Question 1

Solve the problem.
-There are 1000 meters in 1 kilometer. Find a conversion factor between cubic meters and cubic kilometers. Write it in three forms.

Accepted Answer

The correct conversion factor between cubic meters and cubic kilometers is that 1 cubic kilometer equals 1000 meters cubed, which equals 1,000,000,000 cubic meters.

Question 2

Decide which of the two given prices is the better deal.
-You can buy hair product in a 12-ounce bottle for $2.88 or in a 8-ounce bottle for $1.76.

Accepted Answer

The 8-ounce bottle is a better deal because it costs $1.76, while the 12-ounce bottle costs $2.88. This means that the 8-ounce bottle costs $0.22 less per ounce than the 12-ounce bottle.

Question 3

Solve the problem.
-A warehouse is 42 yards long and 26 yards wide with a height of 13 yards. What is the volume of the warehouse?

Accepted Answer

The volume of a rectangular prism is calculated by multiplying its length, width, and height. Thus, the volume is $42 \, \text{yd} \times 26 \, \text{yd} \times 13 \, \text{yd} = 14,196 \, \text{yd}^3$.

Question 4

Convert the measurement to the units specified. Round your answer to the nearest tenth.
-15 cubic inches to milliliters

Accepted Answer

To convert cubic inches to milliliters, use the conversion factor 1 cubic inch = 16.387 milliliters. Therefore, 15 cubic inches * 16.387 milliliters/cubic inch = 245.805 milliliters, which rounds to 245.7 milliliters.

Question 5

Evaluate.
-$\frac { 5 } { 2 } \div \frac { 2 } { 5 }$

Accepted Answer

Dividing by a fraction is the same as multiplying by its reciprocal. So, $\frac { 5 } { 2 } \div \frac { 2 } { 5 } = \frac { 5 } { 2 } \times \frac { 5 } { 2 } = \frac { 25 } { 4 }$.

Question 6

Evaluate.
-$\frac { 1 } { 7 } + \frac { 1 } { 6 }$

Accepted Answer

To add fractions, you need a common denominator. The least common multiple of 7 and 6 is 42. Convert each fraction: $\frac{1}{7} = \frac{6}{42}$ and $\frac{1}{6} = \frac{7}{42}$. Adding these gives $\frac{6}{42} + \frac{7}{42} = \frac{13}{42}$.

Question 7

Decide which of the two given prices is the better deal.
-The same kind of water is sold in two types of bottle. Which type has the lower unit price? Five 10-oz bottles for $2.30
Seven 12-oz bottles for $4.20

Accepted Answer

The answer of Decide which of the two given prices...

Question 8

Use units to help you answer the question. If necessary, round your answer to two decimal places.
-A stockbroker sold 35 shares of stock for $40.31 each. What was the total amount of the sale?

Accepted Answer

The answer of Use units to help you answer the...

Question 9

Solve the problem.
-$10 ^ { 4 } + 10 ^ { 9 }$

Accepted Answer

$10^4 + 10^9 = 10,000 + 1,000,000,000 = 1,000,010,000$.

Question 10

Solve the problem.
-$\frac { 10 ^ { 5 } } { 10 ^ { 9 } }$

Accepted Answer

When dividing powers with the same base, you subtract the exponents: $10^5 / 10^9 = 10^{5-9} = 10^{-4}$.

Question 11

Carry out the indicated unit conversion. Round your answer, if appropriate.
-$\text { Convert a lot size of } \frac { 2 } { 9 } \text { acre to square feet } \left( 1 \text { acre } = 43,560 \mathrm { ft } ^ { 2 } \right) \text {. }$

Accepted Answer

The answer of Carry out the indicated unit conversion. Round...

Question 12

State how much larger or smaller the first unit is than the second.
-centiliter, microliter

Accepted Answer

The answer of State how much larger or smaller the...

Question 13

Solve the problem.
-A 14-gram object has a volume of 35 cubic centimeters. Find its density.

Accepted Answer

Density is calculated as mass divided by volume, which in this case is $14 \mathrm{g} / 35 \mathrm{cm}^3 = 0.4 \mathrm{g}/\mathrm{cm}^3$.

Question 14

Convert the measurement to the units specified. Round your answer to the nearest tenth.
-23 feet to meters

Accepted Answer

1 foot is approximately equal to 0.3048 meters. Therefore, 23 feet is equal to 23 * 0.3048 = 7.01 meters, which rounds to 7 meters.

Question 15

Write as a common fraction.
-$4.2$

Accepted Answer

4.2 can be written as $\frac{42}{10}$, which simplifies to $\frac{21}{5}$ when both numerator and denominator are divided by 2.

Question 16

Answer the following question involving a conversion within the USCS system.
-How many gallons are in 79 barrels of petroleum?

Accepted Answer

In the USCS system, 1 barrel of petroleum is equal to 42 gallons. Therefore, to find out how many gallons are in 79 barrels, you multiply 79 by 42, which equals 3318 gallons.

Question 17

State how much larger or smaller the first unit is than the second.
-gram, milligram

Accepted Answer

A gram is larger than a milligram by a factor of $10^3$ (1 gram = 1000 milligrams).

Question 18

Solve the problem.
-A piece of land in Ottawa with an area of 0.5 square kilometers is priced at 5800 Canadian dollars. If there are 0.9965 Canadian dollars per (U.S.)dollar, then what is the price in dollars per square
Mile?

Accepted Answer

First, convert the price from Canadian dollars to U.S. dollars: 5800 Canadian dollars * (1 U.S. dollar / 0.9965 Canadian dollars) = 5821.68 U.S. dollars. Then, convert square kilometers to square miles: 0.5 square kilometers * (1 square mile / 2.58999 square kilometers) = 0.19305 square miles. Finally, calculate the price per square mile: 5821.68 U.S. dollars / 0.19305 square miles = $30,147.74 per square mile.

Question 19

Solve the problem.
-Your electrical bill states that you used 800 kilowatt-hours of energy in January. Determine your total electrical energy use, in joules.

Accepted Answer

1 kilowatt-hour is equivalent to 3.6 million joules. Therefore, 800 kilowatt-hours is 800 * 3.6 million joules, which equals 2,880,000,000 joules.

Question 20

Solve the problem.
-What is the cost of lighting a 500-watt outdoor light for 8 hours, if electricity costs 7.5¢ per kilowatt-hour?

Accepted Answer

The cost is calculated by multiplying the power consumption (in kilowatts) by the time (in hours) and the cost of electricity per kilowatt-hour. A 500-watt light is 0.5 kilowatts. For 8 hours, the energy consumed is 0.5 kW * 8 h = 4 kWh. At 7.5¢ per kWh, the cost is 4 kWh * 7.5¢ = 30 cents.

Quiz 2: Approaches to Problem Solving

Solve the problem. -There are 1000 meters in 1 kilometer. Find a conversion factor between cubic meters and cubic kilometers. Write it in three forms.

Decide which of the two given prices is the better deal. -You can buy hair product in a 12-ounce bottle for $2.88 or in a 8-ounce bottle for $1.76.

Solve the problem. -A warehouse is 42 yards long and 26 yards wide with a height of 13 yards. What is the volume of the warehouse?

Convert the measurement to the units specified. Round your answer to the nearest tenth. -15 cubic inches to milliliters

Evaluate. - $\frac { 5 } { 2 } \div \frac { 2 } { 5 }$

Evaluate. - $\frac { 1 } { 7 } + \frac { 1 } { 6 }$

Decide which of the two given prices is the better deal. -The same kind of water is sold in two types of bottle. Which type has the lower unit price? Five 10-oz bottles for $2.30 Seven 12-oz bottles for $4.20

Use units to help you answer the question. If necessary, round your answer to two decimal places. -A stockbroker sold 35 shares of stock for $40.31 each. What was the total amount of the sale?

Solve the problem. - $10 ^ { 4 } + 10 ^ { 9 }$

Solve the problem. - $\frac { 10 ^ { 5 } } { 10 ^ { 9 } }$

Carry out the indicated unit conversion. Round your answer, if appropriate. - $\text { Convert a lot size of } \frac { 2 } { 9 } \text { acre to square feet } \left( 1 \text { acre } = 43,560 \mathrm { ft } ^ { 2 } \right) \text {. }$

State how much larger or smaller the first unit is than the second. -centiliter, microliter

Solve the problem. -A 14-gram object has a volume of 35 cubic centimeters. Find its density.

Convert the measurement to the units specified. Round your answer to the nearest tenth. -23 feet to meters

Write as a common fraction. - $4.2$

Answer the following question involving a conversion within the USCS system. -How many gallons are in 79 barrels of petroleum?

State how much larger or smaller the first unit is than the second. -gram, milligram

Solve the problem. -A piece of land in Ottawa with an area of 0.5 square kilometers is priced at 5800 Canadian dollars. If there are 0.9965 Canadian dollars per (U.S.) dollar, then what is the price in dollars per square Mile?

Solve the problem. -Your electrical bill states that you used 800 kilowatt-hours of energy in January. Determine your total electrical energy use, in joules.

Solve the problem. -What is the cost of lighting a 500-watt outdoor light for 8 hours, if electricity costs 7.5¢ per kilowatt-hour?