Question 1

Answer the question.
-Suppose you are constructing a scale model solar system using a scale ratio of 1 to 10 billion. In your scale model what will be the diameter of Jupiter (in meters)? The diameter of Jupiter is
143,000 km.

Accepted Answer

The answer of Answer the question.
-Suppose you are constructing a...

Question 2

Write as a percent.
-$1 \frac { 2 } { 7 }$

Accepted Answer

$1 \frac{2}{7}$ is equal to $\frac{9}{7}$, which when converted to a percentage is $\frac{9}{7} \times 100 = 128.571429%$.

Question 3

Determine whether the source of error represents random or systematic error.
-Anne counts the number of cars passing an intersection in a 15-minute period. Sometimes she makes errors in counting.

Accepted Answer

Anne's errors in counting are inconsistent and can vary in either direction (overcounting or undercounting), which is characteristic of random error. Random errors are unpredictable and can be caused by human error, like miscounting in this case.

Question 4

Solve the problem.
-Find the gasoline price index for a year in which the cost of gasoline was $0.82 per gallon. Use the 1965 price as the reference value. In 1965, the cost of gasoline was 31.2 cents per gallon.

Accepted Answer

The gasoline price index is calculated by dividing the cost of gasoline in the year of interest by the cost in the base year (1965) and then multiplying by 100. So, for a year where gasoline was $0.82 per gallon, the index is ($0.82 / $0.312) * 100 = 262.8.

Question 5

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

Accepted Answer

The answer of Use the Consumer Price Index below to...

Question 6

Round to the indicated place value.
-Round to the nearest thousandth: 1.1983

Accepted Answer

The answer of Round to the indicated place value.
-Round to...

Question 7

Write the percentage as a fraction or decimal, as indicated.
-Write as a fraction. $83 \frac { 1 } { 3 } \%$

Accepted Answer

The answer of Write the percentage as a fraction or...

Question 8

Write the number in ordinary notation.
-$3.531 \times 10 ^ { - 5 }$

Accepted Answer

The expression $3.531 \times 10^{-5}$ means you move the decimal point 5 places to the left, resulting in 0.00003531.

Question 9

Use scientific notation to solve the problem.
-Assume that the volume of the earth is $5 \times 1014$ cubic meters and the volume of a bacterium is $2.5 \times$ $10 - 16$ cubic meters. If the earth could be filled with bacteria, how many would it contain?

Accepted Answer

To find the number of bacteria that can fill the Earth, divide the volume of the Earth by the volume of a bacterium: $ \frac{5 \times 10^{14}}{2.5 \times 10^{-16}} = 2.0 \times 10^{30} $ bacteria.

Question 10

State the number of significant digits and the implied precision of the given number.
-$6.500 \times 10 ^ { 7 }$

Accepted Answer

The number $6.500 \times 10^7$ has 4 significant digits (6, 5, and two zeros after the decimal point). The position of the last significant digit (the second zero) indicates precision to the nearest 10,000 when expanded (65,000,000).

Question 11

Answer the question.
-Find the scale ratio for a map if 6 inches on the map represents 7 miles on the ground.

Accepted Answer

To find the scale ratio, convert miles to inches (1 mile = 63,360 inches). So, 7 miles = 7 * 63,360 inches = 443,520 inches. The scale ratio is 6 inches on the map to 443,520 inches on the ground, which simplifies to 1:73,920.

Question 12

Find the absolute and relative errors.
-It took you one hour and 8 minutes to drive home, you estimated the time to be one hour and 23 minutes.

Accepted Answer

Absolute error is the difference between the estimated value and the actual value, which is $1\text{ hour } 23\text{ minutes} - 1\text{ hour } 8\text{ minutes} = 15\text{ minutes}$. Relative error is the absolute error divided by the actual value, $\frac{15\text{ minutes}}{68\text{ minutes}} \approx 22.1\%$.

Question 13

Use the Consumer Price Index below to answer the question. $$\begin{array}{l}
\text { Average Annual Consumer Price Index (1982-1984 = 100) }\
\begin{array} { c | c | c | c | c | c } 
\text { Year } & \text { CPI } & \text { Year } & \text { CPI } & \text { Year } & \text { CPI } \
\hline 1986 & 109.6 & 1995 & 152.4 & 2004 & 188.9 \
1987 & 113.6 & 1996 & 156.9 & 2005 & 195.3 \
1988 & 118.3 & 1997 & 160.5 & 2006 & 201.6 \
1989 & 124.0 & 1998 & 163.0 & 2007 & 207.3 \
1990 & 130.7 & 1999 & 166.6 & 2008 & 215.3 \
1991 & 136.2 & 2000 & 172.2 & 2009 & 214.5 \
1992 & 140.3 & 2001 & 177.1 & 2010 & 218.1 \
1993 & 144.5 & 2002 & 179.9 & 2011 & 224.9 \
1994 & 148.2 & 2003 & 184.0 & 2012 & 229.6
\end{array}
\end{array}$$
-A book cost $12 in 1987. What was its price in 1990 dollars?

Accepted Answer

To find the price in 1990 dollars, use the formula: Price in 1990 = Price in 1987 * (CPI in 1990 / CPI in 1987). So, $12 * (130.7 / 113.6) ≈ $13.80, which rounds to $14.

Question 14

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible,it does not make sense.
-My age in seconds is about $5 \times 10 ^ { 9 }$

Accepted Answer

The answer of Determine whether the statement makes sense. If...

Question 15

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible,it does not make sense.
-In the next hour, roughly $10 ^ { 9 }$people will die worldwide.

Accepted Answer

The statement does not make sense because the estimated global death rate is far lower than $10^9$ (1 billion) people per hour. Typically, fewer than 10 million people die worldwide in an entire year.

Question 16

True or false?
-If 28% of the students in Mr. Harris's class speak Spanish and 7% speak French, then 35% must
speak either Spanish or French

Accepted Answer

The percentages of students speaking Spanish and French cannot simply be added to find the percentage of students speaking either language, as some students might speak both languages.

Question 17

Use scientific notation to solve the problem.
-Suppose that we could somehow capture all the energy released by the Sun in just one second. For how many years could U.S. energy needs be met by this energy? Assume that the annual energy Generation of the Sun is $1 \times 10 ^ { 34 }$ joules and that U.S. annual energy consumption is 1 $1 \times 10 ^ { 20 }$ joules.
Give your answer in scientific notation.

Accepted Answer

To find out for how many years the energy from the Sun could meet U.S. energy needs, divide the annual energy generation of the Sun by the U.S. annual energy consumption: $ \frac{1 \times 10^{34}}{1 \times 10^{20}} = 1 \times 10^{14} $ joules per year. However, the correct scientific notation for years, given the options, is $3.17 \times 10^{6}$ years, indicating a mistake in calculation. Correctly, it should be calculated as the energy available for one second, not per year, and then find out how many years it could cover. The mistake was in the explanation of the calculation process, not in the selection of the correct answer based on the provided options. The correct calculation should consider the energy available for one second and the annual consumption to find the number of years.

Question 18

Measurements are made at two different times. Find the absolute change and then find the percentage change. Roundanswers to the nearest tenth if necessary.
-The population of Placerville grew from 4360 a decade ago to 6590 today.

Accepted Answer

Absolute change is calculated by subtracting the initial value from the final value, $6590 - 4360 = 2230$. Percentage change is calculated by dividing the absolute change by the initial value and then multiplying by 100, $\frac{2230}{4360} \times 100 \approx 51.1\%$.

Question 19

Write the number in ordinary notation.
-$9 \times 10 ^ { - 6 }$

Accepted Answer

The notation $9 \times 10^{-6}$ means 9 times 10 raised to the power of -6, which translates to moving the decimal point 6 places to the left, resulting in 0.000009.

Question 20

Solve the problem.
-In a local election, 46,800 people voted. This was a decrease of 12% over the last election. How many people voted in the last election?

Accepted Answer

The number of people who voted this time is 88% (100% - 12%) of the last election. So, to find the original number of voters, divide the current number by 88% (or 0.88): 46,800 / 0.88 = 53,182 people.

Quiz 3: Numbers in the Real World

Answer the question. -Suppose you are constructing a scale model solar system using a scale ratio of 1 to 10 billion. In your scale model what will be the diameter of Jupiter (in meters) ? The diameter of Jupiter is 143,000 km.

Write as a percent. - $1 \frac { 2 } { 7 }$

Determine whether the source of error represents random or systematic error. -Anne counts the number of cars passing an intersection in a 15-minute period. Sometimes she makes errors in counting.

Solve the problem. -Find the gasoline price index for a year in which the cost of gasoline was $0.82 per gallon. Use the 1965 price as the reference value. In 1965, the cost of gasoline was 31.2 cents per gallon.

Round to the indicated place value. -Round to the nearest thousandth: 1.1983

Write the percentage as a fraction or decimal, as indicated. -Write as a fraction. $83 \frac { 1 } { 3 } \%$

Write the number in ordinary notation. - $3.531 \times 10 ^ { - 5 }$

Use scientific notation to solve the problem. -Assume that the volume of the earth is $5 \times 1014$ cubic meters and the volume of a bacterium is $2.5 \times$ $10 - 16$ cubic meters. If the earth could be filled with bacteria, how many would it contain?

State the number of significant digits and the implied precision of the given number. - $6.500 \times 10 ^ { 7 }$

Answer the question. -Find the scale ratio for a map if 6 inches on the map represents 7 miles on the ground.

Find the absolute and relative errors. -It took you one hour and 8 minutes to drive home, you estimated the time to be one hour and 23 minutes.

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible,it does not make sense. -My age in seconds is about $5 \times 10 ^ { 9 }$

Determine whether the statement makes sense. If the statement is possible then it makes sense. If it is clearly impossible,it does not make sense. -In the next hour, roughly $10 ^ { 9 }$ people will die worldwide.

True or false? -If 28% of the students in Mr. Harris's class speak Spanish and 7% speak French, then 35% must speak either Spanish or French

Measurements are made at two different times. Find the absolute change and then find the percentage change. Roundanswers to the nearest tenth if necessary. -The population of Placerville grew from 4360 a decade ago to 6590 today.

Write the number in ordinary notation. - $9 \times 10 ^ { - 6 }$

Solve the problem. -In a local election, 46,800 people voted. This was a decrease of 12% over the last election. How many people voted in the last election?

Quiz 3: Numbers in the Real World

Answer the question. -Suppose you are constructing a scale model solar system using a scale ratio of 1 to 10 billion. In your scale model what will be the diameter of Jupiter (in meters) ? The diameter of Jupiter is 143,000 km.

Write as a percent. - 1271 \frac { 2 } { 7 }172​

Determine whether the source of error represents random or systematic error. -Anne counts the number of cars passing an intersection in a 15-minute period. Sometimes she makes errors in counting.

Solve the problem. -Find the gasoline price index for a year in which the cost of gasoline was $0.82 per gallon. Use the 1965 price as the reference value. In 1965, the cost of gasoline was 31.2 cents per gallon.

Round to the indicated place value. -Round to the nearest thousandth: 1.1983

Write the percentage as a fraction or decimal, as indicated. -Write as a fraction. 8313%83 \frac { 1 } { 3 } \%8331​%

Write the number in ordinary notation. - 3.531×10−53.531 \times 10 ^ { - 5 }3.531×10−5

Use scientific notation to solve the problem. -Assume that the volume of the earth is 5×10145 \times 10145×1014 cubic meters and the volume of a bacterium is 2.5×2.5 \times2.5× 10−1610 - 1610−16 cubic meters. If the earth could be filled with bacteria, how many would it contain?

State the number of significant digits and the implied precision of the given number. - 6.500×1076.500 \times 10 ^ { 7 }6.500×107