Calculate the product of the following decimals: (0.67)(0.09)

Correct Answer: A

Rationale: To multiply decimals, align the numbers as whole numbers, multiply as if they were whole numbers, then adjust the decimal point in the final answer. When multiplying 0.67 by 0.09, the result is 0.0603. To get this result, multiply 67 by 9 to get 603, then adjust the decimal point two places to the left in the final product, resulting in 0.0603. Choice B, 0.6, is incorrect because it does not account for the decimal precision in the multiplication. Choice C, 0.603, is incorrect as it has the digits reversed when compared to the correct answer. Choice D, 0.06, is incorrect as it does not reflect the correct product of the two decimals being multiplied.

Correct Answer: B

Rationale: To convert 3 1/2 pints of sour cream to cups, knowing that 1 pint equals 2 cups, we multiply 3.5 by 2, resulting in 7 cups. Therefore, the equivalent amount of sour cream in cups is 7 cups. Choice A is incorrect as it does not consider the correct conversion factor. Choice C is incorrect as it does not account for the accurate conversion from pints to cups. Choice D is incorrect as it underestimates the conversion by not multiplying the pints by the correct factor.

Correct Answer: B

Rationale: Let Mr. Johnson's pay be represented as x. After giving half of his pay to his family, he has x/2 left. Subtracting $250 paid to his landlord, he has x/2 - $250 remaining. Given that this remaining amount is 3/7 of his original pay, the equation becomes x/2 - $250 = 3x/7. Solving this equation shows that x = $3,500. Therefore, Mr. Johnson receives $3,500. Choices A, C, and D are incorrect as they do not align with the correct calculation based on the given conditions in the question.

Correct Answer: C

Rationale: To convert 5 3/4 to a decimal, divide the numerator (3) by the denominator (4) to get 0.75. Adding this to the whole number 5 results in 5.75. When rounding to the nearest tenth, 5.75 rounds to 5.8. Therefore, the correct answer is 5.8. Choice A, 5.75, is the result before rounding to the nearest tenth. Choice B, 5.7, is incorrect as it does not account for the 0.05 difference when rounding. Choice D, 6, is the next whole number and is not the correct decimal equivalent of 5 3/4.

Correct Answer: B

Rationale: To solve the equation 4y - 6 = 14 for y, isolate y by adding 6 to both sides: 4y = 14 + 6 => 4y = 20. Then, divide by 4 to solve for y: y = 20 · 4 = 5. Therefore, the correct answer is 5. Choice A is incorrect as it does not represent the correct solution to the equation. Choice C is incorrect as it is not the solution obtained after correctly solving the equation. Choice D is incorrect as it is not the correct solution to the given equation.

Correct Answer: A

Rationale: The correct answer is A: 0.09%. To convert 0.0009 to a percentage, move the decimal point four places to the right and add a percentage sign. Therefore, 0.0009 is equal to 0.09%. Choice B (9%) is incorrect as it represents 0.09 without the decimal point adjustment. Choice C (0.01%) is incorrect as it represents 0.0009 with one less zero. Choice D (0.90%) is incorrect as it represents 0.9 not 0.0009.

Correct Answer: D

Rationale: To find the total surface area, we need to calculate the surface area of the cylindrical body and both hemispherical ends separately. The surface area of the cylinder is the sum of the lateral surface area (2πrh) and the area of the two circular bases (2πr^2). For the hemispheres, the surface area of one hemisphere is (2πr^2), so for two hemispheres, it would be (4πr^2). Given that the diameter of the cylinder and hemispherical ends is 10cm, the radius (r) is 5cm. Calculating the individual surface areas: Cylinder = 2π(5)(20) + 2π(5)^2 = 200π + 50π = 250π. Hemispheres = 4π(5)^2 = 100π. Adding these together gives a total surface area of 250π + 100π = 350π cm^2, which is approximately equal to 2055 sq cm. Therefore, the correct answer is D. Choice A (785 sq cm) is incorrect as it is significantly lower than the correct calculation. Choices B (1130 sq cm) and C (1570 sq cm) are also incorrect as they do not reflect the accurate surface area calculation for the given dimensions.

Correct Answer: A

Rationale: First, convert the child's weight from pounds to kilograms: 44 lb · 2.2 = 20 kg. Next, calculate the required dosage: 20 kg 20 mg/kg = 400 mg. Since each tablet contains 80 mg, divide the total dosage by the dosage per tablet: 400 mg · 80 mg/tablet = 5 tablets. Therefore, the correct answer is 5 tablets. Choice B is incorrect because it does not account for the actual number of tablets needed. Choice C is incorrect as it is an underestimation of the required tablets. Choice D is incorrect as it is an underestimation of the required tablets.

Correct Answer: B

Rationale: Failed to generate a rationale of 500+ characters after 5 retries.