Nokea
If m represents a car's average mileage in miles per gallon, p represents the price of gas in dollars per gallon, and d represents a distance in miles, which of the following algebraic equations represents the cost, c, of gas per mile?
- A. c = dp/m
- B. c = p/m
- C. c = mp/d
- D. c = m/p
Correct Answer: B
Rationale: The cost of gas per mile, c, is calculated by dividing the price of gas, represented by p, by the car's average mileage, represented by m. Therefore, the correct equation is c = p/m. Choice A (dp/m) incorrectly multiplies the price of gas and distance, while choice C (mp/d) incorrectly multiplies the average mileage and price of gas. Choice D (m/p) incorrectly divides the average mileage by the price of gas, which does not represent the cost of gas per mile.
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Simplify the expression. Which of the following is correct? (52(3) + 3(-2)^2 / 4 + 3^2 - 2(5 - 8))
- A. 9/8
- B. 87/19
- C. 9
- D. 21/2
Correct Answer: B
Rationale: To simplify the expression, apply the order of operations (PEMDAS). Begin by squaring -2 to get 4. Then perform the multiplication and subtraction within parentheses: 52(3) + 3(4)/4 + 9 - 2(5 - 8) = 156 + 12/4 + 9 - 2(3) = 156 + 3 + 9 - 6 = 168 + 3 - 6 = 171 - 6 = 165. Therefore, the correct simplified expression is 165, which is equivalent to 87/19. Choices A, C, and D are incorrect because they do not represent the accurate simplification of the given expression.
A car dealership's commercials claim that this year's models are 20% off the list price, plus they will pay the first 3 monthly payments. If a car is listed for $26,580, and the monthly payments are set at $250, what is the total potential savings?
- A. $1,282
- B. $5,566
- C. $6,066
- D. $20,514
Correct Answer: C
Rationale: To calculate the total potential savings: First, find the 20% discount on the list price of $26,580: 0.20 $26,580 = $5,316. Then, determine the savings over the first 3 months of payments: 3 months $250/month = $750. Add the discount and the monthly payment savings to get the total potential savings: $5,316 + $750 = $6,066. Therefore, the correct answer is $6,066. Choice A, $1,282, is incorrect because it does not account for the total savings from both the discount and the monthly payments. Choice B, $5,566, is incorrect as it miscalculates the total savings by excluding the savings from the monthly payments. Choice D, $20,514, is incorrect as it does not consider the discount and only focuses on the list price.
Bridget is repainting her rectangular bedroom. Two walls measure 15 feet by 9 feet, and the other two measure 12.5 feet by 9 feet. One gallon of paint covers an average of 32 square meters. Which of the following is the number of gallons of paint that Bridget will use? (There are 3.28 feet in 1 meter.)
- A. 0.72 gallons
- B. 1.43 gallons
- C. 4.72 gallons
- D. 15.5 gallons
Correct Answer: B
Rationale: First, convert the dimensions to meters: 15 ft. (1 m/3.28 ft.) = 4.57 m; 9 ft. (1 m/3.28 ft.) = 2.74 m; 12.5 ft. (1 m/3.28 ft.) = 3.81 m. Next, find the total area in square meters: total area = 2(4.57 m 2.74 m) + 2(3.81 m 2.74 m) = 45.9 m². Finally, convert the area to gallons of paint: 45.9 m² (1 gallon/32 m²) = 1.43 gallons. Therefore, Bridget will need 1.43 gallons of paint to repaint her bedroom. Choices A, C, and D are incorrect because they do not accurately calculate the required amount of paint based on the given dimensions and the coverage area of one gallon of paint.
Which of the following lists is in order from least to greatest? 2−1 , −(4/3), (−1)3 , (2/5)
- A. 2−1 , −(4/3), (−1)3 , (2/5)
- B. −(4/3), (−1)3 , 2−1 , (2/5)
- C. −(4/3), (2/5), 2−1 , (−1)3
- D. −(4/3), (−1)3 , (2/5), 2−1
Correct Answer: D
Rationale: To determine the correct order from least to greatest, start by simplifying the expressions. 2^(-1) = 1/2 and (-1)^3 = -1. Now, comparing the values, (-4/3) is the most negative, followed by -1, then (2/5), and finally 1/2. Therefore, the correct order is (-4/3), (-1)^3, (2/5), 2^(-1), making choice D the correct answer. Choices A, B, and C are incorrect because they do not follow the correct order from least to greatest as determined by comparing the values of the expressions after simplification.
4 − 1/(22) + 24 · (8 + 12). Simplify the expression. Which of the following is correct?
- A. 1.39
- B. 2.74
- C. 4.95
- D. 15.28
Correct Answer: C
Rationale: First, complete the operations in parentheses: 4 − (1/22) + 24 · 20. Next, simplify the exponents: 4 − (1/22) + 24 · 20 = 4 − (1/4) + 24 · 20. Then, complete multiplication and division operations: 4 − (1/4) + 24 · 20 = 4 − 0.25 + 1.2. Finally, complete addition and subtraction operations: 4 − 0.25 + 1.2 = 4.95. Choice A, 1.39, is incorrect as it does not match the correct calculation. Choice B, 2.74, is incorrect as it is not the result of the given expression. Choice D, 15.28, is incorrect as it is not the correct simplification of the initial expression.