A rectangular field has an area of 1452 square feet. If the length is three times the width, what is the width of the field?

Correct Answer: A

Rationale: To find the width of the rectangular field, use the formula for the area of a rectangle: A = length width. Given that the length is three times the width, you have A = 3w w. Substituting the given area, 1452 = 3w^2. Solving for w, you get 484 = w^2. Taking the square root gives ±22, but since the width must be positive, the width of the field is 22 feet. Choice B, 44 feet, is incorrect because it represents the length, not the width. Choice C, 242 feet, is incorrect as it is not a factor of the area. Choice D, 1452 feet, is incorrect as it represents the total area of the field, not the width.

Correct Answer: D

Rationale: In this question, we are asked to find the result of the expression (6.4)(2.8) · 0.4. To solve this, we first multiply 6.4 by 2.8, which gives us 17.92. Then, we multiply this result by 0.4 to get the final answer. The correct option is D) 44.8 because 17.92 (result of (6.4)(2.8)) multiplied by 0.4 equals 44.8. This demonstrates the application of the order of operations in mathematics, where multiplication is done before addition or subtraction. The incorrect options can be explained as follows: - Option A) 16.62 is incorrect because it does not represent the result of the given expression. - Option B) 17.92 is the result of the first multiplication but fails to account for the additional multiplication by 0.4. - Option C) 41.55 is incorrect as it is not the correct result obtained through the given operations. Educationally, this question tests the test-taker's understanding of multiplying decimals and applying the order of operations correctly. It reinforces the importance of being meticulous in mathematical calculations and following the correct sequence of operations to arrive at the accurate solution.

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.

Correct Answer: D

Rationale: To calculate Matt's new wage after a 3/20 increase, we need to add this percentage increase to his original wage. The increase in decimal form is 3/20 = 0.15. Therefore, the new wage is w + w(0.15) = w(1 + 0.15) = 1.15w. This means the correct answer is D. Choices A, B, and C are incorrect because they do not account for the full 3/20 increase in the wage. Choice A (0.15w) represents only the increase percentage, not the total new wage. Choice B (0.85w) and Choice C (1.12w) do not accurately calculate the new wage after the increase, leading to incorrect representations of the final wage.

Correct Answer: A

Rationale: The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter. Given C = 49 feet, we can rearrange the formula to solve for d: 49 feet = πd. To find the diameter, we divide both sides by π, giving us d = 49 feet / π ≈ 15.6 feet. Therefore, the diameter of the swimming pool is approximately 15.6 feet. Choices B, C, and D are incorrect because they do not align with the calculation based on the formula for the circumference of a circle.