Correct Answer: C

Rationale: To find the volume of a hemispherical bowl, we use half the formula for a sphere's volume: (2/3) * π * (radius)^3. Given the diameter is 30cm, the radius is half of that, which is 15cm. Substitute the radius into the formula: (2/3) * π * (15cm)^3 ≈ 2700 cu cm. Therefore, the correct volume is approximately 2700 cu cm. Choices A, B, and D are incorrect as they do not correctly calculate the volume of the hemispherical bowl.

Correct Answer: D

Rationale: Rationale: 1. 7 is divisible by 1 because every number is divisible by 1. 2. 7 is divisible by 7 because any number is divisible by itself. 3. 7 is not divisible by 2 because 7 is an odd number and not divisible by 2. 4. 7 is not divisible by 3 because the sum of the digits of 7 (7) is not divisible by 3. Therefore, 7 is divisible by 1, 7, and itself (7), making the correct answer D) 2, 3, and 7.

Correct Answer: A

Rationale: To subtract 7 7/10 from 3 4/5, first convert 3 4/5 to have the same denominator as 7 7/10. Converting 4/5 to 8/10, the subtraction becomes 7 7/10 - 3 8/10. Subtracting, 7 - 3 = 4 and 7/10 - 8/10 = -1/10. Therefore, the result is 3 4/5 - 7 7/10 = 3 9/10. Choices B, C, and D are incorrect because they do not reflect the correct subtraction of fractions and whole numbers in this scenario.

Correct Answer: A

Rationale: To find x, we set up the proportion 15:x = 3:8. Cross multiply to get 15*8 = 3*x, which simplifies to 120 = 3x. Dividing by 3 on both sides gives x = 40. Therefore, x=40 is the correct answer. Choices B, C, and D are incorrect because they do not match the correct calculation. Option B results from incorrectly dividing 15 by 3 instead of multiplying it by 8. Option C comes from dividing 15 by 3, and Option D is the result of dividing 15 by 8 instead of multiplying by 3.

Correct Answer: A

Rationale: To divide fractions, you multiply by the reciprocal of the divisor. (12/15) · (3/5) is the same as (12/15) * (5/3). Cancel out common factors to simplify: 12 · 3 = 4, 15 · 5 = 3. So, the expression simplifies to 4/3, which is 1 1/3 in mixed number form. Choice A, 1 1/3, is the correct answer. Choices B, C, and D are incorrect because they do not represent the simplified form of the division of the given fractions.