Question 1

Write each number in scientific notation and then multiply. Give the answer in scientific notation. (71,000,000)(200,000) A) $142 \times 10 ^ { 11 }$

B) $1.42 \times 10 ^ { 13 }$

C) $14.2 \times 10 ^ { 12 }$

D) $1.42 \times 10 ^ { 12 }$

Accepted Answer

The answer of Write each number in scientific notation and...

Question 2

Change the fraction to an equivalent fraction with the given denominator.
$$\frac { 14 } { 39 } = \frac { ? } { 273 }$$
A) $\frac { 98 } { 273 }$

B) $\frac { 546 } { 273 }$

C) $\frac { 14 } { 273 }$

D) $\frac { 28 } { 273 }$

Accepted Answer

The answer of Change the fraction to an equivalent fraction...

Question 3

Subtract. (-10) - (-16)
A) -6
B) 26
C) 6
D) -26

Accepted Answer

Subtracting a negative number is equivalent to adding its positive counterpart. So, (-10) - (-16) becomes (-10) + 16, which equals 6.

Question 4

Find the least common multiple of 16 and 96.
A) 1
B) 1536
C) 16
D) 96

Accepted Answer

The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both. Since 96 is a multiple of 16, the LCM of 16 and 96 is 96.

Question 5

$\text {The following statement illustrates the\underline{\quad\quad} property of multiplication. $\sqrt { 8 } \times \sqrt { 8 }$ is a real number.}$

A) identity
B) associative
C) commutative
D) closure

Accepted Answer

The closure property of multiplication states that the product of any two real numbers is also a real number. Since $\sqrt{8} \times \sqrt{8}$ results in a real number, it illustrates the closure property.

Question 6

Which property of the real numbers is illustrated by the following statement? 17 × 8 = 8 × 17
A) Identity property for multiplication
B) Commutative property of multiplication
C) Closure property for multiplication
D) Associative property of multiplication

Accepted Answer

The commutative property of multiplication states that the order of the factors does not affect the product. In other words, a × b = b × a. In this case, 17 × 8 = 8 × 17, so the commutative property of multiplication is illustrated.

Question 7

In a recent election $\frac { 493 } { 1000 }$ of all votes cast were for Candidate $\mathrm { A }$ and $\frac { 99 } { 200 }$ were for Candidate B. What fraction of ballots were cast for someone other than Candidate A or Candidate B?

A) $\frac { 247 } { 250 }$

B) $\frac { 1 } { 500 }$

C) $\frac { 487 } { 500 }$

D) $\frac { 3 } { 250 }$

Accepted Answer

The answer of In a recent election \(\frac { 493...

Question 8

The following statement illustrates the property for multiplication. 14 1 = 14
A) closure
B) associative
C) commutative
D) identity

Accepted Answer

The equation 14 × 1 = 14 illustrates the identity property of multiplication, which states that any number multiplied by 1 remains unchanged.

Question 9

Find the least common multiple of 4 and 20.
A) 20
B) 4
C) 80
D) 2

Accepted Answer

The least common multiple (LCM) of 4 and 20 is 20, as 20 is the smallest number that both 4 and 20 divide into without a remainder.

Question 10

What expression will give the sum of the first 11 terms of the following sequence? $5,20,80,320,1280 , \ldots$.

A) $\frac { 5 \left( 1 - 4 ^ { 11 } \right) } { 1 - 4 }$

В) $\frac { 4 \left( 1 - 5 ^ { 10 } \right) } { 1 - 5 }$

C) $\frac { 11 ( 5 - 15 ) } { 2 }$

D) $\frac { 4 \left( 1 - 5 ^ { 11 } \right) } { 1 - 4 }$

Accepted Answer

The answer of What expression will give the sum of...

Question 11

A student deposited $800 in a savings account that pays 3% annual interest. At the end of 10 years, how much money will be in the savings account?
A) $1875.13
B) $1075.13
C) $1840.00
D) $1040.00

Accepted Answer

The future value of the savings account can be calculated using the formula for compound interest: FV = P(1 + r)^n, where P is the principal amount ($800), r is the annual interest rate (0.03), and n is the number of years (10). Plugging in the values, FV = 800(1 + 0.03)^10 = 800(1.34391638) ≈ $1075.13.

Question 12

Perform the indicated operations. -144 ÷ 6 + 2
A) -22
B) 18
C) -18
D) 22

Accepted Answer

The answer of Perform the indicated operations. -144 ÷ 6...

Question 13

The 30-year average snowfall in Coldsville, USA is approximately 18 inches per year. As of January 10, Coldsville received approximately 10 inches. How much more snow will Coldsville receive if this is an average year?
A) 28 inches
B) 12 inches
C) 8 inches
D) 20 inches

Accepted Answer

If Coldsville has received 10 inches by January 10 and the average annual snowfall is 18 inches, then they would need 8 more inches to reach the average for the year.

Question 14

Multiply. Write the answer in scientific notation.
$$\left( 3 \times 10 ^ { 7 } \right) \left( 8 \times 10 ^ { 2 } \right)$$
A) $24 \times 10 ^ { 9 }$

В) $24 \times 10 ^ { 14 }$

C) $2.4 \times 10 ^ { 15 }$

D) $2.4 \times 10 ^ { 10 }$

Accepted Answer

The answer of Multiply. Write the answer in scientific notation.
\[\left(...

Question 15

The number of miles that light travels in one year is called a light-year. One light-year is equal to $5.88 \times 10 ^ { 12 }$ miles. A certain star is 46 light-years away from the earth. How far is this in miles? Round to 5 significant digits if necessary.
A) $1.2783 \times 10 ^ { 12 }$

B) $1.2783 \times 10 ^ { 11 }$

C) $2.7048 \times 10 ^ { 13 }$

D) $2.7048 \times 10 ^ { 14 }$

Accepted Answer

The answer of The number of miles that light travels...

Question 16

Simplify and write the answer in exponential notation using positive exponents. $6 ^ { 7 } \cdot 6 ^ { - 4 }$

A) $6 ^ { 3 }$

B) $36 ^ { 3 }$

C) $36 ^ { - 28 }$

D) $6 ^ { - 28 }$

Accepted Answer

The answer of Simplify and write the answer in exponential...

Question 17

Which property of the real numbers is illustrated by the following statement? -19 × (17 + 8) = -19(17) + (-19)(8)
A) Commutative property of multiplication
B) Closure property of multiplication
C) Distributive property
D) Associative property of addition

Accepted Answer

The statement illustrates the distributive property, which states that a(b + c) = ab + ac.

Question 18

Evaluate. $3 ^ { - 4 }$
A) $- 81$

B) $- 12$

C) $\frac { 1 } { 81 }$

D) $- \frac { 1 } { 81 }$

Accepted Answer

The answer of Evaluate. $3 ^ { - 4 }$
A)...

Question 19

$$\text { Simplify. } 8 ^ { 9 } \cdot 8 ^ { - 9 }$$
A) Undefined
B) 0
C) 1
D) 8

Accepted Answer

When multiplying powers with the same base, you add the exponents. Here, $8^9 \cdot 8^{-9} = 8^{9 + (-9)} = 8^0 = 1$.

Question 20

Perform the indicated operations. (82 - 60) + [(-3 × 4) - 36 ÷ 4]
A) 19
B) 25
C) 1
D) 10

Accepted Answer

First, calculate inside the brackets: (-3 × 4) = -12 and 36 ÷ 4 = 9. So, (-12 - 9) = -21. Then, (82 - 60) = 22. Finally, 22 + (-21) = 1.

Quiz 5: The Real Number System

Write each number in scientific notation and then multiply. Give the answer in scientific notation. (71,000,000)(200,000) A) $142 \times 10 ^ { 11 }$ B) $1.42 \times 10 ^ { 13 }$ C) $14.2 \times 10 ^ { 12 }$ D) $1.42 \times 10 ^ { 12 }$

Change the fraction to an equivalent fraction with the given denominator. $\frac { 14 } { 39 } = \frac { ? } { 273 }$ A) $\frac { 98 } { 273 }$ B) $\frac { 546 } { 273 }$ C) $\frac { 14 } { 273 }$ D) $\frac { 28 } { 273 }$

Subtract. (-10) - (-16)

Find the least common multiple of 16 and 96.

$\text {The following statement illustrates the\underline{\quad\quad} property of multiplication. \sqrt { 8 } \times \sqrt { 8 } is a real number.}$

Which property of the real numbers is illustrated by the following statement? 17 × 8 = 8 × 17

The following statement illustrates the property for multiplication. 14 1 = 14

Find the least common multiple of 4 and 20.

A student deposited $800 in a savings account that pays 3% annual interest. At the end of 10 years, how much money will be in the savings account?

Perform the indicated operations. -144 ÷ 6 + 2

The 30-year average snowfall in Coldsville, USA is approximately 18 inches per year. As of January 10, Coldsville received approximately 10 inches. How much more snow will Coldsville receive if this is an average year?

Multiply. Write the answer in scientific notation. $\left( 3 \times 10 ^ { 7 } \right) \left( 8 \times 10 ^ { 2 } \right)$ A) $24 \times 10 ^ { 9 }$ В) $24 \times 10 ^ { 14 }$ C) $2.4 \times 10 ^ { 15 }$ D) $2.4 \times 10 ^ { 10 }$

Simplify and write the answer in exponential notation using positive exponents. $6 ^ { 7 } \cdot 6 ^ { - 4 }$ A) $6 ^ { 3 }$ B) $36 ^ { 3 }$ C) $36 ^ { - 28 }$ D) $6 ^ { - 28 }$

Which property of the real numbers is illustrated by the following statement? -19 × (17 + 8) = -19(17) + (-19) (8)

Evaluate. $3 ^ { - 4 }$ A) $- 81$ B) $- 12$ C) $\frac { 1 } { 81 }$ D) $- \frac { 1 } { 81 }$

$\text { Simplify. } 8 ^ { 9 } \cdot 8 ^ { - 9 }$

Perform the indicated operations. (82 - 60) + [(-3 × 4) - 36 ÷ 4]