Kuzco has 1 way to get from his palace to Malina's house with exactly one stop over. This is determined by constructing a diagram showing the bus routes between locations and a corresponding matrix. The matrix entry from Kuzco's palace to Malina's house with one stopover is 1, indicating there is 1 way for this route.

1. 1
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2. 2

3. 3
Kuzco and Malina are going on a date, they are using the bus
for transportation. The bus travels from Malina's house to the
Library and to Pyramid Park, it also travels from Kuzco's house
to the Library. There is a bus that travels around Pyramid Park
and ends up at the from gates of the park.
How many ways can Kuzco get from his house to Malina's with
exactly one stop over?

4. 4
• Construct a diagram
• Construct a Matrix
• Answer the question

5. 5
Kuzco and Malina are going on a date, they are using the bus for
transportation. The bus travels from Malina's house to the
Library, Kuzco`s house and to Pyramid Park, it also travels from
Kuzco's house to the Library. There is a bus that travels around
Pyramid Park and ends up at the from gates of the park.
How many ways can Kuzco get from his house to Malina's with
exactly one stop over?
• Construct a diagram
Plot each destination

6. 6
Kuzco and Malina are going on a date, they are using the bus for
transportation. The bus travels from Malina's house to the
Library, Kuzco`s Palace and to Pyramid Park, it also travels from
Kuzco's house to the Library. There is a bus that travels around
Pyramid Park and ends up at the from gates of the park.
How many ways can Kuzco get from his house to Malina's with
exactly one stop over?
• Construct a diagram
Plot each destination
Malina's house

7. 7
Kuzco and Malina are going on a date, they are using the bus for
transportation. The bus travels from Malina's house to the
Library, Kuzco`s Palace, and to Pyramid Park, it also travels
from Kuzco's house to the Library. There is a bus that travels
around Pyramid Park and ends up at the from gates of the park.
How many ways can Kuzco get from his house to Malina's with
exactly one stop over?
• Construct a diagram
Plot each destination
Malina's house Library

8. 8
Kuzco and Malina are going on a date, they are using the bus for
transportation. The bus travels from Malina's house to the
Library, Kuzco`s Palace and to Pyramid Park, it also travels from
Kuzco's house to the Library. There is a bus that travels around
Pyramid Park and ends up at the from gates of the park and near
Malina`s House.
How many ways can Kuzco get from his house to Malina's with
exactly one stop over?
• Construct a diagram
Plot each destination
Malina's house Library
Pyramid Park

9. 9
• Construct a diagram
Plot each destination
Malina's house Library
Pyramid Park Kuzco's Palace
Kuzco and Malina are going on a date, they are using the bus for
transportation. The bus travels from Malina's house to the
Library, Kuzco`s Palace and to Pyramid Park, it also travels from
Kuzco's house to the Library. There is a bus that travels around
Pyramid Park and ends up at the from gates of the park and near
Malina`s House.
How many ways can Kuzco get from his house to Malina's with
exactly one stop over?

10. 10
• Construct a diagram
Malina's house Library
Pyramid Park Kuzco's Palace
Use arrows to describe the
direction that the bus travels
in.
Kuzco and Malina are going on a date, they are using the bus for
transportation. The bus travels from Malina's house to the
Library, Kuzco`s Palace and to Pyramid Park, it also travels from
Kuzco's house to the Library. There is a bus that travels around
Pyramid Park and ends up at the from gates of the park and near
Malina`s House.
How many ways can Kuzco get from his house to Malina's with
exactly one stop over?

11. 11
• Construct a diagram
Malina's house Library
Pyramid Park Kuzco's Palace
Use arrows to describe the
direction that the bus travels
in.
Kuzco and Malina are going on a date, they are using the bus for
transportation. The bus travels from Malina's house to the
Library, Kuzco`s Palace and to Pyramid Park, it also travels from
Kuzco's house to the Library. There is a bus that travels around
Pyramid Park and ends up at the from gates of the park and near
Malina`s House.
How many ways can Kuzco get from his house to Malina's with
exactly one stop over?

12. 12
• Construct a diagram
Use arrows to describe the
direction that the bus travels
in.
Kuzco and Malina are going on a date, they are using the bus for
transportation. The bus travels from Malina's house to the
Library, Kuzco`s Palace and to Pyramid Park, it also travels from
Kuzco's house to the Library. There is a bus that travels around
Pyramid Park and ends up at the from gates of the park and near
Malina`s House.
How many ways can Kuzco get from his house to Malina's with
exactly one stop over?
Malina's house Library
Pyramid Park Kuzco's Palace

13. 13
• Construct a diagram
• Answer the question
• Construct a Matrix

14. 14
• Construct a Matrix
Using the diagram construct a matrix, use
numbers to indicate the number of routes
to and from each destination.
FROM
TO
Malina's house
Pyramid Park
Library
Kuzco's Palace
M
alina's house
Pyram
id ParkLibrary
Kuzco's Palace
Malina's house Library
Pyramid Park Kuzco's Palace

15. 15
• Construct a Matrix
Using the diagram construct a matrix, use
numbers (0 or 1) to indicate the number
of routes to and from each destination.
Malina's house Library
Pyramid Park Kuzco's Palace
FROM
TO
Malina's house
Pyramid Park
Library
Kuzco's Palace
M
alina's house
Pyram
id ParkLibrary
Kuzco's Palace
10 1 1
1 1 0 0
0 0 0 0
10 0 0

16. 16
• Construct a diagram
• Construct a Matrix
• Answer the question

17. 17
FROM
TO
Malina's house
Pyramid Park
Library
Kuzco's Palace
M
alina's house
Pyram
id ParkLibrary
Kuzco's Palace
10 1 1
1 1 0 0
0 0 0 0
10 0 0
• Answer the question
How many ways can Kuzco get from his house to
Malina's with exactly one stop over?
A =
From Kuzco`s to Malina`s with exactly one stopover = A2

18. 18
FROM
TO
Malina's house
Pyramid Park
Library
Kuzco's Palace
M
alina's house
Pyram
id ParkLibrary
Kuzco's Palace
10 1 1
1 1 0 0
0 0 0 0
10 0 0
• Answer the question
How many ways can Kuzco get from his house to
Malina's with exactly one stop over?
A =
From Kuzco`s to Malina`s with exactly one stopover = A2
A2
= FROM
TO
Malina's house
Pyramid Park
Library
Kuzco's Palace
M
alina's house
Pyram
id ParkLibrary
Kuzco's Palace
1
1
1
0 0
0 0 0 0
1 0 0
1 1
2
2

19. 19
Kuzco has 1 way to get from his Palace to
Malina`s house with exactly one stop over.

20. 20

21. 21
For supper Kuzco has the choice of either roast beef and mash
potatoes or burger and fries with either Coffee or Pepsi. If Kuzco eats
burger and fries, the probability of him drinking Pepsi is 4/5, the
probability that he eats burger and fries is 4/6. The probability that he
will drink coffee with roast beef and mash potatoes is 2/3.
What is the probability that he will have eat roast beef with mash
potatoes and drink Pepsi?

22. 22
• Construct a tree diagram

23. 23
For supper Kuzco has the choice of either roast beef and mash potatoes or
burger and fries with either Coffee or Pepsi. If Kuzco eats burger and
fries, the probability of him drinking Pepsi is 4/5, the probability that he eats
burger and fries is 4/6. The probability that he will drink coffee with roast
beef and mash potatoes is 2/3.
What is the probability that he will have eat roast beef with mash potatoes
and drink Pepsi?
• Construct a tree diagram

24. 24
For supper Kuzco has the choice of either roast beef and mash potatoes or
burger and fries with either Coffee or Pepsi. If Kuzco eats burger and
fries, the probability of him drinking Pepsi is 4/5, the probability that he eats
burger and fries is 4/6. The probability that he will drink coffee with roast
beef and mash potatoes is 2/3.
What is the probability that he will have eat roast beef with mash potatoes
and drink Pepsi?
• Construct a tree diagram
Using abreviations, label your tree
diagram.
Legend
BF = Burger & fries
RM = Roast beef &
mash potatoes
P = Pepsi
C = Coffee
BF
RM
P
C
P
C

25. 25
For supper Kuzco has the choice of either roast beef and mash potatoes or
burger and fries with either Coffee or Pepsi. If Kuzco eats burger and
fries, the probability of him drinking Pepsi is 4/5, the probability that he eats
burger and fries is 4/6. The probability that he will drink coffee with roast
beef and mash potatoes is 2/3.
What is the probability that he will have eat roast beef with mash potatoes
and drink Pepsi?
• Construct a tree diagram
Label the probabilities.
Legend
BF = Burger & fries
RM = Roast beef &
mash potatoes
P = Pepsi
C = Coffee
BF
RM
P
C
P
C
4/6
2/6
4/5
1/5
1/3
2/3

26. 26
• Construct a tree diagram
• Answer the question

27. 27
• Answer the question
What is the probability that he will have eat roast beef with
mash potatoes and drink Pepsi?
BF
RM
P
C
P
C
4/6
2/6
4/5
1/5
1/3
2/3
Add or multiply the correct fractions according to what is asked.
NOTE: When dealing with probability remember!
and/with = addition
or = multiply
2
6
1
3
AND
+

28. 28
• Answer the question
What is the probability that he will have eat roast beef with
mash potatoes and drink Pepsi?
2
6
1
3
AND
+ = 3
9

29. 29
The probability of Kuzco eatting roast beef with
mash potatoes and drinking Pepsi is 3
9

30. 30

31. 31
Kuzco and Kronk are trying to break into Yzma`s laboratory.
Inorder to get into her lab they need to punch in Ymza`s secret
code. The code consists of three different letters and three
numbers (0 to 9).
How many different possible codes are there?

32. 32
• Organize the question
• Answer the question

33. 33
Kuzco and Kronk are trying to break into Yzma`s laboratory.
Inorder to get into her lab they need to punch in Ymza`s secret
code. The code consists of three letters and three numbers from 0
to 9.
How many different possible codes are there?
• Organize the question
Place a line for each characteristic in the
code.

34. 34
Kuzco and Kronk are trying to break into Yzma`s laboratory.
Inorder to get into her lab they need to punch in Ymza`s secret code.
The code consists of three different letters and three numbers from 0
to 9.
How many different possible codes are there?
• Organize the question
Place a line for each characteristic in the
code.
green = letters
red = numbers
All together there, it is a 6 characteristic
code.

35. 35
Kuzco and Kronk are trying to break into Yzma`s laboratory.
Inorder to get into her lab they need to punch in Ymza`s secret code.
The code consists of three different letters and three numbers from 0
to 9.
How many different possible codes are there?
• Organize the question
Because it says 3 different letters, every time you write the number
of outcomes on one line, the number of outcomes on the next line is
one less than the previous.
To start, there are 26 letters in the alphabet.
26

36. 36
Kuzco and Kronk are trying to break into Yzma`s laboratory.
Inorder to get into her lab they need to punch in Ymza`s secret code.
The code consists of three different letters and three numbers from 0
to 9.
How many different possible codes are there?
• Organize the question
Because it says 3 different letters, every time you write the number
of outcomes on one line, the number of outcomes on the next line is
one less than the previous.
26 ­ 1 = 25
26 25

37. 37
• Organize the question
Because it says 3 different letters, every time you write the number
of outcomes on one line, the number of outcomes on the next line is
one less than the previous.
25 ­ 1 = 24
26 25 24
Kuzco and Kronk are trying to break into Yzma`s laboratory.
Inorder to get into her lab they need to punch in Ymza`s secret code.
The code consists of three different letters and three numbers from 0
to 9.
How many different possible codes are there?

38. 38
Kuzco and Kronk are trying to break into Yzma`s laboratory.
Inorder to get into her lab they need to punch in Ymza`s secret
code. The code consists of six different letters and three numbers
from 0 to 9.
How many different possible codes are there?
• Organize the question
Now there are no restrictions on repeating numbers or being able to
use certain numbers, therefore all numbers can be reused.
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 = 10 characteristics
All can be repeated.
26 25 24 10 10 10

39. 39
• Organize the question
• Answer the question

40. 40
Kuzco and Kronk are trying to break into Yzma`s laboratory.
Inorder to get into her lab they need to punch in Ymza`s secret
code. The code consists of six different letters and three numbers
from 0 to 9.
How many different possible codes are there?
• Answer the question
Now, multiply each set of digits.
26 25 24 10 10 10x x x x x

41. 41
Kuzco and Kronk are trying to break into Yzma`s laboratory.
Inorder to get into her lab they need to punch in Ymza`s secret
code. The code consists of six different letters and three numbers
from 0 to 9.
How many different possible codes are there?
• Answer the question
Now, multiply each set of digits.
26 25 24 10 10 10x x x x x
= 15,600,000

42. 42
There are 15,600, 000 different possible codes that could
be used as Yzma`s security lab code.

43. 43

44. 44
Kuropatwa City has a population of 3500 teenanger attending high
school, 2200 teenangers attend Kuropatwa Academy and 1300
teenagers attend other local high schools. During the course of
one year, 15% of students from Kuropatwa Academy tranfer to
locals schools and 56% of local high school students transfer to
Kuropatwa Academy
What is the population of Kuropatwa Academy the following
year?

45. 45
• Construct a State Matrix
• Construct a diagram
• Place the diagram into a transition
matix.
• Multiply the state matrix and transition matrix

46. 46

47. 47
• Construct a State Matrix
• Construct a transition matrix
• Contruct a diagram
• Multiply the state matrix and transition matrix

48. 48
Kuropatwa City has a population of 3500 teenanger attending high
school, 2200 teenangers attend Kuropatwa Academy and 1300
teenagers attend other local high schools. During the course of
one year, 15% of students from Kuropatwa Academy tranfer to
locals schools and 56% of local high school students transfer to
Kuropatwa Academy
What is the population of Kuropatwa Academy the following
year?
• Contruct a diagram
Draw a diagram with arrows
describing the direction of where
th students are going.

49. 49
Kuropatwa City has a population of 3500 teenanger attending high
school, 2200 teenangers attend Kuropatwa Academy and 1300
teenagers attend other local high schools. During the course of
one year, 15% of students from Kuropatwa Academy tranfer to
locals schools and 56% of local high school students transfer to
Kuropatwa Academy
What is the population of Kuropatwa Academy the following
year?
• Contruct a diagram
Draw a diagram with arrows
describing the direction of where
th students are going.

50. 50

51. 51

52. 52

53. 53

54. 54

55. 55

56. 56
• Construct a State Matrix
• Contruct a diagram
• Construct a transition
matrix
• Multiply the state matrix and transition matrix

57. 57
• Construct a transition
matrix

58. 58
• Construct a State Matrix
• Contruct a diagram
• Construct a transition matrix
• Multiply the state matrix and
transition matrix

59. 59

60. 60
• Construct a State Matrix
• Contruct a diagram
• Construct a transition matrix
• Multiply the state matrix and transition matrix
• Answer the question

61. 61
• Answer the question
2 x 2
1 x 2
S x T

62. 62
• Answer the question
2 x 2
1 x 2
S x T
= 2065 1804

63. 63
S x T
= 2065 1804

64. 64

65. 65
Kuzco and Malina decide to buy are car. They must take out a
loan of $12, 358.06, they decide to pay $245.00 monthly. The
interest rate for financing is 4%.
How many payments must they make?

66. 66
• Use your the TVM solvers on your
TI­83 graphing calculator.
• Answer the question

67. 67
Kuzco and Malina decide to buy are car. They must take out a
loan of $12, 358.06, they decide to pay $245.00 monthly. The
interest rate for financing is 4%.
How many payments must they make?
• Use your the TVM solvers on your TI­83
graphing calculator.
N =
I% =
PV =
PMT =
FV =
P/Y =
C/Y =
Set up your TVM solver by
filling in the information.

68. 68
Kuzco and Malina decide to buy are car. They must take out a
loan of $12, 358.06, they decide to pay $245.00 monthly. The
interest rate for financing is 4%.
How many payments must they make?
• Use your the TVM solvers on your TI­83
graphing calculator.
N =
I% = 4
PV = 12358.06
PMT = ­ 245.00
FV = 0
P/Y = 12
C/Y = 12
Set up your TVM solver by
filling in the information.

69. 69
Kuzco and Malina decide to buy are car. They must take out a
loan of $12, 358.06, they decide to pay $245.00 monthly. The
interest rate for financing is 4%.
How many payments must they make?
• Use your the TVM solvers on your TI­83
graphing calculator.
• N =
I% = 4
PV = 12358.06
PMT = ­ 245.00
FV = 0
P/Y = 12
C/Y = 12
N = number of payments
**Our unknown
* PRESS (ALPHA) and (ENTER)

70. 70
• Use your the TVM solvers on your TI­83 graphing calculator.
• Answer the question

71. 71
Kuzco and Malina decide to buy are car. They must take out a
loan of $12, 358.06, they decide to pay $245.00 monthly. The
interest rate for financing is 4%.
How many payments must they make till they pay off the loan?
• Use your the TVM solvers on your TI­83
graphing calculator.
• N =
I% = 4
PV = 12358.06
PMT = ­ 245.00
FV = 0
P/Y = 12
C/Y = 12
N = number of payments
**Our unknown
* PRESS (ALPHA) and (ENTER)

72. 72
Kuzco and Malina decide to buy are car. They must take out a
loan of $12, 358.06, they decide to pay $245.00 monthly. The
interest rate for financing is 4%.
How many payments must they make?
• Use your the TVM solvers on your TI­83
graphing calculator.
• N = 55.31820057
I% = 4
PV = 12358.06
PMT = ­ 245.00
FV = 0
P/Y = 12
C/Y = 12
N = number of payments
**Our unknown

73. 73
• N = 55.31820057
I% = 4
PV = 12358.06
PMT = ­ 245.00
FV = 0
P/Y = 12
C/Y = 12
• Answer the question

74. 74
Kuzco and Malina must make 55.31 payment before they fully
pay off their car loan.

75. 75
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