Increasing one number by 5 increases the total sum by 5. If there are n numbers, the mean increases by 5/n.

The original sum of the numbers is 30 * 10 = 300. Adding 50 gives a new sum of 300 + 50 = 350. The new mean is 350 / 11 = 31.82, which rounds to 32.

Let the integers be x, x+1, x+2, x+3, x+4. Mean = (5x + 10) / 5 = 12. Solving gives x = 10.

Let the sum of the five numbers be S. Then, S/5 = 20, so S = 100. Let the removed number be x. The new sum is S - x, and the new mean is (S - x)/4 = 18. Therefore, 100 - x = 72, which gives x = 28.

The first four prime numbers are 2, 3, 5, and 7. Mean = (2 + 3 + 5 + 7) / 4 = 17 / 4 = 4.25.

Mean = (4 + 8 + 10 + 12 + x) / 5 = 10. Solving gives x = 14.

Mean = (4 + 8 + 12 + x) / 4 = 10. Therefore, 4 + 8 + 12 + x = 40. So, x = 40 - 24 = 16.

Let the integers be x, x+1, x+2. Mean = (x + (x+1) + (x+2)) / 3 = 20. Thus, 3x + 3 = 60, so x = 19.

Total of three numbers = 3 * 12 = 36. Sum of the other two numbers = 36 - 8 = 28. Mean of the other two = 28 / 2 = 14.

New mean = (15*3 + 5) / 3 = 20/3 = 16.67.

Let the other two numbers be a and b. Then, (10 + a + b) / 3 = 15. Solving gives (a + b) = 35, so Mean of a and b = 35 / 2 = 17.5.

Let the three numbers be a, b, c. Then, (a + b + 20) / 3 = 30. Thus, a + b = 90, and the mean of a and b = 90 / 2 = 45.

Temperature is a measure of the average kinetic energy of the particles in a substance.

Temperature is a measure of the average kinetic energy of the particles in a substance.

For the median to be 8, x must be less than or equal to 8. The only value that satisfies this is x = 6.

Median = 9 (middle value of the ordered data set)

Arranging the numbers: 2, 3, 5, 7, 11, 13. Median = (5 + 7) / 2 = 6.

Arranging the data: 3, 7, 9, 15, 20. Median = 9 (middle value).

The Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) provides 100 days of guaranteed wage employment in a financial year.

The Mid-Day Meal Scheme was launched in 1995 to improve the nutritional status of school-age children and combat malnutrition.

The vertex of the parabola occurs at x = -b/(2a) = 4/2 = 2. The minimum value is f(2) = 2^2 - 4*2 + 6 = 2.

Finding the derivative f'(x) = 4x^3 - 16x. Setting f'(x) = 0 gives x = 0, ±2. Evaluating f(0) = 16, f(2) = 0, and f(-2) = 0, the minimum value is 0.

Mode is the number that appears most frequently, which is 4.

The modulus of resilience is the energy per unit volume stored in a material up to the yield point.

The Mohorovičić discontinuity, or Moho, separates the Earth's crust from the underlying mantle.

The moment of inertia of a composite body can be calculated using the parallel axis theorem.

The moment of inertia of a hollow cylinder about its central axis is I = MR^2.

The moment of inertia is calculated by summing the mass of each particle times the square of its distance from the axis of rotation: I = Σ(m_i * r_i²).

The Montagu-Chelmsford Reforms aimed to increase Indian participation in governance through the introduction of dyarchy in the provinces.

In active voice, we focus on the director's action, resulting in 'The famous director directed the movie.'