1. Which of the following is a unit of mass?
2. One type of carpet is sold for $4.50 per square yard. How much will a carpet that is 12 feet wide and 27 feet long cost?
3. One mile is equivalent to 1.6093 km. How many miles are in 10 km? Round your answer to three decimal places.
A. 0.161 miles
B. 3.107 miles
C. 6.214 miles
D. 8.047 miles
E. 16.093 miles
4. To convert a temperature from Fahrenheit (°F) to Celsius (°C), the formula is where C and F are the temperatures in Celsius and Fahrenheit, respectively. Convert 131°F to degrees Celsius. Round your answer to the nearest degree.
5. One inch is equivalent to 2.54 cm. How many centimeters are in two feet? Round your answer to two decimal places.
A. 5.08 cm
B. 12.62 cm
C. 15.24 cm
D. 30.48 cm
E. 60.96 cm
6. If the sides of a cube are n yards long, what is its volume in cubic feet?
7. Which of the following is the most reasonable weight of a twenty-year-old man?
A. 20 g
B. 500 g
C. 3 kg
D. 60 kg
E. 750 kg
8. Convert 0.6 km to centimeters.
A. 60 cm
B. 600 cm
C. 6,000 cm
D. 60,000 cm
E. 600,000 cm
9. A carpenter cuts off 1.3 inches from a 4-foot board. What is the new length of the board in inches?
A. 2.7 inches
B. 46.7 inches
C. 49.3 inches
D. 58.7 inches
E. 61.3 inches
10. The perimeter of a rectangular garden is 30 feet. If its length is 6 feet, what is its width?
A. 9 feet
B. 10 feet
C. 18 feet
D. 21 feet
E. 24 feet
1. B. Feet and kilometers are units of distance or length. Liters and tablespoons are units of volume. Of the five choices, only grams is a unit of mass.
2. C. First, find the area of the carpet in square yards since the price is given in dollars per square yard.. To do this, convert the dimensions of the carpet from feet to yards by dividing both measurements by 3. (There are three feet in a yard.) The carpet is 4 yards wide and 9 yards long.
Next multiply the dimensions of the carpet together to find its area.
4 x 9 = 36
Therefore, the area of the carpet is 36 square yards. Multiply this by $4.50 to find the price of the carpet.
$4.50 x 36 = $162.00
Thus, a 36-square-yard carpet will cost $162.00.
3. C. One way to approach the problem is to set up a proportion between the conversion factor (given by the first sentence in the problem) and the unknown distance. In the proportion, make sure to include the units of all the data to make sure it is set it up correctly. Let x be the unknown distance. Then solve for x.
Therefore, there are approximately 6.214 miles in 10 km.
4. D. In the given formula, substitute 131 for F and simplify the result.
Therefore, 131°F is equivalent to 55°C.
5. E. First convert 2 feet to inches and then convert the result to centimeters. One foot is equivalent to 12 inches, so there are 24 inches in 2 feet. Since there are 2.54 cm in a foot, multiply 24 by 2.54 to convert feet to centimeters.
24 x 2.54 = 60.96
Therefore, there are 60.96 cm in 2 feet.
6. E. The problem gives the side length in yards but asks for cubic feet, so first convert the side length to feet. Since there are 3 feet in a yard, there are 3n feet in n yards. Thus, the sides of the cube are 3n feet long.
The volume of a cube is given by the formula [latex]V=s^3[/latex]. Substitute 3n for s in this formula and simplify the result.
Therefore, the volume of the cube is [latex]27n^3[/latex] cubic feet.
7. D. One kilogram is equivalent to about 2.2046 lbs. In other words, a kilogram is a little more than 2 lbs. Thus, if a 20-year old man is about 160 lbs, his mass will be around 70 to 80 kg. The only choice that is close to this is 60 kg.
8. D. The metric system uses powers of 10, so conversion between units can be done by moving the decimal point. First convert 0.6 km to meters. To do this, multiply 0.6 by 1000, or, equivalently, move the decimal point three places to the right. Add zeros as necessary.
Therefore, there are 600 m in 0.6 km. Convert 600 m to centimeters by multiplying by 100 or, equivalently, by moving the decimal two places to the right.
Thus, the correct answer is 60,000 cm.
9. B. Of the two lengths given in the problem, one is inches and the other is in feet. The answer needs to be inches, so convert the length of the board to inches. Since there are 12 inches in one foot, the 4-foot board is 48 inches long. Now subtract the length of the piece the carpenter cut off.
48 – 1.3 = 46.7
Therefore, the new length of the board is 46.7 inches.
10. A. The perimeter of a shape is the distance around it. In particular, the perimeter of a rectangle is given by the formula P = 2W + 2L. Substitute the correct values of the variables into this formula (P = 30 and L = 6) and then solve for the width W:
30 = 2W + 2(6)
30 = 2W + 12
18 = 2W
W = 9
Therefore, the width of the garden is 9 feet.