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.

Correct Answer: D

Rationale: To convert a percentage to a fraction, you write the percentage as the numerator of the fraction over 100. Therefore, 290% is equivalent to 290/100, which simplifies to 29/10. Choices A, B, and C are incorrect because they do not represent 290% as a fraction by placing the percentage value over 100.

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.

Correct Answer: C

Rationale: To create a 5:1 solution in 2.5 liters, 0.5 liters are needed for HCl, which translates to 5 grams. The correct answer is 5 grams, as this amount corresponds to the 5:1 ratio specified in the solution. Choices A, B, and D are incorrect because they do not align with the 5:1 ratio and the volume of the solution.

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.