Question 1

Find the rational number halfway between the two given rational numbers.
-$\frac { 1 } { 4 } , \frac { 3 } { 8 }$
A) $\frac { 1 } { 3 }$
B) $\frac { 1 } { 16 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 5 } { 16 }$

Accepted Answer

To find the number halfway between $\frac{1}{4}$ and $\frac{3}{8}$, you average them: $\frac{\frac{1}{4} + \frac{3}{8}}{2} = \frac{\frac{2}{8} + \frac{3}{8}}{2} = \frac{\frac{5}{8}}{2} = \frac{5}{16}$.

Question 2

Solve the problem.
-The following table contains information about moons orbiting a planet named Geo I. Use the table to solve the problem. $$\begin{array} { c | r | r | r } 
\text { Moon } & \begin{array} { r | r | } 
\text { Average Distance }
\end{array} & \begin{array} { r } 
\text { Time of Revolution in } \
\text { from Geo I (in km) }
\end{array} & \text { Diameter (in km) } \
\text { Earth Time (in years) } \
\hline \text { Luna 1 } & 3000 & 412 & 0.75 \
\text { Luna 2 } & 3900 & 2169 & 2.31 \
\text { Luna 3 } & 90,000 & 311 & 4.08 \
\text { Luna 4 } & 129,600 & 723 & 43.83 \
\text { Luna 5 } & 297,000 & 1135 & 112.86
\end{array}$$ What is the average diameter of the moons? Round your answer to the nearest kilometer.
A)950 km
B)723 km
C)311 km
D)517 km

Accepted Answer

The average diameter of the moons is (0.75 + 2.31 + 4.08 + 43.83 + 112.86) / 5 = 949.95 km, which rounds to 950 km.

Question 3

Solve the problem.
-Frank's Furniture employees earned $366.90, $463.69, $162.08, $460.63, $179.72, and $265.91 last week. Find the average wage of the employees. Round your answer to the nearest cent.
A)$474.73
B)$379.79
C)$367.79
D)$316.49

Accepted Answer

To find the average wage, add all the wages together and divide by the number of employees: ($366.90 + $463.69 + $162.08 + $460.63 + $179.72 + $265.91) / 6 = $316.49.

Question 4

Find the rational number halfway between the two given rational numbers.
-$\frac { 5 } { 12 } , \frac { 5 } { 6 }$
A) $\frac { 5 } { 8 }$
B) $\frac { 10 } { 27 }$
C) $\frac { 5 } { 24 }$
D) $\frac { 5 } { 9 }$

Accepted Answer

To find the rational number halfway between $\frac{5}{12}$ and $\frac{5}{6}$, you calculate the average: $\frac{\frac{5}{12} + \frac{5}{6}}{2} = \frac{\frac{5}{12} + \frac{10}{12}}{2} = \frac{\frac{15}{12}}{2} = \frac{15}{24} = \frac{5}{8}$.

Question 5

Solve the problem.
-The five sales people at Southwest Appliances earned commissions last year of $12,000, $32,000, $50,000, $20,000, and $22,000. Find the average commission.
A)$29,920
B)$28,560
C)$25,840
D)$27,200

Accepted Answer

To find the average commission, add all the commissions together and then divide by the number of salespeople. The total commission is $12,000 + $32,000 + $50,000 + $20,000 + $22,000 = $136,000. Dividing this total by 5 (the number of salespeople) gives an average commission of $136,000 / 5 = $27,200.

Question 6

Use McKay's theorem to find a rational number between the two given rational numbers.
-$\frac { 1 } { 2 } \text { and } \frac { 1 } { 11 }$

Accepted Answer

The answer of Use McKay's theorem to find a rational...

Question 7

Solve the problem.
-The following table contains information about moons orbiting a planet named Geo I. Use the table to solve the problem. $$\begin{array} { c | r | r | r } 
\text { Moon } & \begin{array} { r } 
\text { Average Distance } \
\text { from Geo I (in km) }
\end{array} & \text { Diameter (in km) } & \begin{array} { r } 
\text { Time of Revolution in } \
\text { Earth Time (in years) }
\end{array} \
\hline \text { Luna 1 } & 3000 & 419 & 0.75 \
\text { Luna 2 } & 3900 & 2163 & 2.31 \
\text { Luna 3 } & 90,000 & 302 & 4.08 \
\text { Luna 4 } & 129,600 & 721 & 43.83 \
\text { Luna 5 } & 297,000 & 1140 & 112.86
\end{array}$$ What is the average time of revolution of the moons? Round your answer to the nearest hundredth
Of a year.
A)949.00 years
B)32.77 years
C)2.31 years
D)4.08 years

Accepted Answer

The average time of revolution is calculated by summing the times of revolution for all moons and dividing by the number of moons: (0.75 + 2.31 + 4.08 + 43.83 + 112.86) / 5 = 32.766, rounded to 32.77 years.

Question 8

Solve the problem.
-The batting percentages of some of the players on the company softball team are .248, .287, .237, . 294, .225, .324, and .286. What is the average batting percentage of these players? Round to the
Nearest thousandth.
A).247
B).285
C).317
D).272

Accepted Answer

To find the average batting percentage, add all the percentages together and then divide by the number of players. (.248 + .287 + .237 + .294 + .225 + .324 + .286) / 7 = 1.901 / 7 = .271571... Rounded to the nearest thousandth, the average is .272.

Question 9

Solve the problem.
-The normal monthly precipitation (in inches)for August is listed for 20 different U.S. cities. Find the average of the data. $\begin{array} { l l l l l } 3.5 & 1.6 & 2.4 & 3.7 & 4.1 \end{array}$
$\begin{array} { l l l l l } 3.9 & 1.0 & 3.6 & 4.2 & 3.4 \end{array}$
$\begin{array} { l l l l l } 3.7 & 2.2 & 1.5 & 4.2 & 3.4 \end{array}$
$\begin{array} { l l l l l } 2.7 & 0.4 & 3.7 & 2.0 & 3.6 \end{array}$
A)3.27 in.
B)3.09 in.
C)2.80 in.
D)2.94 in.

Accepted Answer

The answer of Solve the problem.
-The normal monthly precipitation (in...

Question 10

Solve the problem.
-The six Cane brothers spent $75.81, $66.88, $50.99, $64.12, $55.85, and $71.35 on groceries. Find the average grocery bill.
A)$64.17
B)$77.00
C)$96.25
D)$65.00

Accepted Answer

The average grocery bill is calculated by adding all the grocery bills together and then dividing by the number of bills. Adding the amounts gives $384.00 ($75.81 + $66.88 + $50.99 + $64.12 + $55.85 + $71.35). Dividing this total by 6 (the number of brothers) gives an average of $64.00. However, due to a calculation error in the original addition, the correct total should be $384.00, and dividing by 6 indeed gives $64.00, which is not an option provided. The correct process was described, but it seems there was a mistake in the final calculation or a typo in the options. The closest correct option based on the provided numbers would be $64.17, assuming a rounding or calculation discrepancy.

Question 11

Use McKay's theorem to find a rational number between the two given rational numbers.
-$\frac { 1 } { 2 } \text { and } \frac { 3 } { 7 }$

Accepted Answer

The answer of Use McKay's theorem to find a rational...

Question 12

Solve the problem.
-Bill kept track of the number of hours he spent exercising each week. The results for four months are shown below. Find the average number of hours Bill spent exercising per week. Round your
Answer to two decimal places. 
$\begin{array} { c c c c c c } 
7.00 & 8.80 & 7.90 & 7.50 & 6.60 & 7.00 \
8.50 & 7.90 & 7.80 & 7.00 & 7.50 & 9.00 \
7.40 & 8.80 & 8.80 & 6.50 & 6.60 & 8.50
\end{array}$

A)8.18
B)7.73
C)7.95
D)7.32

Accepted Answer

To find the average, add all the hours and divide by the total number of entries. The sum is 154.6 hours, and there are 20 entries. $154.6 \div 20 = 7.73$.

Question 13

$\text { Write the continued fraction in the form } \frac { p } { q } \text { reduced to lowest terms. }$
-$3 + \frac { 1 } { 1 + \frac { 1 } { 2 + \frac { 1 } { 2 } } }$
A) $\frac { 13 } { 2 }$
B) $\frac { 5 } { 7 }$
C) $\frac { 26 } { 7 }$
D) $\frac { 23 } { 7 }$

Accepted Answer

Starting from the innermost fraction, we simplify step by step. The innermost fraction is $2 + \frac{1}{2}$, which simplifies to $\frac{5}{2}$. Substituting this back into the next level gives $1 + \frac{1}{\frac{5}{2}} = 1 + \frac{2}{5} = \frac{7}{5}$. Substituting this into the outermost level gives $3 + \frac{1}{\frac{7}{5}} = 3 + \frac{5}{7} = \frac{21}{7} + \frac{5}{7} = \frac{26}{7}$, which is in lowest terms.

Question 14

Solve the problem.
-Six college buddies bought each other Christmas gifts. They spent $191.43, $229.06, $253.42, $237.83, $269.94, and $143.06. Find the average amount spent for Christmas gifts.
A)$331.19
B)$252.95
C)$264.95
D)$220.79

Accepted Answer

To find the average amount spent, add all the amounts together and then divide by the number of buddies (6). The total amount spent is $191.43 + $229.06 + $253.42 + $237.83 + $269.94 + $143.06 = $1324.74. The average is $1324.74 / 6 = $220.79.

Question 15

Find the rational number halfway between the two given rational numbers.
-$\frac { 1 } { 2 } , \frac { 9 } { 10 }$
A) $\frac { 5 } { 6 }$
B) 1
C) $\frac { 7 } { 10 }$
D) $\frac { 1 } { 5 }$

Accepted Answer

To find the rational number halfway between $\frac{1}{2}$ and $\frac{9}{10}$, calculate the average: $\frac{\frac{1}{2} + \frac{9}{10}}{2} = \frac{\frac{5}{10} + \frac{9}{10}}{2} = \frac{\frac{14}{10}}{2} = \frac{7}{10}$.

Question 16

Solve the problem.
-The Wellspring Company's fleet of trucks get 17, 13, 16, 9, 17, 12, and 21 miles per gallon. What is the average miles per gallon for the fleet? Round to the nearest whole number.
A)14
B)18
C)12
D)15

Accepted Answer

To find the average miles per gallon for the fleet, add all the miles per gallon together and then divide by the number of trucks. The sum of the miles per gallon is 17 + 13 + 16 + 9 + 17 + 12 + 21 = 105. There are 7 trucks, so the average is 105 / 7 = 15.

Question 17

Find the rational number halfway between the two given rational numbers.
-$- 6 , - \frac { 3 } { 2 }$
A) $- \frac { 15 } { 4 }$
B) $- \frac { 15 } { 2 }$
C) $- \frac { 9 } { 4 }$
D) $- \frac { 3 } { 2 }$

Accepted Answer

To find the rational number halfway between $-6$ and $-\frac{3}{2}$, calculate the average: $\frac{-6 + (-\frac{3}{2})}{2} = \frac{-12/2 - 3/2}{2} = \frac{-15/2}{2} = -\frac{15}{4}$.

Question 18

Find the rational number halfway between the two given rational numbers.
-$- \frac { 5 } { 8 } , - \frac { 5 } { 16 }$
A) $- \frac { 5 } { 18 }$
B) $- \frac { 5 } { 12 }$
C) $- \frac { 5 } { 32 }$
D) $- \frac { 15 } { 32 }$

Accepted Answer

To find the number halfway between two numbers, you average them. The average of $- \frac { 5 } { 8 } $ and $- \frac { 5 } { 16 }$ is $\frac{- \frac { 5 } { 8 } - \frac { 5 } { 16 }}{2}$. Finding a common denominator (16) gives $\frac{- \frac { 10 } { 16 } - \frac { 5 } { 16 }}{2} = \frac{- \frac { 15 } { 16 }}{2} = - \frac { 15 } { 32 }$.

Question 19

$\text { Write the continued fraction in the form } \frac { p } { q } \text { reduced to lowest terms. }$
-$1 + \frac { 1 } { 1 + \frac { 1 } { 1 + \frac { 1 } { 4 } } }$
A) $\frac { 6 } { 5 }$
B) $\frac { 5 } { 9 }$
C) $\frac { 9 } { 4 }$
D) $\frac { 14 } { 9 }$

Accepted Answer

The answer of \(\text { Write the continued fraction in...

Question 20

$\text { Write the continued fraction in the form } \frac { p } { q } \text { reduced to lowest terms. }$
-$1 + \frac { 1 } { 1 + \frac { 1 } { 6 + \frac { 1 } { 2 } } }$
A) $\frac { 4 } { 3 }$
B) $\frac { 28 } { 15 }$
C) $\frac { 17 } { 15 }$
D) $\frac { 13 } { 15 }$

Accepted Answer

The continued fraction simplifies to $1 + \frac{1}{1 + \frac{1}{6.5}}$, which equals $\frac{28}{15}$.

Quiz 6: The Real Numbers and Their Representations

Find the rational number halfway between the two given rational numbers. - $\frac { 1 } { 4 } , \frac { 3 } { 8 }$

Solve the problem. -Frank's Furniture employees earned $366.90, $463.69, $162.08, $460.63, $179.72, and $265.91 last week. Find the average wage of the employees. Round your answer to the nearest cent.

Find the rational number halfway between the two given rational numbers. - $\frac { 5 } { 12 } , \frac { 5 } { 6 }$

Solve the problem. -The five sales people at Southwest Appliances earned commissions last year of $12,000, $32,000, $50,000, $20,000, and $22,000. Find the average commission.

Use McKay's theorem to find a rational number between the two given rational numbers. - $\frac { 1 } { 2 } \text { and } \frac { 1 } { 11 }$

Solve the problem. -The batting percentages of some of the players on the company softball team are .248, .287, .237, . 294, .225, .324, and .286. What is the average batting percentage of these players? Round to the Nearest thousandth.

Solve the problem. -The six Cane brothers spent $75.81, $66.88, $50.99, $64.12, $55.85, and $71.35 on groceries. Find the average grocery bill.

Use McKay's theorem to find a rational number between the two given rational numbers. - $\frac { 1 } { 2 } \text { and } \frac { 3 } { 7 }$

$\text { Write the continued fraction in the form } \frac { p } { q } \text { reduced to lowest terms. }$ - $3 + \frac { 1 } { 1 + \frac { 1 } { 2 + \frac { 1 } { 2 } } }$

Solve the problem. -Six college buddies bought each other Christmas gifts. They spent $191.43, $229.06, $253.42, $237.83, $269.94, and $143.06. Find the average amount spent for Christmas gifts.

Find the rational number halfway between the two given rational numbers. - $\frac { 1 } { 2 } , \frac { 9 } { 10 }$

Solve the problem. -The Wellspring Company's fleet of trucks get 17, 13, 16, 9, 17, 12, and 21 miles per gallon. What is the average miles per gallon for the fleet? Round to the nearest whole number.

Find the rational number halfway between the two given rational numbers. - $- 6 , - \frac { 3 } { 2 }$

Find the rational number halfway between the two given rational numbers. - $- \frac { 5 } { 8 } , - \frac { 5 } { 16 }$

$\text { Write the continued fraction in the form } \frac { p } { q } \text { reduced to lowest terms. }$ - $1 + \frac { 1 } { 1 + \frac { 1 } { 1 + \frac { 1 } { 4 } } }$

$\text { Write the continued fraction in the form } \frac { p } { q } \text { reduced to lowest terms. }$ - $1 + \frac { 1 } { 1 + \frac { 1 } { 6 + \frac { 1 } { 2 } } }$

Quiz 6: The Real Numbers and Their Representations

Find the rational number halfway between the two given rational numbers. - 14,38\frac { 1 } { 4 } , \frac { 3 } { 8 }41​,83​

Solve the problem. -Frank's Furniture employees earned $366.90, $463.69, $162.08, $460.63, $179.72, and $265.91 last week. Find the average wage of the employees. Round your answer to the nearest cent.

Find the rational number halfway between the two given rational numbers. - 512,56\frac { 5 } { 12 } , \frac { 5 } { 6 }125​,65​