At the beginning of the day, Xavier has 20 apples. At lunch, he meets his sister Emma and gives her half of his apples. After lunch, he stops by his neighbor Jim's house and gives him 6 of his apples. He then uses ¾ of his remaining apples to make an apple pie for dessert at dinner. At the end of the day, how many apples does Xavier have left?

Correct Answer: D

Rationale: Xavier starts with 20 apples. He gives half to Emma, leaving him with 10 apples. After giving 6 more to Jim, he has 4 apples left. Using ¾ of the remaining 4 apples for the pie leaves him with 1 apple at the end of the day. Choice A is incorrect because it doesn't account for the apple pie Xavier made. Choices B and C are incorrect as they don't reflect the correct calculations of apples remaining after each step.

Correct Answer: D

Rationale: Xavier starts with 20 apples. He gives half to Emma, leaving him with 10 apples. After giving 6 more to Jim, he has 4 apples left. Using ¾ of the remaining 4 apples for the pie leaves him with 1 apple at the end of the day. Choice A is incorrect because it doesn't account for the apple pie Xavier made. Choices B and C are incorrect as they don't reflect the correct calculations of apples remaining after each step.

Correct Answer: A

Rationale: To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. So, (4/3) · (9/13) = (4/3) * (13/9) = 52/27. This fraction is already in its reduced form, making choice A the correct answer. Choices B, C, and D are incorrect as they do not represent the correct result of dividing the fractions 4/3 by 9/13.

Correct Answer: A

Rationale: When rounding a number to the nearest tenth, you look at the digit in the hundredths place. Since 8.067 has a 6 in the hundredths place, which is equal to or greater than 5, you round the tenths place up by 1. Therefore, rounding 8.067 to the nearest tenth gives 8.07. Choice B (8.1) would be incorrect because 8.067 is closer to 8.1 than to 8, but it's not quite there. Choice C (8) is incorrect as it would be rounding down, and Choice D (8.11) is incorrect as it is rounding to the nearest hundredth, not the nearest tenth.

Correct Answer: D

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

Correct Answer: A

Rationale: The correct answer is 'Multiplication.' According to the order of operations (PEMDAS), which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), multiplication should be completed first. In the given expression, 3 2 should be solved before adding 6 to the result. This means that the multiplication operation should be prioritized over addition. Choices B, C, and D are incorrect because, in the order of operations, multiplication takes precedence over addition, division, and subtraction, respectively.

Correct Answer: A

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

Correct Answer: B

Rationale: To find the remaining paint, subtract the amount used from the total gallons bought. 5.0 - 2.5 = 2.5 gallons. Therefore, Shawna has 2.5 gallons of paint left after using 2.5 gallons on the first day. Choices A, C, and D are incorrect because they do not accurately represent the amount of paint left after using 2.5 gallons.

Correct Answer: C

Rationale: The correct answer is C: 'Irrational or rational.' When you multiply two irrational numbers, the result can be either irrational or rational. For example, multiplying the square root of 2 (√2) by itself results in the rational number 2. This shows that the product of two irrational numbers can lead to a rational result. Choices A, B, and D are incorrect because the product of two irrational numbers is not limited to being irrational; it can also be rational.