Mathematics

Let the unknown number be x. The equation is 9000 + (16 2/3)% of x = 10500. Converting 16 2/3% to a fraction gives 1/6. So, 9000 + (1/6)x = 10500. Subtracting 9000 from both sides gives (1/6)x = 1500, so x = 1500 * 6 = 9000. However, this matches option C, but the question asks for the value of '?', which is x. The calculation shows x = 9000, so option C is correct. The initial correct_answer was C, which is correct. The explanation was missing and has been added. The topic is algebra (solving equations). The difficulty is medium because it involves percentage and equation solving.

Multiplying 6.4 by 1.25 equals 8.0. This is because 1.25 is equivalent to 5/4, so multiplying 6.4 by 1.25 is the same as multiplying 6.4 by 5/4, which results in 8.0. The original options do not include 8, so the question or options should be corrected to reflect the correct product. Since the correct product is 8, none of the given options (1, 4, 2, 3) are correct. The question should be updated to include 8 as an option or the options should be changed accordingly.

Step-by-step calculation: 421 * 0.9 = 378.9; 130 * 101 = 13130; adding these and 10000 gives 378.9 + 13130 + 10000 = 23508.9. Among the options, 23500 (option B) is the closest to the actual sum 23508.9, making B the correct answer.

Given the equation x% of 80 equals 20% of y, we write it as (x/100)*80 = (20/100)*y. Simplifying, 0.8x = 0.2y, which leads to y = 4x. If we take x = 20, then y = 4*20 = 80. Therefore, the correct values are x = 20 and y = 80, which corresponds to option C.

The expression is: 12.5 + 10 1/4 of 100 ÷ 10% of 10. First, convert 10 1/4 to decimal: 10 1/4 = 10.25. Calculate 10.25 of 100: 10.25 × 100 = 1025. Calculate 10% of 10: 0.10 × 10 = 1. Now divide 1025 by 1: 1025 ÷ 1 = 1025. Finally, add 12.5 + 1025 = 1037.5. However, the original expression is ambiguous without parentheses. If interpreted as 12.5 + (10 1/4 of 100) ÷ (10% of 10), the result is 1037.5 (option A). But if interpreted as 12.5 + (10 1/4)% of 100 ÷ 10% of 10, then 10 1/4% = 0.1025, so 0.1025 × 100 = 10.25, and 10% of 10 = 1, so 10.25 ÷ 1 = 10.25, and 12.5 + 10.25 = 22.75 (option C). Since the question uses "10 1/4 of 100" without % sign, the first interpretation is more mathematically standard, so the answer should be 1037.5 (option A). But if the question intended "10 1/4% of 100", then the answer is 22.75 (option C). Given the ambiguity, the most reasonable interpretation is the first, so option A is correct. The original correct_answer was C, which is inconsistent with the calculation. Therefore, the correct answer is A (1037.5).

The expression is 2 + [2 + {2 + (2 + (2 + 23))}]. Evaluating from the innermost parentheses: (2 + 23) = 25. Then (2 + 25) = 27. Next, {2 + 27} = 29. Then [2 + 29] = 31. Finally, 2 + 31 = 33. The sum is 33, which as a fraction over 4 is 33/4. Among the given options, 33/4 exactly matches option B. Therefore, the correct answer is B (33/4). The original answer D (129/4) is incorrect as it equals 32.25, which is less than 33.

First, divide 79.98 by 12.51, which is approximately 6.39. Then multiply 6.39 by 2.49, resulting in approximately 15.9, which rounds to 16. Therefore, option C is correct.

Calculate each cube: (2.75)^3 = 20.796875, (2.00)^3 = 8, (0.75)^3 = 0.421875. Then compute the expression: 20.796875 - 8 - 0.421875 = 12.375. Now check the options: Option D is 4.5 * 2.75 = 12.375, which matches the computed value exactly. The other options do not match this value. Therefore, the correct answer is D.

First, simplify inside the brackets: (26/13 + 24/12 + 21) = (2 + 2 + 21) = 25. Then calculate 60% of 25 = 0.6 × 25 = 15. Next, inside the curly braces: 20 + 15 - 2 = 33. Now, the expression inside the square brackets: 50 - 33 + 8 = 25. The equation becomes 25 = 625 / ?. Solving for ?: ? = 625 / 25 = 25. Since 25 corresponds to option A, the correct answer should be A, not B.

First, calculate the denominator: 24 * 0.75 = 18. Then divide 1296 by 18, which equals 72. Therefore, the correct answer is 72, which corresponds to option D.