Mathematics

The problem states: 20% of 40 + ?% of 80 = 120. First, calculate 20% of 40, which is (20/100)*40 = 8. Let the unknown percentage be x%. Then the equation becomes 8 + (x/100)*80 = 120. Simplifying, (x/100)*80 = 120 - 8 = 112. This gives 0.8x = 112, so x = 112 / 0.8 = 140. Therefore, the value of '?' is 140%, which corresponds to option A. The original answer given as D (180) is incorrect. The options represent the percentage values directly, so the correct answer is A (140).

The calculation is performed as follows: First, add 2758 and 20581 to get 23339. Then subtract 17889 from 23339, resulting in 5450. Option B is 5450, which is the correct answer.

The total area of the 64 small squares is 400 cm², so each small square has an area of 400/64 = 6.25 cm². The side length of each small square is √6.25 = 2.5 cm. The chessboard has 8 squares per side, so its side length without the border is 8 × 2.5 = 20 cm. Adding the 3 cm border on each side adds 6 cm total, so the full side length is 20 + 6 = 26 cm. However, the question asks for the length of each side of the chessboard itself, which is 20 cm (without the border). Therefore, the correct answer is 20 cm (option B). Since the original correct answer was D (26 cm), which includes the border, but the question asks for the chessboard side length, the correct answer is B.

Calculating the numerator: 22*495 + 891*44 = 10890 + 39204 = 50094. Calculating the denominator: 33*176 + 55*264 = 5808 + 14520 = 20328. Dividing numerator by denominator: 50094 / 20328 = 69/28 ≈ 2.46428571. This matches option C exactly, so the correct answer is C (69/28). The original answer A (1) is incorrect.

The calculation is 1252 * 23 + 35000. First, multiply 1252 by 23, which equals 28796. Then add 35000 to get 63796. The exact result is 63796, which does not match any of the given options (200, 400, 1600, 800). Since none of the options correspond to the actual result, the question or options appear to be incorrect or incomplete. However, the original correct answer marked as D (800) is not correct based on the calculation. The correct result is 63796, and none of the options are correct. Therefore, the question should be revised to provide the correct options or clarify what is being asked.

The area of the four walls of a room (lateral surface area) is calculated by multiplying the perimeter of the floor by the height of the room. Given the perimeter of the floor is 18 m and the height is 3 m, the area of the four walls is 18 m × 3 m = 54 m². Among the options, 54 Sq.m corresponds to option C, so the correct answer is C.

Calculating step-by-step: 30.9 * 3000 = 92700; 10.1 * 1100 = 11110; then 92700 - 11110 + 8298 - 4302 = 92700 - 11110 = 81590; 81590 + 8298 = 89888; 89888 - 4302 = 85586, which rounds closest to 85000 (option D).

First, calculate 36 * 48 = 1728. Then divide 1728 by 64 to get 27. Next, calculate 36 ÷ 12 = 3. Finally, add 27 + 3 = 30. However, since the calculation shows 30, the correct answer should be D, not A. Rechecking: 36 * 48 = 1728; 1728 ÷ 64 = 27; 36 ÷ 12 = 3; 27 + 3 = 30. So the correct answer is D (30). The original correct_answer was D, which is correct. The explanation was missing and is now provided. The topic is arithmetic operations, and difficulty is easy.

Solving the equation for the unknown denominator, substituting each option shows that when ? = 2000, the equation balances to 1680, confirming A as correct.

To add 25 2/5 + 8 4/5 + 4/5, first add the whole numbers: 25 + 8 = 33. Then add the fractions: 2/5 + 4/5 + 4/5 = 10/5 = 2. Adding these gives 33 + 2 = 35. Therefore, the correct answer is 35, which corresponds to option B.

The equation is ∛(x/9261) = 11/21. Cubing both sides gives x/9261 = (11/21)^3 = 1331/9261. Multiplying both sides by 9261 yields x = 1331. However, the question is written as ∛?/9261 = 11/21, which implies the cube root of (? divided by 9261) equals 11/21, so the value inside the cube root is ?/9261 = (11/21)^3 = 1331/9261. Therefore, ? = 1331. The correct answer is B: 1331.

According to the order of operations, multiplication is performed before addition. Multiplying 2.9928 by 66.84 gives approximately 199.999 (about 200). Adding 183.21 to this product results in approximately 383.21. Among the given options, 383 (option A) is the closest and correct integer approximation of the result.

Calculate 32% of 425: 0.32 × 425 = 136. The equation is 136 - (x% of 250) = 36. Rearranging gives x% of 250 = 136 - 36 = 100. So, (x/100) × 250 = 100, which means x = (100 × 100) / 250 = 40%. Therefore, the value of '?' is 40, which corresponds to option B.

Following the order of operations (multiplication and division from left to right), 5 * 5 ÷ 5 + 5 ÷ 5 equals 5 + 1, which is 6. However, rechecking carefully: 5 * 5 = 25, 25 ÷ 5 = 5, 5 ÷ 5 = 1, so the expression is 5 + 1 = 6. The correct answer is 6, which corresponds to option D, not C. Therefore, the original correct_answer 'D' is correct. The explanation was missing, so it has been added.

Simplify the left side first: (98 / 7) = 14, then 14 / 2 = 7. So the equation becomes 7 / ? = 14. Multiply both sides by ?: 7 = 14 × ?. Divide both sides by 14: ? = 7 / 14 = 1/2. Therefore, the correct answer is A (1/2). The original correct_answer field was B, which is incorrect. The explanation and calculation confirm that the correct answer is A.

Multiplying the numbers step-by-step: 4 × 0.4 = 1.6, then 1.6 × 0.04 = 0.064, and finally 0.064 × 0.004 = 0.000256. Therefore, the correct answer is 0.000256, which corresponds to option C.

Let x be the unknown percentage. The equation is x% of 400 + 40% of 160 = 17% of 400. Converting percentages to decimals and multiplying: (x/100)*400 + 0.4*160 = 0.17*400. This simplifies to 4x + 64 = 68. Solving for x gives 4x = 4, so x = 1. Therefore, the correct value of x is 1%, which corresponds to option C.

Calculating each term: ³√216400 ≈ 60 (since 60³ = 216000, close to 216400), √280 ≈ 16.73, and √322 ≈ 17.94. Summing these gives approximately 60 + 16.73 + 17.94 = 94.67, which is close to 95, but since ³√216400 is not a perfect cube root, the exact cube root is closer to 60.2, making the sum closer to 95. However, the options suggest exact values, so let's check exact roots: ³√216000 = 60, so ³√216400 is slightly more than 60. Adding the square roots, the sum is about 95, matching option D. But the question uses ³√216400, which is not a perfect cube, so the exact cube root is approximately 60.2, sum approximately 95. Therefore, option D (95) is correct.

First, calculate inside the parentheses: 180/3 = 60. Then multiply and divide: 5 * 12 = 60, and 60 / 60 = 1. Finally, add 60 + 1 = 61. Thus, the correct answer is 61 (option D).

Total area = 510 ÷ 8.50 = 60 square meters. Given length = 8 m, so breadth = area ÷ length = 60 ÷ 8 = 7.5 m. Therefore, the correct option is 7.5 m.

According to the order of operations (PEMDAS/BODMAS), multiplication and division are performed from left to right before addition. First, calculate 25 * 25 = 625, then 625 / 25 = 25. Next, calculate 15 * 40 = 600. Finally, add 25 + 600 = 625. Therefore, the correct answer is D (625).

To find the unknown number, convert percentages to decimals and set up the equation: 0.1666 * 0.3333 * 0.6666 * x = 30. Multiplying the decimals gives approximately 0.037, so x ≈ 30 / 0.037 ≈ 810, which matches option C.

To find the missing number, divide 0.00000027 by the product of 0.003 and 0.0003. Calculating 0.003 * 0.0003 = 0.0000009, then 0.00000027 / 0.0000009 = 9. Therefore, the missing number is 9.

First, convert mixed numbers to improper fractions: 6 2/3 = 20/3, 9 3/5 = 48/5, 2 1/3 = 7/3, and 1 1/3 = 4/3. Multiply the first three: (20/3) * (48/5) * (7/3) = (20*48*7)/(3*5*3) = 6720/45 = 149 1/3. Then add 1 1/3 (4/3): 149 1/3 + 1 1/3 = 150 2/3, which matches option B.

Calculating the numerator: 1.9 × 0.021 = 0.0399. Calculating the denominator: 0.095 × 0.105 = 0.009975. Dividing numerator by denominator: 0.0399 ÷ 0.009975 ≈ 4, which corresponds to option C.