To find the value of 5² – 3³ + 2⁴, we start by performing the exponentiation: 5² = 25, 3³ = 27, and 2⁴ = 16. Then, we perform the subtraction and addition: 25 – 27 + 16 = 14. Therefore, the correct answer is  14.

To find the fraction of boys in the class, we subtract the fraction of girls (16/28) from 1, since the total class is represented by 1. Therefore, 1 – 16/28 = 12/28 = 6/14 = 3/7. So, the correct answer is  4/7.

To simplify the expression (2 + 3) × (4 – 1) ÷ 5, we start by performing the addition and subtraction inside the parentheses: (2 + 3) × (4 – 1) = 5 × 3 = 15. Finally, dividing 15 by 5 gives us 3. Therefore, the correct answer is  3.

To solve for y in the equation 4(y + 3) – 2y = 5(y – 1) + 10, we can start by simplifying both sides of the equation. Distributing 4 to (y + 3) gives us 4y + 12. Distributing 5 to (y – 1) gives us 5y – 5. The equation now becomes 4y + 12 – 2y = 5y – 5 + 10. Combining like terms, we have 2y + 12 = 5y + 5. Subtracting 2y from both sides and subtracting 5 from both sides, we get 7 = 3y. Finally, dividing both sides by 3 gives us y = 7/3. Therefore, the correct answer is 7/3 .

To solve the equation 3(2x + 4) – 5(3x – 1) = 4(x – 2) + 6, we can start by simplifying both sides of the equation. Distributing 3 to (2x + 4) gives us 6x + 12. Distributing 5 to (3x – 1) gives us 15x – 5. Distributing 4 to (x – 2) gives us 4x – 8. The equation now becomes 6x + 12 – 15x – 5 = 4x – 8 + 6. Combining like terms, we have -9x + 7 = 4x – 2. Adding 9x to both sides and adding 2 to both sides, we get 11x = 9. Finally, dividing both sides by 11 gives us x = 9/11. Therefore, the correct answer is 9/11 .

To solve the equation 2(3x + 1) – 4(2x – 3) = 3(2x – 4) + 5, we can start by simplifying both sides of the equation. Distributing 2 to (3x + 1) gives us 6x + 2. Distributing -4 to (2x – 3) gives us -8x + 12. Distributing 3 to (2x – 4) gives us 6x – 12. The equation now becomes 6x + 2 – 8x + 12 = 6x – 12 + 5. Combining like terms, we have -2x + 14 = 6x – 7. Adding 2x to both sides and subtracting 14 from both sides, we get 8x = 7. Finally, dividing both sides by 8 gives us x = 7/8. Therefore, the correct answer is 7/8.

To solve for x in the equation 2(3x + 5) – 4(x – 1) = 16, we can start by simplifying both sides of the equation. Distributing 2 to (3x + 5) gives us 6x + 10. Distributing -4 to (x – 1) gives us -4x + 4. The equation now becomes 6x + 10 – 4x + 4 = 16. Combining like terms, we have 2x + 14 = 16. Subtracting 14 from both sides gives us 2x = 2. Finally, dividing both sides by 2 gives us x = 1. Therefore, the correct answer is  1.

The sum of the angles in a triangle is always 180°. Given that two angles measure 40° and 80°, we can find the missing angle by subtracting the sum of the given angles from 180°: 180° – (40° + 80°) = 60°. Therefore, the correct answer is 60°.

The area of a circle is calculated by multiplying the square of its radius by π (pi). In this case, the radius is 6 cm. So, the area is (6^2) × π = 36π square cm. Therefore, the correct answer is  36π sq cm.

To evaluate the expression 3(4 – 2) + 5² – 2³, we follow the order of operations. First, we perform the subtraction inside the parentheses: 4 – 2 = 2. Next, we perform the exponentiation: 5² = 25 and 2³ = 8. Finally, we perform the multiplication and addition: 3(2) + 25 – 8 = 6 + 25 – 8 = 31. Therefore, the correct answer is 13.

To simplify the expression 2/3 + 4/5 – 1/4, we need to find a common denominator for the fractions. The least common multiple of 3, 5, and 4 is 60. Multiplying the numerator and denominator of each fraction to have a denominator of 60, we get 40/60 + 48/60 – 15/60. Combining the numerators, we have 40 + 48 – 15 = 73. Therefore, the correct answer is 19/20.

To solve for y in the equation 5y – 3(2y + 4) = 10 – 4y, we can start by simplifying both sides of the equation. Distributing -3 to (2y + 4) gives us -6y – 12. The equation now becomes 5y – 6y – 12 = 10 – 4y. Combining like terms, we have -y – 12 = 10 – 4y. Adding 4y to both sides and adding y to both sides, we get 3y – 12 = 10. Finally, adding 12 to both sides gives us 3y = 22. Dividing both sides by 3 gives us y = 22/3. Therefore, the correct answer is 22/3.

If the ratio of boys to girls in a class is 3:4, we can set up the proportion 3/4 = 27/x, where x represents the number of girls. Cross-multiplying, we have 3x = 4 * 27, which simplifies to 3x = 108. Dividing both sides by 3, we find x = 108/3 = 36. Therefore, the correct answer is  36.

To simplify the expression 5 + 3 × (8 – 4) ÷ 2, we start by performing the subtraction inside the parentheses: 8 – 4 = 4. Next, we perform the multiplication: 3 × 4 = 12. Finally, we perform the division: 12 ÷ 2 = 6. Adding 5 to 6 gives us 11. Therefore, the correct answer is  11.

The volume of a cylinder is calculated by multiplying the area of the base (πr^2) by the height. In this case, the radius is 4 meters and the height is 10 meters. Plugging in the values, we get volume = π × (4^2) × 10 = 16π × 10 = 160π cubic meters. Therefore, the correct answer is  251.2 cubic meters.

The least common multiple (LCM) of 4 and 6 is the smallest number that is divisible by both 4 and 6. The prime factorization of 4 is 2 × 2, and the prime factorization of 6 is 2 × 3. The LCM is found by taking the highest power of each prime factor. In this case, the highest power of 2 is 2^2, and the highest power of 3 is 3^1. Multiplying 2^2 and 3^1 gives us 4 × 3 = 12. Therefore, the correct answer is  12.

To simplify the expression 2(3x – 5) + 4x – 8, we start by performing the multiplication: 2(3x – 5) = 6x – 10. Then, we combine like terms: 6x – 10 + 4x – 8 = 10x – 18. Therefore, the correct answer is  10x – 18.

The area of a rectangle is calculated by multiplying its length by its width. In this case, the area is 48 square meters and the width is 6 meters. So, the length is 48 square meters / 6 meters = 8 meters. Therefore, the correct answer is 8 meters.

To solve the equation 4x – 7 = 3x + 2, we can start by simplifying both sides of the equation. Subtracting 3x from both sides gives us x – 7 = 2. Adding 7 to both sides gives us x = 9. Therefore, the correct answer is 9.

To solve for y in the equation 3(y – 4) + 2y = 10 – y + 6, we can start by simplifying both sides of the equation. Distributing 3 to (y – 4) gives us 3y – 12. The equation now becomes 3y – 12 + 2y = 10 – y + 6. Combining like terms, we have 5y – 12 = 16 – y. Adding y to both sides and adding 12 to both sides, we get 6y = 28. Finally, dividing both sides by 6 gives us y = 28/6 = 14/3. Therefore, the correct answer is 14/3.

The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is 12 meters and the width is 8 meters. So, the area is 12 meters * 8 meters = 96 square meters. Therefore, the correct answer is  96 sq meters.

The sum of the angles in a triangle is always 180°. Given that two angles measure 50° and 70°, we can find the missing angle by subtracting the sum of the given angles from 180°: 180° – (50° + 70°) = 60°. Therefore, the correct answer is  60°.

The perimeter of a regular hexagon can be found by multiplying the length of one side by 6 since a hexagon has six equal sides. In this case, the side length is 8 cm. So, the perimeter is 8 cm × 6 = 48 cm. Therefore, the correct answer is  48 cm.

To solve for x in the equation 3(2x + 5) = 36 – 4x, we can start by simplifying both sides of the equation. Distributing 3 to (2x + 5) gives us 6x + 15. The equation now becomes 6x + 15 = 36 – 4x. Combining like terms, we have 6x + 15 = 36 – 4x. Adding 4x to both sides and subtracting 15 from both sides, we get 10x = 21. Finally, dividing both sides by 10 gives us x = 21/10. Therefore, the correct answer is 21/10.

The circumference of a circle is calculated by multiplying the diameter by π (pi). In this case, the diameter is 10 cm. So, the circumference is 10 cm * π = 10π cm. Therefore, the correct answer is  10π cm.