The price of a printer was reduced from $400 to $300. What was the percent of decrease?
A)
75%
B)
25%
C)
33.3%
D)
30%
The percent of decrease can be calculated by taking the difference between the original price and the reduced price, dividing it by the original price, and then multiplying by 100.
($400 - $300) / $400 * 100 = 100 / $400 * 100 = 1/4 * 100 = 25%
Therefore, the percent of decrease is 25%.
B) 25%
Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
3(4g + 10) - 12g - 30 = 0
Question 2 options:
A)
Conditional; {4}
B)
Identity; {all real numbers}
C)
Conditional; {0}
D)
Contradiction; ∅
To determine whether the equation is conditional, an identity, or a contradiction, we need to simplify it.
Distributing the 3 on the left side of the equation, we have:
12g + 30 - 12g - 30 = 0
Simplifying further, we can notice that the terms with g cancel out, and we are left with:
0 = 0
This equation simplifies to 0 = 0, which is true for all values of g.
Therefore, the equation is an identity, and the solution set is all real numbers.
B) Identity; {all real numbers}
Solve the problem. Assume that simple interest is being calculated in each case. Round your answer to the nearest cent.
John Lee's savings account has a balance of $85. After 27 months, what will the amount of interest be at 4.0% per year?
Question 3 options:
A)
$7.65
B)
$3.40
C)
$3.15
D)
$30.41
To calculate the amount of interest, we can use the formula:
Interest = Principal * Rate * Time
In this case, the principal is $85, the rate is 4.0% (or 0.04 as a decimal), and the time is 27 months (or 27/12 = 2.25 years).
Interest = $85 * 0.04 * 2.25
Interest = $7.65
Therefore, the amount of interest after 27 months at a rate of 4.0% per year is $7.65.
A) $7.65
Convert.
68 in. = underbar( ) ftunderbar( ) in.
Question 4 options:
A)
5 ft 6 in.
B)
5 ft 8 in.
C)
4 ft 20 in.
D)
8 ft 5 in.
To convert inches to feet and inches, we divide the number of inches by 12.
68 inches is equal to 68/12 = 5 with a remainder of 8.
So, 68 inches is equal to 5 feet 8 inches.
B) 5 ft 8 in.
Solve the problem.
Find the best buy and the unit price.
Brand X 10 oz for $1.30
Brand Y 15 oz for $2.25
Question 5 options:
A)
Brand Y, $0.13
B)
Equal value
C)
Brand X, $0.13
D)
Brand Y, $0.15
To find the best buy and the unit price, we need to compare the prices per ounce for each brand.
For Brand X:
Price per ounce = $1.30 / 10 oz = $0.13/oz
For Brand Y:
Price per ounce = $2.25 / 15 oz = $0.15/oz
Comparing the unit prices, we can see that Brand X has a lower price per ounce.
Therefore, the best buy is Brand X and the unit price is $0.13.
C) Brand X, $0.13
The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year and round answer to the nearest cent.
P = $600
r = 4.25%
t = 3 months
Question 6 options:
A)
$6.38
B)
$76.50
C)
$606.38
D)
$6.95
To calculate the simple interest, we can use the formula:
Interest = P * r * t
Given that P = $600, r = 4.25% (or 0.0425 as a decimal), and t = 3 months (or 3/12 = 0.25 years), we can substitute these values into the formula:
Interest = $600 * 0.0425 * 0.25
Interest = $6.375
Rounding to the nearest cent, the simple interest owed for the use of the money is $6.38.
A) $6.38
Use dimensional analysis to convert the given unit to the unit indicated. Where necessary, round answer to two decimal places.
5236 gal to ft^3
Question 8 options:
A)
52.36 ft^3
B)
523.6 ft^3
C)
70 ft^3
D)
700 ft^3
To convert gallons (gal) to cubic feet (ft^3), we can use the conversion factor:
1 gal = 0.134 ft^3
To convert 5236 gal to ft^3, we can multiply the given value by the conversion factor:
5236 gal * 0.134 ft^3/gal = 701.544 ft^3
Rounding to two decimal places, the conversion of 5236 gal to ft^3 is approximately 701.54 ft^3.
Therefore, the correct answer is not listed among the options provided.
A container of motor oil has a volume of 2000 cubic centimeters. How many liters of oil does the container hold?
Question 9 options:
A)
2 L
B)
20 L
C)
200 L
D)
2000 L
To convert cubic centimeters (cm³) to liters (L), we use the conversion factor:
1 L = 1000 cm³
Given that the container holds 2000 cm³ of oil, we can convert this volume to liters by dividing:
2000 cm³ / 1000 = 2 L
Therefore, the container holds 2 liters of oil.
A) 2 L
A total of 11 gal 3 qt of oil has been removed from a 43-gallon drum. How much oil still remains in the container?
Question 10 options:
A)
32 gal 3 qt
B)
31 gal 5 qt
C)
31 gal 1 qt
D)
32 gal 1 qt
To solve this problem, we need to first convert 3 quarts to gallons.
Since 1 gallon is equal to 4 quarts, we divide 3 quarts by 4:
3 quarts / 4 = 0.75 gallons.
Therefore, the total amount of oil removed from the drum is:
11 gallons + 0.75 gallons = 11.75 gallons.
To find out how much oil still remains in the container, we subtract the amount removed from the total capacity of the drum:
43 gallons - 11.75 gallons = 31.25 gallons.
Since 0.25 gallons is equal to 1 quart, we can convert the remaining amount to quarts:
0.25 gallons * 4 = 1 quart.
Therefore, the amount of oil that still remains in the container is:
31 gallons 1 quart.
C) 31 gal 1 qt
If a boat uses 22 gallons of gas to go 64 miles, how many miles can the boat travel on 110 gallons of gas?
Question 13 options:
A)
340 miles
B)
320 miles
C)
12 miles
D)
640 miles
To solve this problem, we can set up a proportion using the relationship between the gallons of gas and the miles traveled.
Let's set up the proportion:
22 gallons / 64 miles = 110 gallons / x miles
To find the value of x, we can cross-multiply and then divide:
22 * x = 64 * 110
x = (64 * 110) / 22
x = 320
Therefore, the boat can travel 320 miles on 110 gallons of gas.
B) 320 miles
Sarah has grades of 76 and 94 on his first two tests. If she wants an average of at least 90 after her third test, what score must she make on that test?
Question 16 options:
A)
87 or more
B)
90 or more
C)
85 or more
D)
100 or more
To determine what score Sarah must make on her third test, we can set up an equation:
(76 + 94 + x) / 3 ≥ 90
Where x represents the score Sarah must make on her third test. We add up her first two test scores and divide by 3 to find the average.
Expanding the equation, we have:
(170 + x) / 3 ≥ 90
Multiplying both sides of the inequality by 3 to eliminate the denominator, we have:
170 + x ≥ 270
Subtracting 170 from both sides of the inequality, we have:
x ≥ 100
Therefore, Sarah must score 100 or more on her third test in order to have an average of at least 90.
D) 100 or more.
Solve the problem.
3.6 is 72% of what number?
Question 17 options:
A)
0.5
B)
5
C)
0.05
D)
2.592
To find the number that 3.6 is 72% of, we can use the following equation:
0.72x = 3.6
To solve for x, we divide both sides of the equation by 0.72:
x = 3.6 / 0.72
x = 5
Therefore, 3.6 is 72% of 5.
B) 5
Solve the problem.
For each kilogram of a person's weight, 40 milligrams of a drug is to be given. What dosage should be given to an adult who weighs 120 pounds?
Question 18 options:
A)
4800 mg
B)
0.48 mg
C)
2160 mg
D)
10,666.67 mg
To solve this problem, we need to convert the weight of the adult from pounds to kilograms.
1 kilogram is equal to 2.20462 pounds, so we can convert 120 pounds to kilograms by dividing by 2.20462:
120 pounds / 2.20462 = 54.431 kg (rounded to three decimal places).
Next, to find the dosage of the drug that should be given based on the person's weight in kilograms, we multiply the weight in kilograms by 40 milligrams:
54.431 kg * 40 mg/kg = 2,177.24 mg (rounded to two decimal places).
Therefore, the dosage that should be given to an adult who weighs 120 pounds is approximately 2,177.24 mg.
The answer is not listed among the options provided.
Convert. Round to the nearest tenth of a degree, if necessary.
137.2°C to degrees Fahrenheit
Question 19 options:
A)
108.2°F
B)
279°F
C)
44.2°F
D)
215°F
To convert from degrees Celsius (°C) to degrees Fahrenheit (°F), we can use the following formula:
°F = (°C × 9/5) + 32
Given that 137.2°C is the temperature we are converting, we substitute this value into the formula to calculate it in Fahrenheit:
°F = (137.2 × 9/5) + 32
°F = (247.8) + 32
°F = 279.8
Rounding to the nearest tenth of a degree, we get:
°F ≈ 279.8°F
Therefore, the conversion of 137.2°C to degrees Fahrenheit is approximately 279.8°F.
The correct answer is not listed among the options provided.
Solve the problem.
The Smith family is planning a 407-mile trip. If they travel at an average speed of 37 miles per hour, what will be their travel time? (Use d = rt)
Question 20 options:
A)
10 hr.
B)
12 hr.
C)
13 hr.
D)
11 hr.
To calculate the travel time, we can use the formula d = rt, where d is the distance, r is the rate, and t is the time.
Given that the distance is 407 miles and the average speed is 37 miles per hour, we can rearrange the formula to solve for t:
t = d / r
Substituting the values:
t = 407 miles / 37 miles per hour
Calculating the division:
t ≈ 11 hours
Therefore, the travel time for the Smith family on their 407-mile trip at an average speed of 37 miles per hour is approximately 11 hours.
D) 11 hr.
Use the multiplication principle of equality to eliminate the fractions or decimals; then solve.
-9.1q = -67.5 - 1.6q
Question 21 options:
A)
7.6
B)
7.4
C)
-75
D)
9
To eliminate the fractions and decimals, we can multiply every term in the equation by a common multiple of the denominators. In this case, we can multiply by 10 to eliminate the decimal points:
10*(-9.1q) = 10*(-67.5) + 10*(-1.6q)
-91q = -675 - 16q
Next, we can combine like terms on the right side of the equation:
-91q = -675 - 16q
Finally, we can isolate the term with q by subtracting -16q from both sides:
-91q + 16q = -675 - 16q + 16q
-75q = -675
To solve for q, we divide both sides by -75:
q = -675 / -75
q = 9
Therefore, the solution to the equation is q = 9.
D) 9
Use the multiplication principle of equality to eliminate the fractions or decimals; then solve.
3 - 1.1(w - 8) = 0.3(3w - 4)
Question 22 options:
A)
15.1
B)
6.5
C)
-2.3
D)
-0.5
To eliminate the decimals, we can multiply every term in the equation by a common multiple of the denominators. In this case, we can multiply by 10 to eliminate the decimal points:
10[3 - 1.1(w - 8)] = 10[0.3(3w - 4)]
30 - 11(w - 8) = 3(3w - 4)
Next, we can distribute on both sides of the equation:
30 - 11w + 88 = 9w - 12
Combine like terms:
118 - 11w = 9w - 12
To isolate the terms with w, we can add 11w to both sides and add 12 to both sides:
118 + 12 = 9w + 11w
130 = 20w
Finally, we divide both sides by 20:
w = 130 / 20
w = 6.5
Therefore, the solution to the equation is w = 6.5.
B) 6.5
Solve the problem. Round your answer to the nearest cent.
Kaitlyn borrowed $19,000 from her mother to buy a car. She will repay the loan at the end of 5 years at 5% interest compounded annually. Find the amount she will repay.
Question 23 options:
A)
$26,674.28
B)
$99,750.00
C)
$24,249.35
D)
$5249.35
To find the amount Kaitlyn will repay, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the amount, P is the principal amount (the borrowed amount), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
Given that Kaitlyn borrowed $19,000, the interest rate is 5%, and the interest is compounded annually (n = 1), and she will repay the loan in 5 years (t = 5), we can substitute these values into the formula:
A = $19,000(1 + 0.05/1)^(1*5)
A = $19,000(1 + 0.05)^5
A = $19,000(1.05)^5
A ≈ $24,249.35
Therefore, the amount Kaitlyn will repay at the end of 5 years is approximately $24,249.35.
C) $24,249.35
Use dimensional analysis to convert the unit indicated.
2 m to ft
Question 24 options:
A)
2.2 ft
B)
1.8 ft
C)
6.6 ft
D)
0.6 ft
To convert meters (m) to feet (ft), we can use the conversion factor:
1 m = 3.28084 ft
Given that we want to convert 2 meters to feet, we can multiply by the conversion factor:
2 m * 3.28084 ft/m = 6.56168 ft
Rounded to the nearest tenth, 2 meters is approximately equal to 6.6 feet.
Therefore, the correct answer is:
C) 6.6 ft
Use dimensional analysis to convert the unit indicated.
5 in. to cm
Question 26 options:
A)
1.97 cm
B)
12.70 cm
C)
0.51 cm
D)
0.08 cm