Mathematics

Adding the numbers: 2222.2 + 222.22 + 22.222 equals 2466.642. However, careful addition shows the sum is actually 2466.642, matching option D. Rechecking the addition: 2222.2 + 222.22 = 2444.42; 2444.42 + 22.222 = 2466.642. Therefore, option D is correct.

The expression is [(7 * 9) + (2 * 12) + 3] / [(12 * 3) + (81 / 9)]. Calculating the numerator: (7*9) + (2*12) + 3 = 63 + 24 + 3 = 90. Calculating the denominator: (12*3) + (81/9) = 36 + 9 = 45. Dividing numerator by denominator: 90 / 45 = 2. Since 2 is not among the options A (4), B (60), or C (1.75), the correct answer is D (None of these).

Calculating the expression: 25.25 - 23.23 + 24.24 = 2.02 + 24.24 = 26.26, which matches option B.

First, calculate inside the parentheses: (27 + 3) = 30. Then, 33.33% of 30 is approximately 10. Next, divide by 5: 10 ÷ 5 = 2. Multiply by 21: 21 * 2 = 42. Subtract 7: 42 - 7 = 35. Then, take 3/7 of 35: (3/7) * 35 = 15. Finally, subtract 8: 15 - 8 = 7. Thus, the answer is 7, which corresponds to option A.

The equation simplifies to ((50 - x/29) × 4200%) = 3√196. Since 4200% = 42 and 3√196 = 3 × 14 = 42, the equation becomes (50 - x/29) × 42 = 42. Dividing both sides by 42 gives 50 - x/29 = 1. Solving for x gives x/29 = 49, so x = 49 × 29 = 1421. Therefore, the correct value of ? is 1421, which corresponds to option D.

To find 43% of 784, multiply 784 by 0.43: 784 × 0.43 = 337.12. This matches option C. Therefore, the correct answer is C, not B.

First, solve inside the parentheses: (3 - 2) = 1. Then, [7 - 1] = 6. Next, 20 - 6 = 14. Calculate 1/3 of 4.2, which is 1.4. Add this to 14 to get 15.4. Finally, divide 15.4 by 1.4 to get 11, which corresponds to option A.

The product of 105 * 99 * 299 is calculated as follows: 105 * 99 = 10395, then 10395 * 299 = 3,108,105. This matches the calculation in the explanation. The options given (A: 785600, B: 315000, C: 845000, D: 442000) do not include the correct product 3,108,105. Therefore, the options are incorrect for the question as stated. However, since the question asks for the product of 105 * 99 * 299, the correct answer is the actual product 3,108,105, which is not among the options. The original correct_answer 'D' (442000) is incorrect. The question options need correction to include the correct product. The explanation correctly states the calculation and the mismatch with the options.

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.

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.