Suppose that x is the probability that a randomly selected person is left handed. the value (1-x) is the probability that the person is not left handed. in a sample of 1000 people, the function v(x)=1000x(1-x) represents the variance of the number of left-handed people in a group of 1000. what is the maximum variance?

The maximum variance is 250.

Step-by-step explanation:

Consider the provided function.

Differentiate the above function as shown:

The double derivative of the provided function is:

To find maximum variance set first derivative equal to 0.

The double derivative of the function at is less than 0.

Therefore, is a point of maximum.

Thus the maximum variance is:

Hence, the maximum variance is 250.

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)