Nokea
How many gallons are in 1,000 fluid ounces?
- A. 7.8125 gallons
- B. 15.625 gallons
- C. 31.25 gallons
- D. 62.5 gallons
Correct Answer: A
Rationale: To convert fluid ounces to gallons, you need to divide the number of fluid ounces by the number of fluid ounces in a gallon. Since there are 128 fluid ounces in a gallon, to find out how many gallons are in 1,000 fluid ounces, you divide 1,000 by 128. The correct calculation is 1,000 / 128 = 7.8125 gallons. Therefore, the correct answer is A. Choices B, C, and D are incorrect as they do not accurately represent the conversion from fluid ounces to gallons.
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A piece of wood that is 7 1/2 feet long has 3 1/4 feet cut off. How many feet of wood remain?
- A. 4 1/4 feet
- B. 4 1/2 feet
- C. 3 1/2 feet
- D. 3 3/4 feet
Correct Answer: A
Rationale: To find the remaining length of wood, you need to subtract 3 1/4 feet from 7 1/2 feet. When you subtract the fractions, 7 1/2 - 3 1/4, you get 15/2 - 13/4 = 30/4 - 13/4 = 17/4 = 4 1/4 feet. Therefore, the correct answer is 4 1/4 feet. Choice B (4 1/2 feet) is incorrect because the subtraction result is not 1/2. Choice C (3 1/2 feet) is incorrect as it does not match the correct result of 4 1/4 feet. Choice D (3 3/4 feet) is also incorrect as it does not align with the correct answer obtained from the subtraction of fractions.
Solve the inequality for the unknown.
- A. x > 5
- B. x < 5
- C. x >= 5
- D. x <= 5
Correct Answer: A
Rationale: When solving an inequality, the direction of the inequality sign changes depending on the operation performed. In this case, if the given inequality simplifies to x > 5, it means that the unknown value x must be greater than 5 for the inequality to hold true. Therefore, x > 5 is the correct solution. Option A is correct. Choices B, C, and D are incorrect because they do not correctly represent the relationship between x and 5 based on the given inequality.
Solve for x in the equation: 3x - 5 = 16
- A. 7
- B. 5
- C. 8
- D. 9
Correct Answer: C
Rationale: To solve for x, add 5 to both sides of the equation: 3x - 5 + 5 = 16 + 5, which simplifies to 3x = 21. Next, divide both sides by 3: x = 21 · 3 = 7. Therefore, the correct answer is x = 7, making option A the correct choice. Option C, '8,' is incorrect as it is not the solution obtained from the correct calculations. Options B and D, '5' and '9,' are also incorrect and not the solution to the given equation.
What is the mean for the data set 16, 18, 17, 15, 19, 14, 12, 11, 10, 16, 18, and 17?
- A. 14.25
- B. 15.25
- C. 16
- D. 17
Correct Answer: C
Rationale: To find the mean of a data set, you add up all the values and then divide by the total number of values. In this case, the sum of the data set is 185. Dividing this sum by the total number of values (12) gives you a mean of 16. Therefore, the correct answer is 16. Choice A (14.25), Choice B (15.25), and Choice D (17) are incorrect because they do not accurately represent the average value of the given data set.
Simplify (x^2 - y^2) / (x - y)
- A. x + y
- B. x - y
- C. 1
- D. (x + y)/(x - y)
Correct Answer: A
Rationale: The expression x^2 - y^2 is a difference of squares, which follows the identity: x^2 - y^2 = (x + y)(x - y). Therefore, the given expression becomes: (x^2 - y^2) / (x - y) = (x + y)(x - y) / (x - y). Since (x - y) appears in both the numerator and the denominator, they cancel each other out, leaving x + y. Thus, the simplified form of (x^2 - y^2) / (x - y) is x + y. Therefore, the correct answer is A (x + y). Option B (x - y) is incorrect as it does not result from simplifying the given expression. Option C (1) is incorrect as it does not account for the variables x and y present in the expression. Option D ((x + y)/(x - y)) is incorrect as it presents the simplified form in a different format than the correct answer.