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Math Project Matrix

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Math Project Matrix

  1. 1. Problems
  2. 2. <ul><li>A soccer club has 22 players, including C.Ronaldo and Fredinand. </li></ul>Ronaldo Ferdinand
  3. 3. <ul><li>One day, the coach has to choose 12 players from 22 players to participate in the league. </li></ul>Whoa! We MUST win this little thing !!!
  4. 4. <ul><li>What’s the probability that : </li></ul>Ronaldo and Ferdinand are both chosen for the team ? You two come here ! Quick ! What ??? YAY !!!
  5. 5. <ul><li>In this problem, the coach has to choose 12 players amongst 22 players . </li></ul>
  6. 6. <ul><li>In this problem, the coach has to choose 12 players amongst 22 players. </li></ul><ul><li>So the order doesn’t matter (because we do not really care who the coach will choose first.) </li></ul>
  7. 7. <ul><li>In this problem, the coach has to choose 12 players amongst 22 players. </li></ul><ul><li>So the order doesn’t matter (because we do not really care who the coach will choose first.) </li></ul>=> We can use the “Choose” formula to solve this problem.
  8. 8. <ul><li>In this problem, the coach has to choose 12 players amongst 22 players. </li></ul><ul><li>FIRST STEP... </li></ul>
  9. 9. <ul><li>In this problem, the coach has to choose 12 players amongst 22 players. </li></ul><ul><li>FIRST STEP... </li></ul>Calculate the number of ways to choose 12 players from 22 players
  10. 10. <ul><li>The number of ways to choose 12 player from 22 players is presented by this equation : </li></ul>
  11. 11. <ul><li>The number of ways to choose 12 player from 22 players is presented by this equation : </li></ul><ul><li>C </li></ul>
  12. 12. <ul><li>The number of ways to choose 12 player from 22 players is presented by this equation : </li></ul><ul><li> C </li></ul>22 22 players of the club
  13. 13. <ul><li>The number of ways to choose 12 player from 22 players is presented by this equation : </li></ul><ul><li>22 C </li></ul>12 Choose 12 players from 22 players
  14. 14. <ul><li>The number of ways to choose 12 player from 22 players is presented by this equation : </li></ul><ul><li>22 C 12 = </li></ul>
  15. 15. <ul><li>The number of ways to choose 12 player from 22 players is presented by this equation : </li></ul><ul><li>22 C 12 = 646646 </li></ul>Ok now we got this : 646646
  16. 16. <ul><li>In this problem, the coach has to choose 12 players amongst 22 players. </li></ul>SECOND STEP...
  17. 17. <ul><li>In this problem, the coach has to choose 12 players amongst 22 players. </li></ul>SECOND STEP... Calculate the number of ways to choose both Ronaldo and Ferdinand
  18. 18. <ul><li>The number of ways to choose both Ronaldo and Ferdinand is presented by this equation: </li></ul><ul><li>C </li></ul>
  19. 19. <ul><li>The number of ways to choose both Ronaldo and Ferdinand is represented by this equation: </li></ul><ul><li>C </li></ul>2 2 This number represents 2 players (Ronaldo and Ferdinand) Choose 2 players (both Ronaldo and Ferdinand)
  20. 20. <ul><li>The number of ways to choose both Ronaldo and Ferdinand is represented by this equation: </li></ul><ul><li>2 C 2 . C </li></ul>20 The remaining of the team ( after both Ronaldo and Ferdinand are chosen.)
  21. 21. <ul><li>The number of ways to choose both Ronaldo and Ferdinand is presented by this equation: </li></ul><ul><li>2 C 2 . 20 C </li></ul>10 Choose another 10 players from the remaining of the team
  22. 22. <ul><li>The number of ways to choose both Ronaldo and Ferdinand is presented by this equation: </li></ul><ul><li>2 C 2 . 20 C 10 = 184756 </li></ul>Now we got this second number : 184756 ways
  23. 23. <ul><li>The probability that both Ronaldo and Ferdinand are chosen is represented by this equation : </li></ul>2 C 2 . 20 C 10 Number of ways to choose both Ronaldo and Ferdinand P =
  24. 24. <ul><li>The probability that both Ronaldo and Ferdinand are chosen is represented by this equation : </li></ul>2 C 2 . 20 C 10 22 C 12 Number of ways to choose 12 players from 22 players P = =
  25. 25. <ul><li>The probability that both Ronaldo and Ferdinand are chosen is represented by this equation : </li></ul>2 C 2 . 20 C 10 22 C 12 P = = 28.57%
  26. 26. The team goes to final and wins the Cup. We won ? Ooh, I’m not surprised.
  27. 27. <ul><li>To celebrate, the coach decides to buy a new car … </li></ul>Nissan ? Acura ? Dodge ? Chevrolet ?
  28. 28. <ul><li>Finally, the coach decided to buy the 2009 Lamborghini Gallardo </li></ul>Perfect !!! <3 <3 this …
  29. 29. <ul><li>The price of the car is $ 200,000 (taxes added already.) </li></ul>
  30. 30. <ul><li>The price of the car is $ 200,000 plus taxes. They had $ 150,000 as the prize for winning the Cup. They need a loan to buy that car. </li></ul>$ 150,000
  31. 31. <ul><li>The bank charges 7% interest compound monthly and the loan must be repaid in 3 years !! </li></ul>I% = 7 N = 3 years
  32. 32. <ul><li>Question : </li></ul>
  33. 33. <ul><li>Question : </li></ul><ul><li>Calculate the monthly payment of the team if they decide to loan. </li></ul>
  34. 34. <ul><li>Open your calculator and launch the TVM Solver program. Then enter the value in next slide: </li></ul>TVM Solver
  35. 35. Step by Step <ul><li>N = 36 (3 years = 36 months) </li></ul>
  36. 36. Step by Step <ul><li>N = 36 </li></ul><ul><li>I% = 7 (The interest rate is 7% ) </li></ul>
  37. 37. Step by Step <ul><li>N = 36 </li></ul><ul><li>I% = 7 </li></ul><ul><li>PV = $200,000 – $150,000 </li></ul><ul><li> = $50,000 </li></ul>The prize money
  38. 38. Step by Step <ul><li>N = 36 </li></ul><ul><li>I% = 7 </li></ul><ul><li>PV = $ 50,000 </li></ul><ul><li> </li></ul>
  39. 39. Step by Step <ul><li>N = 36 </li></ul><ul><li>I% = 7 </li></ul><ul><li>PV = $ 50,000 </li></ul><ul><li>FV = 0 (the loan will be repaid after 3 years) </li></ul><ul><li> </li></ul>
  40. 40. Step by Step <ul><li>N = 36 </li></ul><ul><li>I% = 7 </li></ul><ul><li>PV = $ 50,000 </li></ul><ul><li>FV = 0 </li></ul><ul><li>P/Y = 12 (pay monthly) </li></ul>
  41. 41. Step by Step <ul><li>N = 36 </li></ul><ul><li>I% = 7 </li></ul><ul><li>PV = $ 50,000 </li></ul><ul><li>FV = 0 </li></ul><ul><li>P/Y = 12 </li></ul><ul><li>C/Y = 12 (compound monthly) </li></ul>
  42. 42. Step by Step <ul><li>N = 36 </li></ul><ul><li>I% = 7 </li></ul><ul><li>PV = $ 50,000 </li></ul><ul><li>FV = 0 </li></ul><ul><li>P/Y = 12 </li></ul><ul><li>C/Y = 12 </li></ul>And move the cursor to the PMT and press [alpha] [enter] to solve for the monthly payment.
  43. 43. Step by Step <ul><li>N = 36 </li></ul><ul><li>I% = 7 </li></ul><ul><li>PV = $ 50,000 </li></ul><ul><li>FV = 0 </li></ul><ul><li>P/Y = 12 </li></ul><ul><li>C/Y = 12 </li></ul><ul><li>PMT = - $1543.85 </li></ul>
  44. 44. Conclusion <ul><li>The monthly payment that the club would pay if they decided to take the loan is : </li></ul>$ 1543.85

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