Suppose that you need to create a list of n values that have a specific known mean. some of the n values can be freely selected. how many of the n values can be freely assigned before the remaining values are determined

  n-1

Step-by-step explanation:

All but one of the values may be freely chosen. The last one must be chosen to bring the sum to the a value that is n times the mean.

a maximum of n-1 can be freely selected

Step-by-step explanation:

The fact that we already know the mean means that, if we have n values:

X = (x₁ + x₂ + + xₙ)/n

where X is known and n is known.

Now, suppose we can assign n freely therms: this is not the case, because if X is different than 0, we could assign the n values equal to zero and the equality would be false.

Now suppose we can assign n-1 values freely, then we would have the equation:

X = (x₁ + x₂ +)/n + xₙ/n

where the term (x₁ + x₂ + ..) is conformed with the random values and xₙ must be chosen in order to satisfy the equation. So we would have the equation:

(X -  (x₁ + x₂ +)/n)*n = n*X -  (x₁ + x₂ +) = xₙ  

The equation that can be solved, so a maximum of n-1 can be freely selected.

256π units²   (answer b)

step-by-step explanation:

the formula for the surface area of a sphere of radius r

is             a = 4πr²

and so, if r = 8 units, then the surface area is:

a = 4π(8 units)² = 256π units²   (answer b)

the answer is 0.071

good luck! : d