sign in sign up
<<
Home , Albert Pujols, Al Downing (baseball), Al Simmons, Babe Herman, Batting average, Billy Gardner

Mathematics for Practical Applications - Exam File Spring 2010

Exam #1

In exercises #1 - 5, a statement is given. For each exercise, identify one AND ONLY ONE of our fallacies that is exhibited in that statement. GIVE A DETAILED EXPLANATION TO JUSTIFY YOUR CHOICE. DO NOT USE THE SAME ANSWER TWICE.

1.) "He's made his last five shots so he's bound to miss this one." 2.) "Who is going to win the this year, the Yankees or the Nationals?" 3.) " does that Ford commercial so I'm going to buy a Ford. Jeter wouldn't do the commercial if Ford's weren't great cars." 4.) "A-Rod isn't a very good . After all, in 2008, he had more than RBIs." 5.) " is such a jerk, he can't be the best hitter of all time."

6.) The part of a major league that is inside the bases is a square that is 90 feet on each side. How many acres is that? You must show the use of units and conversion factors.

7.) Suppose you went back in time 1,000,000,000 (1 billion) seconds. What year would it be?

8.) If a pitch is thrown 97 miles per hour, how fast is it in meters per second?

9.) CC Sabathia signed a contract with the for $161 million. Convert the contract amount to Mexican pesos. You must show the use of units and conversion factors.

10.) On September 10, 1960, a home against Paul Foytack that cleared the right-field roof at . Based on where it was found, it was later estimated to have traveled 643 feet. How many millimeters did the ball travel? You must show the use of units and conversion factors.

11.) A person is interested in finding what college football team people in the like most. In order to do that, he does a survey by asking people in Arkansas what their favorite college football team is. Are his results likely to be representative of Americans? Why or why not?

12.) CNN is doing a poll on their web site. Explain why this poll is biased.

13.) For each of the following, tell whether it is an example of a qualitative statistic or a quantitative statistic. a.) height of people who play baseball professionally b.) of times a batter strikes out with men on base and less than two out c.) eye color of students at Henderson State University d.) percentage of freshmen students at Henderson State University who finish with a GPA of 3.0 or higher

14.) Name five different rule changes or changes in style of play that we discussed that make it difficult to compare statistics different eras of baseball history.

Exam #2

1.) In 1972, Nate Colbert, of the Padres, had 111 runs batted in. The entire team only scored 488 runs. What percentage of the Padres' runs did Colbert knock in? 2.) In 2004, of the St. Louis Cardinals was paid $7,000,000. For 2005, his salary went up 57.14285714%. For 2006, his salary went up 27.27272727%. What was his 2006 salary? 3.) A car was on sale for $10,875. That was 13% off the original price. What was the original price? 4.) The following chart shows the number of times Baby Doll Jacobson was hit by pitches (HBP) during 1920 to 1925. Year 1920 1921 1922 1923 1924 1925 HBP 2 3 9 2 4 1 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 HBP in those seasons. a.) the mean b.) the median c.) the mode

5.) The following are the major league leaders in at bats (AB) from 1960. Name AB Name AB 590 Don Hoak 553 600 568 597 574 552 595 629 595 569 Minnie Minoso 591 570 652 555 580 605 595 592 571 557 581 573 Bill Tuttle 559 Bill White 554

For the above data, find the following. a.) minimum b.) lower quartile c.) median d.) upper quartile e.) maximum f.) mean g.) mode

6.) Comparisons a.) and both played for the 1966 . Killebrew's average was .281. Oliva's was .307. Explain why this does not necessarily indicate that Oliva was a better hitter that year. Give at least two reasons. b.) In 1967, Sam McDowell of the Indians struck out 236 batters. In 1929, of the Athletics struck out 170 batters. Explain why this does not necessarily indicate that McDowell was a better in 1967 than Grove was in 1929. Give at least two reasons. c.) In 1879, the Providence Grays won 59 games. In 1966, the Cubs won 59 games. Explain why this does not necessarily indicate that the 1966 Cubs and the 1879 Grays had the same level of success. Give at least two reasons.

7.) The following chart shows some batting statistics for from 1924. Fill in the blanks.

At Hits Doubles Triples Home Batting On Base Slugging OPS Total Bats Runs Average Percentage Percentage Bases 536 227 43 14 25 .507

8.) The following are the pitching statistics for in 1973. Fill in the blanks.

Wins Losses Winning Hits Earned Hits per Percentage Average Pitched Runs 3 9 88.66 109 97

9.) The following are the standings for the East after the games of September 3, 1986.

Team W L PCT GB Magic Number for Mets to eliminate team 89 44 ------ 69 64 .519 St. Louis Cardinals 67 66 .504 64 66 ------ 55 78 .414 ------ Pirates 54 78 ------

10.) The following table gives the major league leaders in OPS from 1930. Fill in the blanks.

OPS On Base Average 1 .493 .732 2 1.194 .721 3 1.177 .454 4 .455 .678 5 1.130 .708 6 1.123 .436 7 1.071 .452 .619 8 .429 .637 9 1.059 .652 10 Lefty O'Doul 1.057 .453

11.) The following are Lance Alworth's statistics for the 1965 San Diego Chargers. Fill in the blanks.

Receiving Rushing Games Receptions Yards Yards per Receptions Attempts Yards Yards Reception per Game per Attempt 14 69 1602 3 -12

12.) The following are Wilt Chamberlain's statistics for the 1961-1962 NBA . Fill in the blanks.

Games Field Field Goals Field Rebounds Rebounds Points Points Goals Attempted Goal per game per % Game 80 1597 3159 2052 4029

13.) The following are some statistics for Lady Reddies volleyball player Quen Banks from 2008. Fill in the blanks.

Sets Kills Kills Attack Total Kill played per set Errors attacks Percentage 104 334 141 834

14.) Matching - For each item in Column B, place in the blank the number of the associated name from Column A. Note that there are more choices in Column A than in Column B. No answer should be used more than once.

Column A Column B 1.) 1869 Red ______"The Father of Baseball" Stockings ______began collecting players' lifetime statistics that were not available 2.) 1884 Troy Trojans anywhere, eventually publishing a book, Who's Who in Baseball, in 1912 3.) Alan Roth ______hired the first full-time statistician 4.) Albert Spalding ______In 1977, he published his first Abstract, giving statistics along with analysis and 5.) Art Richmond commentary. According to Schwarz, he did more than anyone else to 6.) Babe Ruth popularize the study of and analysis. 7.) ______National League secretary and statistics fanatic, particularly pitching 8.) statistics ______star pitcher, , helped form 9.) National League in 1876, started sporting goods company 10.) ______the appeal of his home runs led

baseball to try to help increase power 11.) hitting

12.) John Lawres ______the first openly professional team ______was hired as first full-time statistician 13.) Lee Allen ______Was the preeminent baseball historian of the era of the 20th 14.)

Exam #3

1.) The following chart gives the number of triples hit during his first eight years in the major leagues. Draw a line graph to illustrate the data. Year Triples 1897 4 1898 3 1899 13 1900 22 1901 11 1902 16 1903 19 1904 14

2.) The following pie chart shows the 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? 3.) The following chart gives career statistics for Grover Cleveland Alexander. Answer the questions below based on the information in the chart.

Year W L W-L% ERA G CG SHO IP SO 1911 28 13 .683 2.57 48 31 7 367 227 1912 19 17 .528 2.81 46 25 3 310-1/3 195 1913 22 8 .733 2.79 47 23 9 306-1/3 159 1914 27 15 .643 2.38 46 32 6 355 214 1915 31 10 .756 1.22 49 36 12 376-1/3 241 1916 33 12 .733 1.55 48 38 16 389 167 1917 30 13 .698 1.83 45 34 8 388 200 1918 2 1 .667 1.73 3 3 0 26 15 1919 16 11 .593 1.72 30 20 9 235 121 1920 27 14 .659 1.91 46 33 7 363-1/3 173 1921 15 13 .536 3.39 31 21 3 252 77 1922 16 13 .552 3.63 33 20 1 245-2/3 48 1923 22 12 .647 3.19 39 26 3 305 72 1924 12 5 .706 3.03 21 12 0 169-1/3 33 1925 15 11 .577 3.39 32 20 1 236 63 1926 12 10 .545 3.05 30 15 2 200-1/3 47 1927 21 10 .677 2.52 37 22 2 268 48 1928 16 9 .640 3.36 34 18 1 243-2/3 59 1929 9 8 .529 3.89 22 8 0 132 33 1930 0 3 .000 9.14 9 0 0 21-2/3 6 Total 373 208 .642 2.56 696 437 90 5190 2198

a.) How many times did Alexander have an (ERA) below 2.00? b.) What was the most wins Alexander ever had in one season? What year? c.) How many wins did Christy Matthewson have in 1914? d.) What is the most consecutive seasons in which Alexander had at least 100 strikeouts (SO)?

4.) 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?

5.) The following are the leader totals in triples for the 1986 Minnesota Twins. 7 6 5 4 6 4 Without using your calculator, find the following. Be sure to show or explain how you got each answer.

a.) mean b.) median c.) mode d.) maximum e.) minimum

6.) The following chart gives the strikeout leaders from 1964. Name Strikeouts Name Strikeouts 219 206 207 Sam McDowell 177 163 213 217 Orlando Pena 184 237 205 172 162 245 181 171 181 223 Dick Stigman 159 185 250 192 164 214 166 Find the following: (You may use your calculator) a.) mean

b.) mode

c.) five number summary: minimum lower quartile median upper quartile maximum

7.) In 1897, all three for the Phillies batted at least .400. Billy Hamilton hit .404 and and each hit .407. We will view their batting averages as probabilities, assume that all at bats are independent events and ignore walks, etc.

a.) Assume that the three bat right after each other in one inning. What is the probability that all three get hits?

b.) Assume that the three bat right after each other in one inning. What is the probability that all three make outs?

c.) Assume that the three bat right after each other in one inning. What is the probability that Hamilton gets a hit but Thompson and Delahanty make outs?

d.) If Delahanty has two at bats, what is the probability that he gets hits both times?

e.) If Hamilton bats six times, what is the probability he gets at least one hit?

f.) If Delahanty and Hamilton bat, what is the probability that one, but not both, gets a hit?

8.) Consider the eight letters G, H, I, J, K, M, L, and N. For our purposes, a "word" is ANY arrangement of letters.

a.) How many four letter "words" can be made from these letters if repetitions are allowed?

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

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.) You are managing a baseball team and want to pick the nine players for a game. On your team you have 10 , three , six and six outfielders. You must choose a pitcher and a . From the infielders, you must pick a first baseman, a , a and a shortstop. From the outfielders, you must pick three. How many different nine player arrangements can you pick?

11.) 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?

12.) In 1920, Babe Ruth had the following probabilities for the given batting events. made an out 0.624 singled 0.159 doubled 0.079 tripled 0.020 homered 0.118 What was the expected value for the number of bases Ruth would get on a given ?

13.) The following are the National League 1st baseman from 1997 with at least 400 plate appearances.

Batting Homers Runs Slugging Fielding Average Batted In Percentage Average Andres Galarraga .318 41 140 .585 .991 David Segui .307 21 68 .505 .995 .266 31 104 .459 .992 Fred McGriff .277 22 97 .441 .990 J.T. Snow .281 28 104 .510 .995 .286 43 135 .592 .993 .242 17 61 .405 .992 .294 22 102 .489 .995 .319 13 78 .465 .995 Rico Brogna .252 20 81 .433 .994 .327 13 83 .486 .996

a.) Which player was the best? Give reasons for your answer.

b.) Which player was the worst? Give reasons for your answer.

14.) 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.

15.) Fill in the blank a.) ______is the man cited in Schwarz's book for starting www..org. b.) ______invented the pie chart.

Exam #4

1.) You put $2500 in the bank. The account gets an annual percentage rate of interest of 1.21% compounded quarterly. The money is left in the account for 4 years. No other money is added or removed from the accounts.

a.) Without inserting any numbers, write the formula you will need for this problem.

b.) Without doing any simplification, insert the right numbers in the right places in the formula.

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

2.) You start putting money in your retirement fund at age 23. You put in $400 each month. The interest of 10.25% is compounded monthly. You retire at age 65.

a.) Without inserting any numbers, write the formula you will need for this problem.

b.) Without doing any simplification, insert the right numbers in the right places in 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?

3.) Maher-Shalal-Hash-Baz started putting money in a college savings account. He wants to have $125,000 in 18 years when his son will be ready for college. The interest rate of 5.5% is compounded quarterly. He'll make quarterly payments.

a.) Without inserting any numbers, write the formula you will need for this problem.

b.) Without doing any simplification, insert the right numbers in the right places in the formula.

c.) How much money will he have to pay each quarter?

d.) What is the total of all of his payments?

e.) How much interest did his money earn?

4.) 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 30 year mortgage is 4.35%.

a.) Without inserting any numbers, write the formula you will need for this problem.

b.) Without doing any simplification, insert the right numbers in the right places in 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?

5.) Find the area and perimeter of the following parallelogram. All measurements are in feet.

6.) 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.

7.) A conical container 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.

8.) In 1985, the highest paid 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.)

9.) Below is the 1923 baseball design of the in . Approximate the area (in acres) of fair territory. BE SURE TO SHOW ALL OF YOUR WORK.

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

11.) Suppose a ball is hit from a height of 4 feet with a velocity of 79 miles per hour (115.8667 feet per second) at an angle of elevation of 43. Find the following.

a.) how far it travels

b.) if it is a home run over an 8 foot tall fence at 400 feet (explain the reasoning for your answer)

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

13.) Suppose the following are the votes received for the Most Valuable Player.

a.) Calculate the total points for each player shown. (1st place gets 14 points, 2nd place gets 9, 3rd place gets 8, 4th place gets 7, 5th place gets 6, 6th place gets 5, 7th place gets 4, 8th place gets 3, 9th place gets 2, 10th place gets 1)

Player, Club 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th Points , NYM 10 15 6 1 Albert Pujols, STL 5 3 5 4 4 11 , PHI 2 7 8 4 3 7 1

b.) What is the type of vote that this represents?

Final Exam

In exercises #1 - 3, a statement is given. For each exercise, identify one AND ONLY ONE of our fallacies that is exhibited in that statement. Do not use the same fallacy for two different problems. GIVE A DETAILED EXPLANATION TO JUSTIFY YOUR CHOICE.

1.) "More people drink Coca Cola than any other soft drink so it must be good." 2.) "The Cubs haven't won the world series for 104 years so they are due to win this year." 3.) "Derek Jeter did a commercial for Ford so I'm going to go buy a Ford. After all, Jeter wouldn’t endorse a bad car."

4.) The area inside the base paths in baseball is a 90 foot by 90 foot square. a.) What is that area in acres? b.) What is that area converted to meters?

5.) If Jose Reyes hits an inside the park home run, running 385 feet (the base paths would be 360 feet but a 90 degree turn is tough) in 12.5 seconds, then what is his average speed in miles per hour?

6.) C.C. Sabathia, a pitcher for the Yankees, is 6'7" tall and weighs 290 pounds. Convert his weight to kilograms and his height to meters. ALL NECESSARY WORK MUST BE SHOWN!! YOU MUST SHOW THE USE OF UNITS!!

7.) In 1920, Babe Ruth hit 54 home runs for the Yankees. As a team, the Yankees hit a total of 115 home runs. The next highest team total in the league was the St. Louis Browns' total of 50, so Ruth out homered every other team in the league. The entire league hit 369 home runs. a.) What percentage of the league's home runs were hit by Babe Ruth? b.) What percentage of the league's home runs were hit by Yankees?

8.) In 2005, Jose Guillen was paid $3,500,000. That was a raise of 59.09090909% from his 2004 salary. How much was he paid in 2004?

9.) In 2008, Jose Guillen had 598 at bats, 158 hits, 42 doubles, one and 20 home runs. a.) What was his ? b.) What percentage of his hits were doubles? c.) How many did he have? d.) What was his slugging percentage? 10.) In 1915, Grover Cleveland Alexander had 31 wins, 10 losses, 376.333 , 241 strikeouts and allowed 51 earned runs. a.) What was his ? b.) What was his earned run average? c.) How many strikeouts did he have per inning?

11.) The following table gives career statistics for William "Baby Doll" Jacobson. He was not in the major leagues in 1916 or 1918. Year AB R H 2B 3B HR RBI BA TB 1915 180 18 38 12 3 1 13 .211 59 1917 529 53 131 23 7 4 55 .248 180 1919 455 70 147 31 8 4 51 .323 206 1920 609 97 216 34 14 9 122 .355 305 1921 599 90 211 38 14 5 90 .352 292 1922 555 88 176 22 16 9 102 .317 257 1923 592 76 183 29 6 8 81 .309 248 1924 579 103 184 41 12 19 97 .318 306 1925 540 103 184 30 9 15 76 .341 277 1926 576 62 172 51 2 8 90 .299 251 1927 293 27 72 17 3 1 42 .246 98 totals 5507 787 1714 328 94 83 819 .311 2479

a.) What was the most home runs (denoted HR) he hit in a season? What year? b.) How many times was his batting average (denoted BA) higher than his career batting average? c.) How many doubles (denoted 2B) did have in 1923? d.) How many times did Jacobson have at least 120 singles? (hint: enough information IS given to answer this question) 12.) The following chart shows the major league pitchers who had at least 250 innings pitched in 1966. Innings Wins Losses Walks Strike Earned Run Pitched Outs Average Bob Gibson 280 21 12 78 225 2.44 Bob Veale 268 16 12 102 229 3.02 Chris Short 272 20 10 68 177 3.54 Denny McLain 264 20 14 104 192 3.92 Earl Wilson 264 18 11 74 200 3.07 255-2/3 21 8 40 201 2.99 Jim Bunning 314 19 14 55 252 2.41 Jim Kaat 304-2/3 25 13 55 205 2.75 Juan Marichal 307 25 6 36 222 2.23 Sandy Koufax 323 27 9 77 317 1.73

a.) Draw a bar graph to illustrate the number of wins for these pitchers.

b.) Based on these statistics, tell who you think were the four best among these pitchers. Give a detailed argument.

13.) The following chart gives the major league leaders in extra base hits from 1929.

Al Simmons 84 59 Lou Gehrig 77 Babe Herman 76 Hack Wilson 74 81 Babe Ruth 78 63 66 77 61 73 Chick Hafey 85 72 Pinky Whitney 65 Chuck Klein 94 Jimmie Foxx 65 59 83 Johnny Frederick 82 Rogers Hornsby 94 64 Lefty O'Doul 73 69 74 65 66

a.) What is the mean? b.) What is the median? c.) What is the mode? d.) What is the minimum? e.) What is the lower quartile? f.) What is the upper quartile? g.) What is the maximum? h.) Who hit the most home runs in major leagues in 1929?

14.) The Mets are going to start the following people in a game: , Rod Barajas, Luis Castillo, Ike Davis, Jose Reyes, David Wright, , , and Angel Pagan. Santana is going to bat 9th. Either Pagan or Reyes will bat 1st or 2nd. Davis, Wright, Bay and Francoeur are going to bat 3rd, 4th, 5th and 6th (though not necessarily in that order). Castillo and Barajas will bat 7th or 8th. How many different lineups can the Mets use?

15.) The following chart lists the players with the most home runs from 2005-2009. It also tells how many doubles and triples each of these players had.

a.) Which player hit the most home runs from 2005-2009? b.) Which major leaguer had the most doubles from 2005-2009? c.) How many home runs did Albert Pujols hit from 2005-2009? d.) How many home runs did hit in 2007? e.) Of these players, which player had the most triples from 2005-2009? f.) How many players had at least 200 home runs from 2005-2009? g.) Of these players, how many had at least 150 doubles from 2005-2009? h.) Who does Dr. Worth think is the best baseball player of all time?

16.) 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 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? e.) How many pitchers won at least two games for the 1916 Athletics? f.) The 1916 Athletics lost 117 games. What percentage of their games did they win? g.) Who led the in wins in 1916? h.) According to the notes for this class, who invented the pie chart?

17.) For the 1894 Phillies, Sam Thompson had a batting average of .415, Ed Delahanty hit .404 and Billy Hamilton hit .403. Using the batting averages as probabilities of getting a hit, answer the following questions.

a.) If the three players each bat, what is the probability all three will get a hit? b.) If the three players each bat, what is the probability all three make outs? c.) If the three players each bat, what is the probability at least one will get a hit? d.) If Thompson bats six times, what is the probability he will get at least one hit?

18.) a.) Draw a tree diagram to illustrate the flipping of three coins. b.) What is the probability of getting at least two heads? c.) What is the probability of getting at least one tail?

19.) You put $5400 in the bank. The account gets an annual percentage rate of interest of 1.21% compounded quarterly. 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?

20.) Mephibosheth started putting money in a college savings account. He wants to have $110,000 in 18 years when his son will be ready for college. The interest rate of 5.75% 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?

21.) You are buying a house. After the down payment, you need to borrow $112,000. You will take out a mortgage to cover the remaining cost of the house. The interest rate for your 30 year mortgage is 4.655%. 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?

22.) Mineral Springs, Arkansas had a population of 546 in 1880. By 1900, it had lost half of its population. Assuming the population continued to decline exponentially at the same rate, what would the population be in 2005? (Note: the actual 2000 population was 1,264.)

23.) 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!! 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.) The following chart shows the leading vote getters for the American League Award in 2007.

a.) If the players get 5 points for a first place vote, 3 for a second place vote and one for a 3rd place vote, fill in the total points for each player. Pitcher 1st 2nd 3rd Total , L.A. 1 5 16 , Bos 8 14 4 CC Sabathia, Cle 19 8 0

b.) What type of vote is this?