Question 1

Decide whether the given set of numbers is a group under the given operation.
-Prime numbers; multiplication

Accepted Answer

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

Question 2

Decide whether or not the modulo system forms a group.
-{1, 2}; multiplication modulo 3

Accepted Answer

A)  Not a group 
B)  Group 
A)  Not a group 
B)  Group

Question 3

Perform the modular arithmetic operation.
-42 - 29 (mod 4)

Accepted Answer

A)  0 
B)  52 
C)  1 
D)  2 
A)  0 
B)  52 
C)  1 
D)  2

Question 4

Provide an appropriate response.
-Give the additive and multiplicative inverses of 6 for the set of rational numbers.

Accepted Answer

The answer of Provide an appropriate response.
-Give the additive and...

Question 5

Perform the indicated operation.
-Let $\mathrm { A } = \left[ \begin{array} { l l } - 5 & 2 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { l l } 1 & 0 \end{array} \right]$. Find $3 \mathrm {~A} + 4 \mathrm {~B}$.

Accepted Answer

A)  $[ - 15\ 4 ]$ 
B)  $[ - 11\ 6 ]$ 
C)  $\left[ \begin{array} { l l } - 2 & 2 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l } - 9 & 4 \end{array} \right]$ 
A)  $[ - 15\ 4 ]$ 
B)  $[ - 11\ 6 ]$ 
C)  $\left[ \begin{array} { l l } - 2 & 2 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l } - 9 & 4 \end{array} \right]$

Question 6

Perform the indicated operation.
-Let $B = \left[ \begin{array} { l l l l } - 1 & 1 & 4 & - 3 \end{array} \right]$. Find -3B.

Accepted Answer

A)  $\left[ \begin{array} { l l l l } 3 & - 3 & - 12 & 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l l } - 3 & 3 & 12 & - 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l l } 3 & 1 & 4 & - 3 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l l } - 3 & - 1 & 2 & - 5 \end{array} \right]$ 
A)  $\left[ \begin{array} { l l l l } 3 & - 3 & - 12 & 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { l l l l } - 3 & 3 & 12 & - 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { l l l l } 3 & 1 & 4 & - 3 \end{array} \right]$ 
D)  $\left[ \begin{array} { l l l l } - 3 & - 1 & 2 & - 5 \end{array} \right]$

Question 7

Determine the sum or difference in clock 12 arithmetic.
-(12 + 7) + 12

Accepted Answer

A)  31 
B)  3 
C)  8 
D)  7 
A)  31 
B)  3 
C)  8 
D)  7

Question 8

Solve the problem.
-A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount Of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers J and K. What is The cost of 100 batches from supplier J?  $\quad $ $\quad $ $\quad $ $\quad $$\text { sugar choc milk } \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \mathrm{J} \quad\mathrm{K}$
$$A = \left[ \begin{array} { r r r } 
6 & 8 & 1 \
6 & 4 & 1 \
5 & 7 & 1
\end{array} \right] \text { cherry } \text { almond } \quad B = \left[ \begin{array} { l l } 
4 & 3 \
4 & 5 \
2 & 2
\end{array} \right] \text { misingar } \text { moc }$$

Accepted Answer

A)  $6,000 
B)  $15,000 
C)  $15,200 
D)  $12,000 
A)  $6,000 
B)  $15,000 
C)  $15,200 
D)  $12,000

Question 9

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.
-$$\begin{array} { c | c c c } 
? & 3 & 8 & 11 \ 
\hline 3 & 8 & 11 & 3 \
8 & 11 & 3 & 8 \
11 & 3 & 8 & 11
\end{array}$$

Accepted Answer

A)  All of them 
B)  Closure, identity, inverse, and associative only 
C)  Closure, identity, associative, and commutative only 
D)  Identity, inverse, and commutative only 
A)  All of them 
B)  Closure, identity, inverse, and associative only 
C)  Closure, identity, associative, and commutative only 
D)  Identity, inverse, and commutative only

Question 10

Determine the sum or difference in the given clock arithmetic.
-4 - 3 (clock 7)

Accepted Answer

A)  3 
B)  1 
C)  5 
D)  2 
A)  3 
B)  1 
C)  5 
D)  2

Question 11

Find all replacements (less than the modulus) for the question mark that make the statement true.
-5 - 8 ≡ ? (mod 13)

Accepted Answer

A)  2 
B)  10 
C)  4 
D)  11 
A)  2 
B)  10 
C)  4 
D)  11

Question 12

Perform the modular arithmetic operation.
-[(9 ∙ 7) - 1] (mod 5)

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
A)  1 
B)  2 
C)  3 
D)  4

Question 13

Solve the problem.
-If Thursday is your starting day, what day will it be 2 years, 24 days from Thursday? (Assume no Leap years.)

Accepted Answer

A)  Friday 
B)  Wednesday 
C)  Thursday 
D)  Tuesday 
A)  Friday 
B)  Wednesday 
C)  Thursday 
D)  Tuesday

Question 14

Find the modulo class to which the number belongs for the given modulo system.
-78, mod 4

Accepted Answer

A)  1 
B)  3 
C)  0 
D)  2 
A)  1 
B)  3 
C)  0 
D)  2

Question 15

Decide whether the given set of numbers is a group under the given operation.
-Natural numbers; subtraction

Accepted Answer

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

Question 16

Perform the modular arithmetic operation.
-[(5 - 7) ∙ 7] (mod 5)

Accepted Answer

A)  4 
B)  1 
C)  0 
D)  3 
A)  4 
B)  1 
C)  0 
D)  3

Question 17

Decide whether the given set of numbers is a commutative group under the given operation.
-Even integers; addition

Accepted Answer

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

Question 18

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.
-$$\begin{array} { l | l l l } 
?   & \wedge & £ & \Phi \
\hline \wedge & \wedge & £ & \Phi \
£ & £ & \wedge & \Phi \
\Phi & \Phi & £ & \wedge
\end{array}$$

Accepted Answer

A)  Closure, identity, inverse, and associative only 
B)  Closure, identity, and inverse only 
C)  All of them 
D)  Closure only 
A)  Closure, identity, inverse, and associative only 
B)  Closure, identity, and inverse only 
C)  All of them 
D)  Closure only

Question 19

Solve the problem.
-A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount Of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers R and S. What is The cost of 100 batches from supplier R?

Accepted Answer

A)  $16,800 
B)  $6,600 
C)  $13,200 
D)  $17,900 
A)  $16,800 
B)  $6,600 
C)  $13,200 
D)  $17,900

Question 20

Decide whether or not the modulo system forms a group.
-{0, 1, 2, 3, 4, 5, 6, 7}; addition modulo 8

Accepted Answer

A)  Group 
B)  Not a group 
A)  Group 
B)  Not a group

Decide whether the given set of numbers is a group under the given operation. -Prime numbers; multiplication

Decide whether or not the modulo system forms a group. -{1, 2}; multiplication modulo 3

Perform the modular arithmetic operation. -42 - 29 (mod 4)

Provide an appropriate response. -Give the additive and multiplicative inverses of 6 for the set of rational numbers.

Perform the indicated operation. -Let $\mathrm { A } = \left[ \begin{array} { l l } - 5 & 2 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { l l } 1 & 0 \end{array} \right]$ . Find $3 \mathrm {~A} + 4 \mathrm {~B}$ .

Perform the indicated operation. -Let $B = \left[ \begin{array} { l l l l } - 1 & 1 & 4 & - 3 \end{array} \right]$ . Find -3B.

Determine the sum or difference in clock 12 arithmetic. -(12 + 7) + 12

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for the given system. - ? 3 8 11 3 8 11 3 8 11 3 8 11 3 8 11

Determine the sum or difference in the given clock arithmetic. -4 - 3 (clock 7)

Find all replacements (less than the modulus) for the question mark that make the statement true. -5 - 8 ≡ ? (mod 13)

Perform the modular arithmetic operation. -[(9 ∙ 7) - 1] (mod 5)

Solve the problem. -If Thursday is your starting day, what day will it be 2 years, 24 days from Thursday? (Assume no Leap years.)

Find the modulo class to which the number belongs for the given modulo system. -78, mod 4

Decide whether the given set of numbers is a group under the given operation. -Natural numbers; subtraction

Perform the modular arithmetic operation. -[(5 - 7) ∙ 7] (mod 5)

Decide whether the given set of numbers is a commutative group under the given operation. -Even integers; addition

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for the given system. - ? \wedge £ \Phi \wedge \wedge £ \Phi £ £ \wedge \Phi \Phi \Phi £ \wedge

Solve the problem. -A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount Of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers R and S. What is The cost of 100 batches from supplier R?

Decide whether or not the modulo system forms a group. -{0, 1, 2, 3, 4, 5, 6, 7}; addition modulo 8

Critical Thinking Skills

Sets

Logic

Systems of Numeration

Number Theory and the Real Number System

Algebra, Graphs, and Functions

The Metric System

Consumer Mathematics

Probability

Voting and Apportionment

Filters

Exam 9: Geometry

Decide whether the given set of numbers is a group under the given operation. -Prime numbers; multiplication

Decide whether or not the modulo system forms a group. -{1, 2}; multiplication modulo 3

Perform the modular arithmetic operation. -42 - 29 (mod 4)

Provide an appropriate response. -Give the additive and multiplicative inverses of 6 for the set of rational numbers.

Perform the indicated operation. -Let A=[−52]\mathrm { A } = \left[ \begin{array} { l l } - 5 & 2 \end{array} \right]A=[−5​2​] and B=[10]\mathrm { B } = \left[ \begin{array} { l l } 1 & 0 \end{array} \right]B=[1​0​] . Find 3 A+4 B3 \mathrm {~A} + 4 \mathrm {~B}3 A+4 B .

Perform the indicated operation. -Let B=[−114−3]B = \left[ \begin{array} { l l l l } - 1 & 1 & 4 & - 3 \end{array} \right]B=[−1​1​4​−3​] . Find -3B.

Determine the sum or difference in clock 12 arithmetic. -(12 + 7) + 12

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for the given system. - ? 3 8 11 3 8 11 3 8 11 3 8 11 3 8 11

Determine the sum or difference in the given clock arithmetic. -4 - 3 (clock 7)

Find all replacements (less than the modulus) for the question mark that make the statement true. -5 - 8 ≡ ? (mod 13)

Perform the modular arithmetic operation. -[(9 ∙ 7) - 1] (mod 5)

Solve the problem. -If Thursday is your starting day, what day will it be 2 years, 24 days from Thursday? (Assume no Leap years.)

Find the modulo class to which the number belongs for the given modulo system. -78, mod 4

Decide whether the given set of numbers is a group under the given operation. -Natural numbers; subtraction

Perform the modular arithmetic operation. -[(5 - 7) ∙ 7] (mod 5)

Decide whether the given set of numbers is a commutative group under the given operation. -Even integers; addition

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for the given system. - ? \wedge £ \Phi \wedge \wedge £ \Phi £ £ \wedge \Phi \Phi \Phi £ \wedge

Solve the problem. -A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the amount Of ingredients in one batch. Matrix B gives the costs of ingredients from suppliers R and S. What is The cost of 100 batches from supplier R?

Decide whether or not the modulo system forms a group. -{0, 1, 2, 3, 4, 5, 6, 7}; addition modulo 8

Critical Thinking Skills

Sets

Logic

Systems of Numeration

Number Theory and the Real Number System

Algebra, Graphs, and Functions

The Metric System

Consumer Mathematics

Probability

Voting and Apportionment

Filters

Perform the indicated operation. -Let $\mathrm { A } = \left[ \begin{array} { l l } - 5 & 2 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { l l } 1 & 0 \end{array} \right]$ . Find $3 \mathrm {~A} + 4 \mathrm {~B}$ .

Perform the indicated operation. -Let $B = \left[ \begin{array} { l l l l } - 1 & 1 & 4 & - 3 \end{array} \right]$ . Find -3B.