Mathematics

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.

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.

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).

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.

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).

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.

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.

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.

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.

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.