Question 1

Use scientific notation to solve the problem.
-How many liters of oil are needed to supply the electrical energy needs of an average U.S. home for 7 weeks? Assume that the energy released by burning one liter of oil is $1.2 \times 10 ^ { 7 }$joules and that the
Electrical energy used daily in an average U.S. home is  $5 \times 10 ^ { 7 }$ joules. Round your answer to the
Nearest tenth of a liter.

Accepted Answer

The answer of Use scientific notation to solve the problem.
-How...

Question 2

Solve the problem.
-The table below shows the result of a polygraph test conducted on 2000 college students. Students were asked whether they had ever cheated on a test. All of them denied having cheated. Use the
Table to answer the question. $$\begin{array} { l | c c c } 
& \begin{array} { c } 
\text { Test finds } \
\text { student lying }
\end{array} & \begin{array} { c } 
\text { Test finds } \
\text { student }
\end{array} \
\hline \text { Has cheated } & 85 & 11 & \text { Thuthful } \
\text { Has not cheated } & 228 & 1676 & 1904 \
\text { Total } & 313 & 1687 & 2000
\end{array}$$ What percentage of those that were telling the truth were found to be lying?

Accepted Answer

The number of students who were truthful but found to be lying is 228. The total number of truthful students is 1904. The percentage is (228/1904) * 100 = 12%.

Question 3

Solve the problem.
-Find the gasoline price index for 1965 using the 2000 price as the reference value. Use the table below. $$\begin{array}{l}
\text { YEAR|GASOLINE PRICE }\
\begin{array} { l | l } 
& \text { (cents per gallon) } \
\hline 1955 & 29.1 \
1965 & 31.2 \
1975 & 56.7 \
1985 & 119.6 \
1995 & 120.5 \
2000 & 155.0 \
2010 & 284.0
\end{array}
\end{array}$$

Accepted Answer

To find the gasoline price index for 1965 using the 2000 price as the reference value, you divide the 1965 price by the 2000 price and then multiply by 100. So, $\frac{31.2}{155.0} \times 100 = 20.1$.

Question 4

Write the number in scientific notation.
-$302.23$

Accepted Answer

To convert 302.23 to scientific notation, we move the decimal point two places to the left, which gives us $3.0223$. Since we moved the decimal to the left, the exponent on the 10 is positive, making the correct notation $3.0223 \times 10^2$.

Question 5

Answer the question.
-Find the scale ratio for a map if 3 centimeters on the map represents 0.6 kilometer on the ground.

Accepted Answer

To find the scale ratio, convert kilometers to centimeters: 0.6 km = 60,000 cm. The scale ratio is 3 cm : 60,000 cm, which simplifies to 1 : 20,000.

Question 6

Answer the question.
-Find the scale ratio for a map if 1 centimeter on the map represents 100 kilometers on the ground.

Accepted Answer

To convert 100 kilometers to centimeters (since 1 km = 100,000 cm), multiply 100 by 100,000 to get 10,000,000. Thus, the scale ratio is $1 : 10,000,000$.

Question 7

Use the Consumer Price Index below to answer the question. $$\begin{array}{l}
\text { Average Annual Consumer Price Index (1982-1984 = 100) }\
\begin{array} { c | c | c | c | c | c } 
\text { Year } & \text { CPI } & \text { Year } & \text { CPI } & \text { Year } & \text { CPI } \
\hline 1986 & 109.6 & 1995 & 152.4 & 2004 & 188.9 \
1987 & 113.6 & 1996 & 156.9 & 2005 & 195.3 \
1988 & 118.3 & 1997 & 160.5 & 2006 & 201.6 \
1989 & 124.0 & 1998 & 163.0 & 2007 & 207.3 \
1990 & 130.7 & 1999 & 166.6 & 2008 & 215.3 \
1991 & 136.2 & 2000 & 172.2 & 2009 & 214.5 \
1992 & 140.3 & 2001 & 177.1 & 2010 & 218.1 \
1993 & 144.5 & 2002 & 179.9 & 2011 & 224.9 \
1994 & 148.2 & 2003 & 184.0 & 2012 & 229.6
\end{array}
\end{array}$$
-In 1991, the federal minimum hourly wage was $3.5. Convert this to 2000 dollars.

Accepted Answer

To convert the 1991 federal minimum hourly wage to 2000 dollars, use the formula: $$ \text{Amount in 2000 dollars} = \text{Amount in 1991 dollars} \times \frac{\text{CPI in 2000}}{\text{CPI in 1991}} $$ Substituting the given values: $$ $3.5 \times \frac{172.2}{136.2} = $3.5 \times 1.264 \approx $4.43 $$

Question 8

Determine whether the source of error represents random or systematic error.
-When scientists estimate the height of a mountain there is a certain amount of error involved in measuring distances and angles.

Accepted Answer

The error involved in measuring distances and angles when estimating the height of a mountain is typically random error, as it can vary in magnitude and direction from one measurement to another due to unpredictable factors such as atmospheric conditions, instrument precision, and human error.

Question 9

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is thanthe second.
-$10 ^ { 12 } , 10 ^ { 36 }$

Accepted Answer

The difference in magnitude between $10^{12}$ and $10^{36}$ is found by dividing the smaller number by the larger number, which gives $10^{12} / 10^{36} = 10^{12-36} = 10^{-24}$.

Question 10

Determine whether the source of error represents random or systematic error.
-Athlete's are timed in the 100-m dash by a person with a stop watch. There is some error involved in stopping the watch at the correct instant.

Accepted Answer

This represents random error because the inaccuracies in stopping the watch at the exact moment can vary in either direction (starting too early or too late, stopping too early or too late), and these variations are unpredictable and random in nature.

Question 11

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is thanthe second.
-1 billion, 1 thousand

Accepted Answer

1 billion is $10^9$ and 1 thousand is $10^3$, so the factor is $10^9 / 10^3 = 10^6$.

Question 12

Determine ratio of A to B. Round as indicated.
-$A = 36 \pi$ square inches is the area of a circle with diameter 12 inches. $B = 144$ square inches is the area of a square with sides of length $< 12$ inches. (Do not round.)

Accepted Answer

The answer of Determine ratio of A to B. Round...

Question 13

Determine ratio of A to B. Round as indicated.
-$\mathrm { A } = 24.7 \%$ is the divorce rate in City A
$B = 28.7 \%$ is the divorce rate in City B
(Round to the nearest hundredth when necessary.)

Accepted Answer

To find the ratio of A to B, divide A by B: $24.7\% / 28.7\% = 0.8606$, which rounds to $0.86$ to the nearest hundredth.

Question 14

True or false?
-If somebody tells you that their exam score was 70%, up 80% from the last exam, you would
conclude that they must be lying or bad at math, because that is impossible.

Accepted Answer

An increase of 80% from the last exam does not mean the score reached 150%. If their previous score was 40%, an 80% increase of that score (which is 32%) would result in a new score of 72%, making a claim of a 70% score plausible.

Question 15

Write the percentage as a fraction or decimal, as indicated.
-Write as a decimal. 51.5%

Accepted Answer

To convert a percentage to a decimal, divide by 100. Thus, 51.5% becomes 0.515.

Question 16

Determine ratio of A to B. Round as indicated.
-$A = 3.1$ million is the population of City A
$B = 1.3$ million is the population of City B
(Round to the nearest hundredth when necessary.)

Accepted Answer

The ratio of A to B is calculated as $A/B = 3.1/1.3 = 2.384615...$, which rounds to $2.38$ to the nearest hundredth.

Question 17

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is thanthe second.
-One million, one millionth

Accepted Answer

The first number is one million, or $10^6$, and the second number is one millionth, or $10^{-6}$. To find how many times larger the first number is than the second, you divide the first by the second: $10^6 / 10^{-6} = 10^{6 - (-6)} = 10^{12}$.

Question 18

Use scientific notation to perform the following operations. Leave your answer in scientific notation.
-$\left( 5 \times 10 ^ { - 3 } \right) \div \left( 10 \times 10 ^ { - 4 } \right)$

Accepted Answer

The answer of Use scientific notation to perform the following...

Question 19

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated.
-963 people voted for the incumbent candidate out of 1778 voters. What percent voted for the incumbent?

Accepted Answer

To find the percentage of voters who voted for the incumbent, divide the number of people who voted for the incumbent (963) by the total number of voters (1778) and then multiply by 100. $ \frac{963}{1778} \times 100 \approx 54.2\% $.

Question 20

Solve the problem.
-Computer sales for a certain company have reached $49 million per year and are growing at 12% 211) annually. At this growth rate, what will the amount of sales be next year? Round to the nearest
Tenth of a million.

Accepted Answer

To find the sales amount for next year, we calculate the growth by multiplying the current sales by the growth rate (12%), and then add that to the current sales. $49 million * 12% = $5.88 million. Adding this to the current sales gives us $49 million + $5.88 million = $54.88 million, which rounds to $54.9 million.

Quiz 3: Numbers in the Real World

Write the number in scientific notation. - $302.23$

Answer the question. -Find the scale ratio for a map if 3 centimeters on the map represents 0.6 kilometer on the ground.

Answer the question. -Find the scale ratio for a map if 1 centimeter on the map represents 100 kilometers on the ground.

Determine whether the source of error represents random or systematic error. -When scientists estimate the height of a mountain there is a certain amount of error involved in measuring distances and angles.

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is thanthe second. - $10 ^ { 12 } , 10 ^ { 36 }$

Determine whether the source of error represents random or systematic error. -Athlete's are timed in the 100-m dash by a person with a stop watch. There is some error involved in stopping the watch at the correct instant.

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is thanthe second. -1 billion, 1 thousand

Determine ratio of A to B. Round as indicated. - $A = 36 \pi$ square inches is the area of a circle with diameter 12 inches. $B = 144$ square inches is the area of a square with sides of length $< 12$ inches. (Do not round.)

Determine ratio of A to B. Round as indicated. - $\mathrm { A } = 24.7 \%$ is the divorce rate in City A $B = 28.7 \%$ is the divorce rate in City B (Round to the nearest hundredth when necessary.)

True or false? -If somebody tells you that their exam score was 70%, up 80% from the last exam, you would conclude that they must be lying or bad at math, because that is impossible.

Write the percentage as a fraction or decimal, as indicated. -Write as a decimal. 51.5%

Determine ratio of A to B. Round as indicated. - $A = 3.1$ million is the population of City A $B = 1.3$ million is the population of City B (Round to the nearest hundredth when necessary.)

Determine by what factor the numbers differ. In other words, determine how many times larger the first number is thanthe second. -One million, one millionth

Use scientific notation to perform the following operations. Leave your answer in scientific notation. - $\left( 5 \times 10 ^ { - 3 } \right) \div \left( 10 \times 10 ^ { - 4 } \right)$

Solve the problem. Round your answer to the nearest tenth unless otherwise indicated. -963 people voted for the incumbent candidate out of 1778 voters. What percent voted for the incumbent?

Solve the problem. -Computer sales for a certain company have reached $49 million per year and are growing at 12% 211) annually. At this growth rate, what will the amount of sales be next year? Round to the nearest Tenth of a million.