION TO JUSTIFY YOUR CHOICE. 1.) "Yesterday, my grandfather forgot where he put his glasses. Sounds like

grandpa has Alzheimer's Disease." [Hint: This is NOT personal attack.] 2.) Quoting Senator Joseph McCarthy in the 1950s alleging a member of the state

department was a communist sympathizer: "I do not have much information on [him] except the general statement of the agency…that there is nothing in the files to disprove his communist connections." [from http://www.fallacyfiles.org]

3.) "Every time my brother Bill accompanies me to Fenway Park, the Red Sox are

sure to lose. I won't let him go with me tomorrow because I want the Red Sox to win." [from http://www.don-lindsay- archive.org/skeptic/arguments.html]

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.) A Canadian company is advertising a jacket for $59.99 (Can.). How much would

it cost in Austrian shillings? 6.) During spring training in 1995, Mark Wohlers, then of the Atlanta Braves, was

clocked throwing a baseball at a speed of 103.0 miles per hour. What is that speed in feet per second? You must show the use of units. (data from http://baseball-almanac.com/)

7.) Do these problems.

a.) You are considering buying 13 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. How can you determine the lightweight coin in a maximum of three weighings on a balance scale? (A balance scale just indicates which of two items is heavier.)

b.) You have a seven minute hour glass and a nine minute hour glass. You

are cooking something that must be cooked for exactly one minute. 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.]

8.) Do either of these two problems. BE SURE TO CIRCLE THE LETTER OF THE

ONE YOU WANT TO COUNT!!!!!!!

a.) 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.

(i.) How many socks must you pull out so that it is certain you have a

matching pair of socks? Explain your answer. (ii.) How many socks must you pull out so that it is certain you have a

matching pair of green socks? Explain your answer.

b.) There are 10 rectangular tables in a rectangular room. You must set up the tables so there are 3 tables against each wall.

9.) Bubba's salary in 2002 was $10,000. He received a 7% raise in 2003 and a 3%

raise in 2004. How much did Bubba earn in 2004? 10.) In 1910, the population of Leslie, Arkansas was 1,898. By 1990, the population

had dropped 76.5%. What was the population in 1990. (Think about how you should round off the answer.) [data from US census bureau]

11.) In 2003, Hank Blalock of the Texas Rangers was paid $302,500. That was an

increase of 51.25% over his 2002 salary. What was his 2002 salary? 12.) You start putting money in your retirement fund at age 27. You put in $650 each

quarter. The interest of 10.75% 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 63.

b.) Without doing any simplification, insert all of the numbers into the formula. c.) How much money will you have at age 63?

d.) What is the total of all of your payments? e.) How much interest did your money earn? 13.) Bubba is borrowing $40,000 to buy a new double-wide. The interest rate for his 15

year mortgage is 5.35%. 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 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? 14.) You put $2000 in the bank. The interest, which is compounded continuously, is

4.55%. No additional money is deposited. No money is withdrawn.

a.) WITHOUT SUBSTITUTING IN ANY NUMBERS, write the formula you will use to find how much money you have after 4 years.

b.) WITHOUT SIMPLIFYING ANYTHING, insert the correct numbers into the

formula. c.) Find the amount of money you would have after 4 years.

15.) The following table tells how many home runs (HR) Hall of Famer Ralph Kiner hit during each year of his career. Draw a line graph illustrating this data. Year HR 1946 23

1947 51

1948 40

1949 54

1950 47

1951 42

1952 37

1953 35

1954 22

1955 18 16.) A box contains five regular tacos, seven soft tacos, eight bean burritos, and four

tostadas. You reach into the box and randomly choose an item.

a.) What is the probability that you pulled out a regular taco? b.) Without replacing the first item, you pull out another. What is the

probability that this one is also a regular taco?

17.) Explain what is meant when an election requires a super majority. Give 2 examples of votes that require a super majority.

18.) The following chart gives the games won by Warren Spahn during each year that

he played in the major leagues.

Year W Year W

1942 0 195620

1946 8 195721

1947 21 195822

1948 15 195921

1949 21 196021

1950 21 196121

1951 22 196218

1952 14 196323

1953 23 1964 6

1954 21 1965 7

1955 17 a.) For the number of wins, find the mean. b.) For the number of wins, find the median. c.) For the number of wins, find the mode.

d.) Extra Credit: Notice Spahn didn't play from 1943 - 1945. Why not? [Note: "Insufficient information given to answer the question" is not a good enough answer.]

19.) You roll two dice. What is the probability that the sum of the numbers on the

dice is greater than 9? 20.) The following chart shows the number of major league baseball players, by

decade, that were born on February 24, June 29 and December 24.

0

1

2

3

4

5

6

7

8

1840

s

1850

s

1860

s

1870

s

1880

s

1890

s

1900

s

1910

s

1920

s

1930

s

1940

s

1950

s

1960

s

1970

s

1980

s

24-Feb29-Jun24-Dec

a.) Which date had the most player births in the 1950s? b.) How many players share my birthday of February 24, 1958? c.) Which date in which decade had the most player births? d.) Which decade(s), if any, had all dates have at least 4 player births?

21.) In 1969, Tommie Agee, Cleon Jones, Ron Swoboda, Art Shamsky, Rod Gaspar, and Amos Otis were the main outfielders for the New York Mets. They needed to have a right fielder, a left fielder and a center fielder. 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? 22.) Middle C has a frequency of 260 cycles per second. Find the frequency of the

note that is:

a.) 5 half-steps above Middle C. b.) 7 half-steps below Middle C. c.) one octave above Middle C. d.) two octaves below Middle C.

23.) In 1953, the Braves baseball franchise started playing in Milwaukee instead of Boston. A large factor in the move was dwindling attendance. The graph below shows the attendance in Boston during the last 12 years before the move.

Boston Braves Attendance

0200,000400,000600,000800,000

1,000,0001,200,0001,400,0001,600,000

1941

1942

1943

1944

1945

1946

1947

1948

1949

1950

1951

1952

Year

Att

enda

nce

a.) What was the Braves attendance in 1944? b.) In which of these years was the attendance the highest? What was it that

year? c.) In how many of these years was the attendance over 1,000,000? d.) How many games did the Braves win in 1944?

240.) Consider the letters E, F, G, H, I, J, K, M, L, N, and O. For our purposes, a

"word" is ANY arrangement of letters (for example, GGKKJ is a "word"). a.) How many five letter "words" can be made from these letters if repetitions

are allowed? b.) How many five letter "words" can be made from these letters if no

repetitions are allowed?

25.) 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!!

Area_________________

Perimeter_________________