Total = Average × Number of items = 50 × 8 = 400.

Total sum = Average × Number of items = 50 × 8 = 400.

Total = Average × Count = 50 × 10 = 500.

Sum of the numbers = Average × Number of items = 30 × 5 = 150.

Let the integers be (x-1), x, and (x+1). Their average is (x-1 + x + x+1) / 3 = x.

Let the two numbers be a and b. (a + b) / 2 = 30. If a = 20, then 20 + b = 60, hence b = 40.

Let the other number be x. The average is (30 + x) / 2 = 40. Solving gives x = 50.

In base 'b', '10' represents 'b'. In base 'b+1', it becomes '11'.

To convert from base-2 to decimal, calculate 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 8 + 4 + 0 + 1 = 13.

The sum of the coefficients in the expansion of (x + 1)^n is found by substituting x = 1, which gives 2^n.

The coefficient of x^2 in the expansion of (x + 2)^3 is given by C(3, 2) * 2^1 = 3 * 2 = 6.

The term containing x^2 is C(4,2) * x^2 * 2^2 = 6 * x^2 * 4 = 24x^2.

The term containing x^2y^2 in the expansion of (x + y)^4 is given by 4C2 * x^2 * y^2 = 6x^2y^2.

The constant term occurs when x^0, which is the term with k = 4: C(4, 4)(-2)^4 = 16, thus the constant term is -16.

The number of terms in the expansion of (a + b)^n is n + 1, so for n = 7, there will be 8 terms.

The term containing x^0 occurs when k = 3, which gives 6C3 * 1^3 * (1/x)^3 = 20.

Circumference = 2πr. Therefore, r = circumference / (2π) = 31.4 / (2 * 3.14) = 5 cm.

Using the formula C = 2πr, we find r = C/(2π) = 31.4/(2*3.14) = 5 cm.

C(n,k) represents the number of ways to choose k items from n, which corresponds to the coefficient of x^k.

In a GP with a negative common ratio, the terms will alternate in sign, starting from the sign of the first term.

Using the formula CI = P[(1 + r)^n - 1], we can set up the equation 400 = 1600[(1 + r)^2 - 1]. Solving gives r = 12.5%.

Solving the equations x + y = 10 and x - y = 2 simultaneously gives x = 6 and y = 4.

Setting y = 0 in the equation -3x + 6 = 0 gives x = 2.

The slope m is calculated as (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 4/2 = 2.

Profit = Selling Price - Cost Price = 600 - 500 = 100. Profit Percentage = (Profit/Cost Price) * 100 = (100/500) * 100 = 20%.

Gain = Selling Price - Cost Price = 600 - 500 = 100. Gain percentage = (Gain/Cost Price) * 100 = (100/500) * 100 = 20%.

The decimal number 10 is represented as 1010 in binary.

The decimal number 15 is represented as 1111 in binary.

The decimal number 255 converts to binary as 11111111.

If the derivative of a function is positive for all x, it indicates that the function is increasing throughout its domain.