Total sum = Mean * Number of items = 12 * 6 = 72.

Total sum = Mean * Number of items = 12 * 6 = 72.

Total = Mean * Number of Items = 25 * 8 = 200.

Total sum = Mean * Number of elements = 30 * 6 = 180.

Mean = Total Sum / Number of Items. Therefore, Total Sum = Mean * Number of Items = 20 * 5 = 100.

Mean = Sum / 5. Therefore, Sum = Mean * 5 = 6 * 5 = 30.

Mean = n(n + 1) / (2n) = 10.\n\n(n + 1) / 2 = 10\n\n(n + 1) = 20\n\nn = 19.

Mean = (15 + 18 + 22 + x + 25) / 5 = 20. Solving gives x = 24.

Arranging the data: 3, 5, 7, 9, 11. Median = 7.

For the median to be 9, x must be 9. The ordered set is 3, 7, 9, 9, 15.

Removing 5, which is the mode, leaves 3 as the new mode since it appears twice.

The original mode is 4. Increasing it by 1 gives a new mode of 5.

Arranging the numbers: 3, 5, 7, 8, 12. The median is the middle number, which is 7.

The mode is 5, as it appears 3 times, more than any other number.

Perimeter = 2(length + width). So, 50 = 2(15 + width). Solving gives width = 10 cm.

Perimeter = DE + EF + DF. Therefore, DF = 36 - (10 + 12) = 14 cm.

Substituting x = 0: 4(0) - 5y = 20 => -5y = 20 => y = -4.

Distance = |r| = √(2^2 + 3^2 + 4^2) = √(4 + 9 + 16) = √29.

The x-component of r is 2.

The x-coordinate of point P is the coefficient of i in the position vector, which is 2.

Distance = |r| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

Probability of not A = 1 - P(A) = 1 - 0.4 = 0.6.

Probability of not occurring = 1 - P(event) = 1 - 0.3 = 0.7.

By Vieta's formulas, the sum of the roots p + q = -b/a.

The equation can be factored as (x + 1)(x + 1) = 0, giving the root -1 with multiplicity 2.

The discriminant is 0, indicating that the roots are real and equal.

Substituting x = -1 into the equation gives (-1)^2 + 2(-1) + k = 0, leading to 1 - 2 + k = 0, thus k = 1.

The product of the roots is 1 * (-3) = -3, hence k = -3.

For both roots to be negative, k must be greater than 0.

The product of the roots is given by c/a = 6/1 = 6.