Consider the linear regression model y = -1.5x +5.6+e, where e is a normal random variable with mean 0 and variance 0² = 4. Determine the mean and standard deviation of when x=2 and x = 4.5

Solve the following mathematical problems:

A place of stone fell from a balloon when it was flying in the upward direction with a velocity 20 m/sec. What will be the height of the balloon when the stone hit the ground in 10 seconds?

Solve the following mathematical problems:

Find the maximum value of z=6x+2y, subject to the conditions $x\ge 0, y\ge 0, x+y=5, x\le 2, y\le 4.$

Solve the following mathematical problems:

The sum of the digits of a two-digit number is subtracted from the number. How two-digit numbers can be formed so that the digit in the unit place of the resulting number many such 6?

Solve the following mathematical problems:

How many ways are there to divide 50 people into 3 groups so that each group contains members equal to a prime number?

Solve the following mathematical problems:

A semi circular sheet of metal of diameter 28 cm is bent into an open conical cup. Find the depth and capacity of cup.