Question 1

Answer the question.
-The distance from the Earth to the Sun is about $1.5 \times 10 ^ { 8 } \mathrm {~km}$, while the distance from the Earth to the moon is about $3.8 \times 10 ^ { 5 } \mathrm {~km}$. If a scale model of the solar system is constructed so that the distance from the Earth to the Sun is 100 meters, what will be the distance from the Earth to the moon?
A) $6.36 \mathrm {~m}$
B) $0.25 \mathrm {~m}$
C) $39.5 \mathrm {~m}$
D) $39,474 \mathrm {~m}$

Accepted Answer

To find the scale distance from the Earth to the Moon, use the ratio of the actual distances. The actual distance to the Sun is $1.5 \times 10^8 $ km, represented by 100 meters in the model. Therefore, $1.5 \times 10^8 $ km corresponds to 100 meters, so $3.8 \times 10^5 $ km (the distance to the Moon) would correspond to $(3.8 \times 10^5 / 1.5 \times 10^8) \times 100 = 0.2533$ meters, which rounds to approximately 0.25 meters.

Question 2

Write the number in scientific notation.
-$0.00949$
A) $9.49 \times 10 ^ { - 4 }$
B) $- 9.49 \times 10 ^ { 3 }$
C) $9.49 \times 10 ^ { - 3 }$
D) $9.49 \times 10 ^ { - 2 }$

Accepted Answer

The answer of Write the number in scientific notation.
-$0.00949$
A) \(9.49...

Question 3

Use the Consumer Price Index below to answer the question. $$\begin{array}{l}
\text { Average Annual Consumer Price Index (1982-1984 = 100) }\
\begin{array} { c | c | c | c | c | c } 
\text { Year } & \text { CPI } & \text { Year } & \text { CPI } & \text { Year } & \text { CPI } \
\hline 1986 & 109.6 & 1995 & 152.4 & 2004 & 188.9 \
1987 & 113.6 & 1996 & 156.9 & 2005 & 195.3 \
1988 & 118.3 & 1997 & 160.5 & 2006 & 201.6 \
1989 & 124.0 & 1998 & 163.0 & 2007 & 207.3 \
1990 & 130.7 & 1999 & 166.6 & 2008 & 215.3 \
1991 & 136.2 & 2000 & 172.2 & 2009 & 214.5 \
1992 & 140.3 & 2001 & 177.1 & 2010 & 218.1 \
1993 & 144.5 & 2002 & 179.9 & 2011 & 224.9 \
1994 & 148.2 & 2003 & 184.0 & 2012 & 229.6
\end{array}
\end{array}$$
-Suppose you needed $56,000 to maintain a particular standard of living in 2000. How much would you have needed in 1990 to maintain the same standard of living?
A)$74,000
B)$44,000
C)$43,000
D)$41,000

Accepted Answer

To maintain the same standard of living in 1990 as in 2000, you would need to adjust for inflation. The CPI in 2000 was 172.2 and in 1990 it was 130.7. So, you would need to multiply $56,000 by 130.7/172.2 to get the amount needed in 1990. This comes out to $43,000.

Question 4

Restate the fact as indicated.
-The speed of light is approximately 5,866,000,000,000 miles per year. Express this speed in miles per second.
A)4,460,000 miles per second
B)3100.2 miles per second
C)186,009.6 miles per second
D)11,160,578.4 miles per second

Accepted Answer

To convert miles per year to miles per second, divide by the number of seconds in a year (31,536,000 seconds). 5,866,000,000,000 miles/year ÷ 31,536,000 seconds/year ≈ 186,009.6 miles/second.

Question 5

Solve the problem.
-The table below shows the number of people testing positive for a certain disease amongst those who do have the disease and amongst those who don't. Use the table to answer the question.  What percentage of those that don't have the disease tested negative?
A)98.6%
B)90.1%
C)99.8%
D)88.9%

Accepted Answer

The answer of Solve the problem.
-The table below shows the...

Question 6

Round to the indicated place value.
-Round to the nearest whole number: $715.854$
A) 715
B) $715.9$
C) 716

Accepted Answer

When rounding to the nearest whole number, you look at the digit to the right of the decimal point. If it is 5 or greater, you round up. Since the digit right after the decimal in 715.854 is an 8, you round up to 716.

Question 7

Solve the problem.
-The percentage of registered voters who voted in this election was 54%, up 20% from the last election. What was the percentage that voted at the last election?
A)45%
B)64.8%
C)43.2%
D)34%

Accepted Answer

The percentage that voted at the last election was 54% - 20% = 34%.

Question 8

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits.
-Find your speed by dividing the distance you traveled, 259 kilometers, by the time, 2.1 hours.
A)123.3 kilometers per hour
B)123 kilometers per hour
C)100 kilometers per hour
D)120 kilometers per hour

Accepted Answer

The answer of Use the appropriate rounding rule to answer...

Question 9

Determine ratio of A to B. Round as indicated.
-$A = 260$ and $B = 360$ (Do not round.)
A) $\frac { 1 } { 36 }$
B) $\frac { 18 } { 13 }$
C) $\frac { 1 } { 26 }$
D) $\frac { 13 } { 18 }$

Accepted Answer

The ratio of A to B is $A:B = 260:360$. Simplifying this ratio by dividing both numbers by their greatest common divisor, 20, gives $13:18$, or $\frac{13}{18}$.

Question 10

Answer the question.
-Suppose you are constructing a scale model solar system using a scale ratio of 1 to 100 billion. In your scale model what will be the distance from Neptune to the Sun (in meters)? The distance from
Neptune to the Sun is 4497 million km.
A)0.4497 m
B)4.497 m
C)44.97 m
D)0.04497 m

Accepted Answer

The actual distance from Neptune to the Sun is 4497 million km, which is 4,497,000,000 km. Using a scale of 1 to 100 billion, the model distance is 4,497,000,000 km / 100,000,000,000 = 44.97 meters.

Question 11

Solve the problem.
-Suppose the current cost of gasoline is $3.28 per gallon. Find the current price index using the 1995 price as the reference value. In 1995, the cost of gasoline was 120.5 cents per gallon.
A)36.7
B)2.7
C)272.2
D)207.5

Accepted Answer

The price index is calculated by taking the current price, dividing it by the base year price, and then multiplying by 100. So, using the 1995 price as the reference (base year price = 120.5 cents or $1.205), the calculation is ($3.28 / $1.205) * 100 = 272.2.

Question 12

Write the number in scientific notation.
-14,000,000
A) $1.4 \times 10 ^ { - 6 }$
B) $1.4 \times 10 ^ { 6 }$
C) $1.4 \times 10 ^ { - 7 }$
D) $1.4 \times 10 ^ { 7 }$

Accepted Answer

To convert 14,000,000 into scientific notation, you move the decimal point 7 places to the left, which gives $1.4 \times 10^7$.

Question 13

Two measurements are given. Find the absolute difference and then find the relative difference as a percentage. Assumethat the first quantity is the compared value and the second quantity is the reference value. Round answers to the nearesttenth if necessary.
-In a certain country, the life expectancy for men is 70.2 years while the life expectancy for women is 76.6 years.
A)Absolute difference: -6.4 years
B)Absolute difference: -6.4 years Relative difference: -8.4% Relative difference: -0.8%
C)Absolute difference: 6.4 years
D)Absolute difference: -6.4 years Relative difference: 9.1% Relative difference: -9.1%

Accepted Answer

The absolute difference is the difference between the two measurements, regardless of their signs. In this case, the absolute difference is 76.6 - 70.2 = 6.4 years.The relative difference is the absolute difference divided by the reference value, expressed as a percentage. In this case, the relative difference is (6.4 / 76.6) * 100 = -8.4%.

Question 14

Determine ratio of A to B. Round as indicated.
-A = 64.9 is the average number of points scored in a college basketball game. B = 49.5 is the average number of points scored in a high school basketball game. (Round to the nearest hundredth when
Necessary.)
A)13.11
B)0.76
C)0.13
D)1.31

Accepted Answer

To find the ratio of A to B, divide A by B: 64.9 / 49.5 = 1.31 (rounded to the nearest hundredth).

Question 15

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits.
-A city has a deficit of $31.4 million. How much is this per person if the population of the city is 263,300?
A)$100 per person
B)$119 per person
C)$120 per person
D)$119.3 per person

Accepted Answer

The answer of Use the appropriate rounding rule to answer...

Question 16

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits.
-You have covered 72.6 miles of a 1600 mile journey. How much further do you have to go?
A)1527.4 miles
B)1500 miles
C)1530 miles
D)1527 miles

Accepted Answer

The answer of Use the appropriate rounding rule to answer...

Question 17

Use scientific notation to perform the following operations. Leave your answer in scientific notation.
-$\left( 2 \times 10 ^ { 7 } \right) \times \left( 6 \times 10 ^ { - 4 } \right)$
A) $1.2 \times 10 ^ { 2 }$
B) $1.2 \times 10 ^ { - 2 }$
C) $1.2 \times 10 ^ { 4 }$
D) $1.2 \times 10 ^ { 3 }$

Accepted Answer

Multiply the coefficients: $2 \times 6 = 12$. Add the exponents: $7 + (-4) = 3$. So, $12 \times 10^3 = 1.2 \times 10^4$.

Question 18

Find the absolute and relative errors.
-The length of the room is 12 feet but you measure it to be 12 feet and 5 inches.
A)absolute error: -5 inches
B)absolute error: 5 inches relative error: -3.5% relative error: 3.4%
C)absolute error: 5 inches
D)absolute error: 5 inches relative error: 3.5% relative error: 4.2%

Accepted Answer

The absolute error is the difference between the measured value and the true value, which is 5 inches. The relative error is calculated as (absolute error / true value) * 100%, which is not provided correctly in the options.

Question 19

Solve the problem.
-Brand X copier advertises that its copiers run 16% longer between service calls than its competitor. If Brand X copiers run 55,300 copies between services, how many copies would the competitor run?
A)46,452 copies
B)47,672 copies
C)64,148 copies
D)30,054 copies

Accepted Answer

The answer of Solve the problem.
-Brand X copier advertises that...

Question 20

Answer the question.
-Find the scale ratio for a map if 4 centimeters on the map represents 10 kilometers on the ground.
A)1 : 250,000
B)1 : 2500
C)1 : 25,000
D)1 : 1,000,000

Accepted Answer

To convert 4 cm on the map to 10 km on the ground into a scale ratio, first convert 10 km to centimeters (since 1 km = 100,000 cm, 10 km = 1,000,000 cm). Then, the scale ratio is 4 cm (map) to 1,000,000 cm (ground), which simplifies to 1 : 250,000 when both numbers are divided by 4.

Quiz 3: Numbers in the Real World

Write the number in scientific notation. - $0.00949$

Restate the fact as indicated. -The speed of light is approximately 5,866,000,000,000 miles per year. Express this speed in miles per second.

Solve the problem. -The table below shows the number of people testing positive for a certain disease amongst those who do have the disease and amongst those who don't. Use the table to answer the question. What percentage of those that don't have the disease tested negative?

Round to the indicated place value. -Round to the nearest whole number: $715.854$

Solve the problem. -The percentage of registered voters who voted in this election was 54%, up 20% from the last election. What was the percentage that voted at the last election?

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits. -Find your speed by dividing the distance you traveled, 259 kilometers, by the time, 2.1 hours.

Determine ratio of A to B. Round as indicated. - $A = 260$ and $B = 360$ (Do not round.)

Answer the question. -Suppose you are constructing a scale model solar system using a scale ratio of 1 to 100 billion. In your scale model what will be the distance from Neptune to the Sun (in meters) ? The distance from Neptune to the Sun is 4497 million km.

Solve the problem. -Suppose the current cost of gasoline is $3.28 per gallon. Find the current price index using the 1995 price as the reference value. In 1995, the cost of gasoline was 120.5 cents per gallon.

Write the number in scientific notation. -14,000,000

Determine ratio of A to B. Round as indicated. -A = 64.9 is the average number of points scored in a college basketball game. B = 49.5 is the average number of points scored in a high school basketball game. (Round to the nearest hundredth when Necessary.)

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits. -A city has a deficit of $31.4 million. How much is this per person if the population of the city is 263,300?

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits. -You have covered 72.6 miles of a 1600 mile journey. How much further do you have to go?

Use scientific notation to perform the following operations. Leave your answer in scientific notation. - $\left( 2 \times 10 ^ { 7 } \right) \times \left( 6 \times 10 ^ { - 4 } \right)$

Find the absolute and relative errors. -The length of the room is 12 feet but you measure it to be 12 feet and 5 inches.

Solve the problem. -Brand X copier advertises that its copiers run 16% longer between service calls than its competitor. If Brand X copiers run 55,300 copies between services, how many copies would the competitor run?

Answer the question. -Find the scale ratio for a map if 4 centimeters on the map represents 10 kilometers on the ground.

Quiz 3: Numbers in the Real World

Write the number in scientific notation. - 0.009490.009490.00949

Restate the fact as indicated. -The speed of light is approximately 5,866,000,000,000 miles per year. Express this speed in miles per second.

Solve the problem. -The table below shows the number of people testing positive for a certain disease amongst those who do have the disease and amongst those who don't. Use the table to answer the question. What percentage of those that don't have the disease tested negative?

Round to the indicated place value. -Round to the nearest whole number: 715.854715.854715.854

Solve the problem. -The percentage of registered voters who voted in this election was 54%, up 20% from the last election. What was the percentage that voted at the last election?

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits. -Find your speed by dividing the distance you traveled, 259 kilometers, by the time, 2.1 hours.

Determine ratio of A to B. Round as indicated. - A=260A = 260A=260 and B=360B = 360B=360 (Do not round.)

Answer the question. -Suppose you are constructing a scale model solar system using a scale ratio of 1 to 100 billion. In your scale model what will be the distance from Neptune to the Sun (in meters) ? The distance from Neptune to the Sun is 4497 million km.

Solve the problem. -Suppose the current cost of gasoline is $3.28 per gallon. Find the current price index using the 1995 price as the reference value. In 1995, the cost of gasoline was 120.5 cents per gallon.

Write the number in scientific notation. -14,000,000

Determine ratio of A to B. Round as indicated. -A = 64.9 is the average number of points scored in a college basketball game. B = 49.5 is the average number of points scored in a high school basketball game. (Round to the nearest hundredth when Necessary.)

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits. -A city has a deficit of $31.4 million. How much is this per person if the population of the city is 263,300?

Use the appropriate rounding rule to answer the question with the correct precision or correct number of significantdigits. -You have covered 72.6 miles of a 1600 mile journey. How much further do you have to go?

Use scientific notation to perform the following operations. Leave your answer in scientific notation. - (2×107) ×(6×10−4) \left( 2 \times 10 ^ { 7 } \right) \times \left( 6 \times 10 ^ { - 4 } \right) (2×107) ×(6×10−4)

Find the absolute and relative errors. -The length of the room is 12 feet but you measure it to be 12 feet and 5 inches.

Solve the problem. -Brand X copier advertises that its copiers run 16% longer between service calls than its competitor. If Brand X copiers run 55,300 copies between services, how many copies would the competitor run?

Answer the question. -Find the scale ratio for a map if 4 centimeters on the map represents 10 kilometers on the ground.

Write the number in scientific notation. - $0.00949$

Round to the indicated place value. -Round to the nearest whole number: $715.854$

Determine ratio of A to B. Round as indicated. - $A = 260$ and $B = 360$ (Do not round.)

Use scientific notation to perform the following operations. Leave your answer in scientific notation. - $\left( 2 \times 10 ^ { 7 } \right) \times \left( 6 \times 10 ^ { - 4 } \right)$