Deck 8: The Nature of Measurement

Question 1

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 ruler
E. a sphere

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

Answer 1

A, B, C, D and E

Question 2

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

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

Answer 2

it will cross the curve an odd number of times

Question 3

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.

Answer 3

A; B AND D; C

Question 4

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

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

Question 5

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.

Question 6

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

Question 7

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 bolt
B. a brick
C. a horseshoe
D. a pencil

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

Question 8

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
​
C

Question 9

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 bolt
B) a straw
C) a sewing needle
D) a funnel with a handle

Question 10

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

Question 11

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

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

Question 12

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.

Question 13

Read the poem in the News Clip. Is a right-handed mitten topologically equivalent to a left-handed mitten? Answer yes or no.
If a right-handed mitten is turned inside out, as is suggested in the poem, will it still fit a right hand? Answer yes or no.

Question 14

Determine whether the graph is a tree.

A) tree
B) not a tree

Question 15

Read the poem in the News Clip. a. If a right-handed mitten is turned inside out, as is suggested in the poem, will it still fit a right hand? b. Is a right-handed mitten topologically equivalent to a left-handed mitten?

A) a. no, b. yes
B) a. no, b. no
C) a. yes, b. no
D) a. yes, b. yes

Question 16

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

Question 17

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
​
B

Question 18

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, 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 19

Is this figure tessellation?

A) No
B) Yes

Question 20

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

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 21

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

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 22

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.

A)
B)
C)
D)
E)

Question 23

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

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

Question 24

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 ​
__________ ft

Question 25

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 brute-force method. ​
​

A) 1493 mi
B) 1495 mi
C) 1500 mi
D) 1487 mi
E) 2486 mi

Question 26

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. ​
​

A) 1558 mi
B) 1,073 mi
C) 1,072 mi
D) 1,071 mi
E) 1,070 mi

Question 27

The map in figure shows driving distances and times between California and Nevada cities. Use Kruskal's algorithm to find the minimum spanning tree for the following cities: Santa Rosa, San Francisco, Oakland, Manteca, Yosemite Village, Merced, Fresno, and San Jose. __________ mi

Question 28

Find two different spanning trees for the graph.

A)
B)
C)
D)
E)

Question 29

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. ​
​

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

Question 30

Determine whether the graph is a tree or not a tree.

Question 31

Can you pass the floor plan in b) through all the rooms while going through each door only once? ​ ​

A) traversable
B) not traversable

Question 32

Draw graph for the molecule. Isobutane

A)
B)
C)
D)
E)

Question 33

The map in figure shows driving distances and times between California and Nevada cities. Use Kruskal's algorithm to find the minimum spanning tree for the following cities: Santa Rosa, San Francisco, Oakland, Manteca, Yosemite Village, Merced, Fresno, and San Jose.

A) 426 mi
B) 211 mi
C) 370 mi
D) 786 mi
E) 375 mi

Question 34

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

A) notpossible
B)
C)
D)
E)

Question 35

Draw graph for the molecule. Cyclopropane

A)
B)
C)
D)
E)

Question 36

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

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 37

Find two different spanning trees for the graph.

A)
B)
C)
D)
E)

Question 38

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 ​

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

Question 39

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

A)
B)
C)
D)
E) not possible

Question 40

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 __________.

Question 41

On a planet far, far away, Luke finds himself in a strange building with hexagon-shaped rooms as shown in the figure below. In his search for the princess, he always moves to an adjacent room and always in a southerly direction. How many paths are there to room 1?
​ ​
__________ path0

Question 42

Does the network in the picture below have Hamiltonian cycles? If the network has one, describe it. If not, answer not possible.

Question 43

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

Question 44

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

Question 45

Can you pass the floor plan in through all the rooms while going through each door only once? Answer traversable or not traversable.

Question 46

On a planet far, far away, Luke finds himself in a strange building with hexagon-shaped rooms as shown in the figure below. In his search for the princess, he always moves to an adjacent room and always in a southerly direction. How many paths are there to room 13? ​ ​

A) 381 paths
B) 378 paths
C) 375 paths
D) 377 paths
E) 256 paths

Question 47

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 brute-force method.
​
​
__________ mi.

Question 48

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.

Question 49

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.
​
​
__________ mi.

Question 50

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