Question 1

Determine whether the graph is a tree.

Accepted Answer

A)  tree 
B)  not a tree 
A)  tree 
B)  not a tree A

Question 2

Find two different spanning trees for the graph.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    A, E

Question 3

Suppose you wish to install a drip sprinkler system and need to run a drip water line to five areas, as shown in the given graph. The numbers show the distances in feet. What is the smallest number of feet of drip hose necessary to install? ​   ​
Where   ​

Accepted Answer

A)  The smallest number of feet of drip 214 ft 
B)  The smallest number of feet of drip 111 ft 
C)  The smallest number of feet of drip 126 ft 
D)  The smallest number of feet of drip 216 ft 
E)  The smallest number of feet of drip 153 ft 
A)  The smallest number of feet of drip 214 ft 
B)  The smallest number of feet of drip 111 ft 
C)  The smallest number of feet of drip 126 ft 
D)  The smallest number of feet of drip 216 ft 
E)  The smallest number of feet of drip 153 ft A

Question 4

Find the minimum spanning tree for the of the graph.
​   ​
Where   ​
The sum of the numbers associated with the edges of the minimum spanning tree is __________.

Accepted Answer

The answer of Find the minimum spanning tree for the...

Question 5

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve.
​   1. Point C
2. Point A
3. Point B
a. outside
b. inside
​
-A

Accepted Answer

The answer of Determine whether each of the points A,...

Question 6

Find the minimum spanning tree for the of the graph. ​   ​
Where   ​

Accepted Answer

A)  The sum of the numbers associated with the edges of the minimum spanning tree is 196 
B)  The sum of the numbers associated with the edges of the minimum spanning tree is 202 
C)  The sum of the numbers associated with the edges of the minimum spanning tree is 127 
D)  The sum of the numbers associated with the edges of the minimum spanning tree is 136 
E)  The sum of the numbers associated with the edges of the minimum spanning tree is 133 
A)  The sum of the numbers associated with the edges of the minimum spanning tree is 196 
B)  The sum of the numbers associated with the edges of the minimum spanning tree is 202 
C)  The sum of the numbers associated with the edges of the minimum spanning tree is 127 
D)  The sum of the numbers associated with the edges of the minimum spanning tree is 136 
E)  The sum of the numbers associated with the edges of the minimum spanning tree is 133

Question 7

Does the network in a) have a Hamiltonian cycle? If this network has one, describe it. ​   ​

Accepted Answer

A)  notpossible 
B)    
C)    
D)    
E)    
A)  notpossible 
B)    
C)    
D)    
E)

Question 8

A saleswoman wants to visit eastern cities, New York City, Boston, Cleveland, and Washington,
D.C. Driving distances are as shown in the figure below. What is the shortest trip starting in New York that visits each of these cities, if   ? Find a solution using the nearest-neighbor method.
​   
​
__________ mi.

Accepted Answer

The answer of A saleswoman wants to visit eastern cities,...

Question 9

Let X be a point obviously outside the figure. Draw   . How many times does it cross the curve? ​   ​

Accepted Answer

A)  it will cross the curve an odd number of times 
B)  it will cross the curve an even number of times 
A)  it will cross the curve an odd number of times 
B)  it will cross the curve an even number of times

Question 10

Is the network in d) an Euler circuit? Can this network can be traversed? ​   ​

Accepted Answer

A)  an Euler circuit; traversable 
B)  not an Euler circuit; traversable 
C)  not an Euler circuit; not traversable 
D)  an Euler circuit; not traversable 
A)  an Euler circuit; traversable 
B)  not an Euler circuit; traversable 
C)  not an Euler circuit; not traversable 
D)  an Euler circuit; not traversable

Question 11

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.
A) a glass
B) a bowling ball
C) a sheet of typing paper
D) a sheet of two-ring-binder paper
E) a sphere

Accepted Answer

The answer of Group the objects into classes so that...

Question 12

Is this figure tessellation?

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 13

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.

Accepted Answer

A)  A, B and D; C 
B)  A; B and D; C 
C)  A; B, C and D 
D)  A,B,C, and D 
E)  A, C and D; B 
A)  A, B and D; C 
B)  A; B and D; C 
C)  A; B, C and D 
D)  A,B,C, and D 
E)  A, C and D; B

Question 14

Use a tree to show the following family tree. You have two children, Shannon and Melissa. Shannon has two children, Soren and Thoren. Melissa has three children, Hannah, Banana, and Mike.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Let X be a point obviously outside the figure. Draw   . How many times does it cross the curve? ​   ​

Accepted Answer

A)  it will cross the curve an odd number of times 
B)  it will cross the curve an even number of times 
A)  it will cross the curve an odd number of times 
B)  it will cross the curve an even number of times

Question 16

Is the network a Euler circuit or a Hamiltonian circuit?   Can this network be traversed? Answer yes or no.

Accepted Answer

a Hamilton

Question 17

A saleswoman wants to visit eastern cities, New York City, Boston, Cleveland, and Washington,D.C. Driving distances are as shown in the figure below. What is the shortest trip starting in New York that visits each of these cities, if   Find a solution using the sorted-edge method. ​  
​

Accepted Answer

A)  1,646 mi 
B)  1,645 mi 
C)  1,151 mi 
D)  1,643 mi 
E)  1,644 mi 
A)  1,646 mi 
B)  1,645 mi 
C)  1,151 mi 
D)  1,643 mi 
E)  1,644 mi

Question 18

Does the network in the picture below have a Hamiltonian cycle? If the network has one, describe it.
​

Accepted Answer

The answer of Does the network in the picture below...

Question 19

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve.

Accepted Answer

A)  B and C are outside, A is inside 
B)  A and B are outside, C is inside 
C)  A and C are outside, B is inside 
D)  A is outside, B and C are inside 
E)  All are outside 
A)  B and C are outside, A is inside 
B)  A and B are outside, C is inside 
C)  A and C are outside, B is inside 
D)  A is outside, B and C are inside 
E)  All are outside

Question 20

Let ​X be a point obviously outside the figure. Draw   . How many times does it cross the curve?
​   ​
It will cross the curve an __________ (even, odd) number of times.

Accepted Answer

The answer of Let ​X be a point obviously outside...

Determine whether the graph is a tree.

Find two different spanning trees for the graph.

Suppose you wish to install a drip sprinkler system and need to run a drip water line to five areas, as shown in the given graph. The numbers show the distances in feet. What is the smallest number of feet of drip hose necessary to install? Where

Find the minimum spanning tree for the of the graph. Where The sum of the numbers associated with the edges of the minimum spanning tree is __________.

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve. 1. Point C 2. Point A 3. Point B a. outside b. inside -A

Find the minimum spanning tree for the of the graph. Where

Does the network in a) have a Hamiltonian cycle? If this network has one, describe it.

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve?

Is the network in d) an Euler circuit? Can this network can be traversed?

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent. A) a glass B) a bowling ball C) a sheet of typing paper D) a sheet of two-ring-binder paper E) a sphere

Is this figure tessellation?

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.

Use a tree to show the following family tree. You have two children, Shannon and Melissa. Shannon has two children, Soren and Thoren. Melissa has three children, Hannah, Banana, and Mike.

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve?

Is the network a Euler circuit or a Hamiltonian circuit? Can this network be traversed? Answer yes or no.

A saleswoman wants to visit eastern cities, New York City, Boston, Cleveland, and Washington,D.C. Driving distances are as shown in the figure below. What is the shortest trip starting in New York that visits each of these cities, if Find a solution using the sorted-edge method.

Does the network in the picture below have a Hamiltonian cycle? If the network has one, describe it.

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve.

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve? It will cross the curve an __________ (even, odd) number of times.

The Nature of Problem Solving

The Nature of Sets

The Nature of Logic

The Nature of Numeration Systems

The Nature of Numbers

The Nature of Algebra

The Nature of Geometry

The Nature of Networks and Graph Theory

The Nature of Growth

The Nature of Sequences, Series, and Financial Management

The Nature of Counting

The Nature of Probability

The Nature of Statistics

The Nature of Graphs and Functions

The Nature of Mathematical Systems

The Nature of Voting and Apportionment

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Exam 8: The Nature of Measurement

Determine whether the graph is a tree.

Find two different spanning trees for the graph.

Suppose you wish to install a drip sprinkler system and need to run a drip water line to five areas, as shown in the given graph. The numbers show the distances in feet. What is the smallest number of feet of drip hose necessary to install? ​ ​ Where ​

Find the minimum spanning tree for the of the graph. ​ ​ Where ​ The sum of the numbers associated with the edges of the minimum spanning tree is __________.

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve. ​ 1. Point C 2. Point A 3. Point B a. outside b. inside ​ -A

Find the minimum spanning tree for the of the graph. ​ ​ Where ​

Does the network in a) have a Hamiltonian cycle? If this network has one, describe it. ​ ​

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve? ​ ​

Is the network in d) an Euler circuit? Can this network can be traversed? ​ ​

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent. A) a glass B) a bowling ball C) a sheet of typing paper D) a sheet of two-ring-binder paper E) a sphere

Is this figure tessellation?

Group the objects into classes so that all the elements within each class are topologically equivalent and no elements from different classes are topologically equivalent.

Use a tree to show the following family tree. You have two children, Shannon and Melissa. Shannon has two children, Soren and Thoren. Melissa has three children, Hannah, Banana, and Mike.

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve? ​ ​

Is the network a Euler circuit or a Hamiltonian circuit? Can this network be traversed? Answer yes or no.

A saleswoman wants to visit eastern cities, New York City, Boston, Cleveland, and Washington,D.C. Driving distances are as shown in the figure below. What is the shortest trip starting in New York that visits each of these cities, if Find a solution using the sorted-edge method. ​ ​

Does the network in the picture below have a Hamiltonian cycle? If the network has one, describe it. ​

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve.

Let ​X be a point obviously outside the figure. Draw . How many times does it cross the curve? ​ ​ It will cross the curve an __________ (even, odd) number of times.

The Nature of Problem Solving

The Nature of Sets

The Nature of Logic

The Nature of Numeration Systems

The Nature of Numbers

The Nature of Algebra

The Nature of Geometry

The Nature of Networks and Graph Theory

The Nature of Growth

The Nature of Sequences, Series, and Financial Management

The Nature of Counting

The Nature of Probability

The Nature of Statistics

The Nature of Graphs and Functions

The Nature of Mathematical Systems

The Nature of Voting and Apportionment

Filters

Suppose you wish to install a drip sprinkler system and need to run a drip water line to five areas, as shown in the given graph. The numbers show the distances in feet. What is the smallest number of feet of drip hose necessary to install? Where

Find the minimum spanning tree for the of the graph. Where The sum of the numbers associated with the edges of the minimum spanning tree is __________.

Determine whether each of the points A, B, and C is inside or outside of the simple closed curve. 1. Point C 2. Point A 3. Point B a. outside b. inside -A

Find the minimum spanning tree for the of the graph. Where

Does the network in a) have a Hamiltonian cycle? If this network has one, describe it.

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve?

Is the network in d) an Euler circuit? Can this network can be traversed?

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve?

A saleswoman wants to visit eastern cities, New York City, Boston, Cleveland, and Washington,D.C. Driving distances are as shown in the figure below. What is the shortest trip starting in New York that visits each of these cities, if Find a solution using the sorted-edge method.

Does the network in the picture below have a Hamiltonian cycle? If the network has one, describe it.

Let X be a point obviously outside the figure. Draw . How many times does it cross the curve? It will cross the curve an __________ (even, odd) number of times.