Question 1

Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation.
-"Is a cousin of"
A)Transitive; not an equivalence relation
B)Symmetric and transitive; not an equivalence relation
C)Symmetric; not an equivalence relation
D)None; not an equivalence relation

Accepted Answer

The relation "is a cousin of" is symmetric because if person A is a cousin of person B, then person B is also a cousin of person A. However, it is not reflexive because a person is not a cousin of themselves, and it is not transitive because if person A is a cousin of person B, and person B is a cousin of person C, it does not necessarily mean that person A is a cousin of person C. Therefore, it is not an equivalence relation.

Question 2

Solve the problem.
-A cable company charges by the number of movie channels a subscriber chooses. The cost is given by 11.90 + 3.70x, where x is the number of movie channels. What is the cost for 2 movie channels.
A)$27.50
B)$88.06
C)$31.20
D)$19.30

Accepted Answer

The cost is calculated by substituting x = 2 into the equation: 11.90 + 3.70(2) = 11.90 + 7.40 = 19.30.

Question 3

Solve the problem.
-A cab ride costs $1.70 base plus $0.90 a mile. How far can you go for $13.40?
A)15 miles
B)16 miles
C)14 miles
D)13 miles

Accepted Answer

The answer of Solve the problem.
-A cab ride costs $1.70...

Question 4

Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation.
-"Is the same weight as"
A)Reflexive, symmetric and transitive; equivalence relation
B)Reflexive and transitive; not an equivalence relation
C)Symmetric and transitive; not an equivalence relation
D)Reflexive and symmetric; not an equivalence relation

Accepted Answer

The relation "is the same weight as" is reflexive because every person is the same weight as themselves, symmetric because if person A is the same weight as person B, then person B is the same weight as person A, and transitive because if person A is the same weight as person B, and person B is the same weight as person C, then person A is the same weight as person C. Since it satisfies all three properties, it is an equivalence relation.

Question 5

Solve the problem.
-A long distance phone call costs $2.40 for the first minute plus $1.20 each additional minute. What is the cost of a 17 minute call?
A)$21.60
B)$22.80
C)$48.96
D)$57.60

Accepted Answer

The cost of the first minute is $2.40. The cost of the remaining 16 minutes is $1.20 x 16 = $19.20. The total cost of the call is $2.40 + $19.20 = $21.60.

Question 6

Solve the problem.
-The cost of a cab ride in dollars is given by C(x)= 1.80 + 1.10x, where x is the number of miles. What are the charges for a ride of 25 miles?
A)$46.10
B)$72.50
C)$49.50
D)$29.30

Accepted Answer

The answer of Solve the problem.
-The cost of a cab...

Question 7

Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation.
-"Is a sibling of"
A)Reflexive and symmetric; not an equivalence relation
B)Reflexive and transitive; not an equivalence relation
C)Symmetric and transitive; not an equivalence relation
D)Reflexive, symmetric and transitive; equivalence relation

Accepted Answer

The relation "is a sibling of" is symmetric (if A is a sibling of B, then B is a sibling of A) and transitive (if A is a sibling of B and B is a sibling of C, then A is a sibling of C), but it is not reflexive (a person is not a sibling of themselves). Therefore, it is not an equivalence relation.

Question 8

Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation.
-"Lives next door to"
A)Reflexive and symmetric; not an equivalence relation
B)Transitive; not an equivalence relation
C)Symmetric; not an equivalence relation
D)Symmetric and transitive; equivalence relation

Accepted Answer

The relation "lives next door to" is symmetric because if person A lives next door to person B, then person B lives next door to person A. However, it is not reflexive because a person does not live next door to themselves, and it is not transitive because if person A lives next door to person B, and person B lives next door to person C, it does not necessarily mean that person A lives next door to person C. Therefore, it is not an equivalence relation.

Question 9

Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation.
-"Is thinner than"
A)Transitive; not an equivalence relation
B)Reflexive and transitive; not an equivalence relation
C)Symmetric and transitive; not an equivalence relation
D)Symmetric; not an equivalence relation

Accepted Answer

The relation "is thinner than" is transitive because if person A is thinner than person B, and person B is thinner than person C, then person A is thinner than person C. It is not reflexive because a person cannot be thinner than themselves, and it is not symmetric because if person A is thinner than person B, it does not imply that person B is thinner than person A. Since it lacks reflexivity and symmetry, it is not an equivalence relation.

Question 10

Solve the problem.
-A private message agency charges 65 cents for the first ounce and 30 cents for each additional ounce or fraction of an ounce to send a message across town. How much does it cost to send a
Message weighing 1.5 ounces?
A)60 cents
B)$1.30
C)90 cents
D)95 cents

Accepted Answer

The cost for the first ounce is 65 cents, and for the additional 0.5 ounce (or fraction thereof), it's 30 cents. Adding these together gives 95 cents.

Question 11

Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation.
-"Is a son of"
A)Symmetric; not an equivalence relation
B)Reflexive; not an equivalence relation
C)Transitive; not an equivalence relation
D)None; not an equivalence relation

Accepted Answer

The relation "is a son of" is not reflexive because no person is a son of themselves, not symmetric because if person A is a son of person B, it does not imply that person B is a son of person A, and it is transitive. However, due to the lack of reflexivity and symmetry, it is not an equivalence relation.

Quiz 8: Real Numbers and Algebraic Thinking

Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation. -"Is a cousin of"

Solve the problem. -A cable company charges by the number of movie channels a subscriber chooses. The cost is given by 11.90 + 3.70x, where x is the number of movie channels. What is the cost for 2 movie channels.

Solve the problem. -A cab ride costs $1.70 base plus $0.90 a mile. How far can you go for $13.40?

Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation. -"Is the same weight as"

Solve the problem. -A long distance phone call costs $2.40 for the first minute plus $1.20 each additional minute. What is the cost of a 17 minute call?

Solve the problem. -The cost of a cab ride in dollars is given by C(x) = 1.80 + 1.10x, where x is the number of miles. What are the charges for a ride of 25 miles?

Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation. -"Is a sibling of"

Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation. -"Lives next door to"

Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation. -"Is thinner than"

Solve the problem. -A private message agency charges 65 cents for the first ounce and 30 cents for each additional ounce or fraction of an ounce to send a message across town. How much does it cost to send a Message weighing 1.5 ounces?

Tell whether the relation is reflexive, symmetric, or transitive on the set of all people. Also tell whether the relation is an equivalence relation. -"Is a son of"