Post on 19-Jun-2015
2. Ajanis Notes Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east. 3. Ajanis Notes Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east.Eagle Rock The Clearing 4. Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east.He also knew he needed to steer clear of the wolves den and the watering hole.Ajanis Notes Eagle Rock The Clearing Watering Hole Wolves Den 5. Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east.He also knew he needed to steer clear of the wolves den and the watering hole.Ajanis Notes Eagle Rock The Clearing Watering Hole Wolves Den What Ajani wanted to know was: 6. Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east.He also knew he needed to steer clear of the wolves den and the watering hole.Ajanis Notes Eagle Rock The Clearing Watering Hole Wolves Den
7. Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east.He also knew he needed to steer clear of the wolves den and the watering hole.Ajanis Notes Eagle Rock The Clearing Watering Hole Wolves Den
8. Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east.He also knew he needed to steer clear of the wolves den and the watering hole.Ajanis Notes Eagle Rock The Clearing Watering Hole Wolves Den
9. Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east.He also knew he needed to steer clear of the wolves den and the watering hole.Ajanis Notes Eagle Rock The Clearing Watering Hole Wolves Den
10. Ajani knew he needed to get from Eagle Rock to the clearing, so he drew a grid of the land to help organize his path. The quickest way to get to the clearing would be on paths moving only north or east.He also knew he needed to steer clear of the wolves den and the watering hole.Ajanis Notes Eagle Rock The Clearing Watering Hole Wolves Den
11. Something to Think About; Pascals Triangle: 12. Something to Think About;
13. Something to Think About;
14. Something to Think About;
15. Applying Pascals TrianglePascals Triangle can be applied to grid problems: 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 16. Applying Pascals TrianglePascals Triangle can be applied to grid problems: It can be used to illustrate the number of ways to reach a given point from another.1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 17. Applying Pascals TrianglePascals Triangle can be applied to grid problems: It can be used to illustrate the number of ways to reach a given point from another.For example from the bottom left hand corner there are 462 ways to reach the top right hand corner.1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 18. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
19. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
To find the probability of passing the wolves den Ajani needs to know how many ways there are from Eagle Rock to the wolves den and how many ways from the wolves den there are to the clearing.Using the grid it is easy to see there are 21 ways to reach the wolves den from eagle rock. 20. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
To find the probability of passing the wolves den Ajani needs to know how many ways there are from Eagle Rock to the wolves den and how many ways from the wolves den there are to the clearing.Using the grid it is easy to see there are 21 ways to reach the wolves den from eagle rock. To find the number of ways from eagle rock to the clearing Ajani must reapply the triangle: 21. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityTo find the number of ways from eagle rock to the clearing Ajani must reapply the triangle: The Clearing Wolves Den 1 1 1 1 2 3 4 22. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityTo find the number of ways from eagle rock to the clearing Ajani must reapply the triangle: Therefore there are four ways to reach the clearing from the wolves den. The Clearing Wolves Den 1 1 1 1 2 3 4 23. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityThe Clearing Wolves Den 1 1 1 1 2 3 4
24. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityThe Clearing Wolves Den 1 1 1 1 2 3 4
= 2 11 25. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
26. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
27. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
1 1 1 1 The Clearing Watering Hole 28. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
1 1 1 1 The Clearing Watering Hole Therefore: P (passing hole)= (56)(1) 462 P (passing hole)= 56 462 = 4 33 29. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
30. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
31. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
32. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
33. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
34. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
35. 1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for Probability
P (passing den)= 84 462 P (passing hole)= 56 462 36.
1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityP (passing den)= 84 462 P (passing hole)= 56 462 Total number of paths passing both the watering hole and wolves den= 84 462 + 56462 37.
1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityTotal number of paths passing both the watering hole and wolves den= 84 462 + 56462 = 140462 38.
1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityTotal number of paths passing both the watering hole and wolves den= 84 462 + 56462 = 140462 Number of paths that wont bypass the wolves den and watering hole= 462462 140462 - 39.
1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityNumber of paths that wont bypass the wolves den and watering hole= 462462 140462 - = 322462 40.
1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityNumber of paths that wont bypass the wolves den and watering hole= 462462 140462 - = 322462 Therefore, Ajani could take 322 different ways that would not pass the Wolves Den or Watering Hole. 41.
1 1 1 1 1 1 1 1 1 1 1 2 3 4 4 5 5 6 6 7 3 6 10 10 15 15 20 35 35 21 28 21 56 56 70 126 126 252 462 84 210 Eagle Rock The Clearing Watering Hole Wolves Den Solving for ProbabilityNumber of paths that wont bypass the wolves den and watering hole= 462462 140462 - = 322462 Therefore, Ajani could take 322 different ways that would not pass the Wolves Den or Watering Hole. The probability of ways he could take that would not pass either place would be: P (passing neither )=322 462 = 2333 42.
Solving for Distance and Time Eagle Rock The Clearing 43. Solving for Distance and Time
Eagle Rock The Clearing 5m 5m 44. Solving for Distance and Time
Eagle Rock The Clearing 5m 5m 45. Solving for Distance and Time
Eagle Rock The Clearing 5m 5m 46. Solving for Distance and Time The distance from Eagle Rock to the Clearing is 55m.If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Eagle Rock The Clearing 5m 5m 47. Solving for Distance and Time The distance from Eagle Rock to the Clearing is 55m.If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Ajanis pace:Distance to Clearing 0.25km55m 60 mintime Eagle Rock The Clearing 5m 5m First the 55m needs to be converted to km by dividing by 1000. 55m=0.055km 48. Solving for Distance and Time The distance from Eagle Rock to the Clearing is 55m.If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Ajanis pace:Distance to Clearing 0.25km0.055km 60 mintime Eagle Rock The Clearing 5m 5m By cross multiplying and dividing time can be calculated: (60 minutes)(0.055m)=(0.25km)(time) (60minutes)(0.055m)=time 0.25km 49. Solving for Distance and Time The distance from Eagle Rock to the Clearing is 55m.If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Ajanis pace:Distance to Clearing 0.25km0.055km 60 mintime Eagle Rock The Clearing 5m 5m By cross multiplying and dividing time can be calculated: (60 minutes)(0.055m)=(0.25km)(time) (60minutes)(0.055m)=time 0.25km Time=13.2 minutes 50. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes 51. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes The number of seconds: 1 minute0.2 minutes 60 secondsseconds 52. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes The number of seconds: 1 minute0.2 minutes 60 secondsseconds Cross multiply and divide to find the number of seconds: 53. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes The number of seconds: 1 minute0.2 minutes 60 secondsseconds Cross multiply and divide to find the number of seconds: (0.2minutes)(60seconds)=(1 minute)(seconds) (0.2minutes)60seconds)=Seconds 1 minute 54. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes The number of seconds: 1 minute0.2 minutes 60 secondsseconds Cross multiply and divide to find the number of seconds: (0.2minutes)(60seconds)=(1 minute)(seconds) (0.2minutes)60seconds)=Seconds 1 minuteSeconds=12 55. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes 0.2 minutes=12 seconds Therefore the amount of time it will take Ajani to cross the jungle at 0.25km/h is 13 minutes and 12 seconds approximately. 56. Solving for Distance and Time Eagle Rock The Clearing 5m 5m If Ajani walks at a pace of 0.25km per hour how long in minutes and seconds will it take him to reach the Clearing? Time=13.2 minutes 0.2 minutes=12 seconds Therefore the amount of time it will take Ajani to cross the jungle at 0.25km/h is 13 minutes and 12 seconds approximately.The amount it would take to go to the clearing and back to eagle rock would be 26 minutes and 24 seconds since it would be twice the amount of time it took to get to the clearing.