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.

5x + 5

step-by-step explanation:

you should always add the diagrams and graphs we cannot see. this particular question is kind of borderline because we can make a graph for you.

(f + g)x = -x^2 +3x + 5 + x^2 + 2x

(f + g)x = 5x + 5

the graph of z = 5x + 5 is shown below. always use desmos when in doubt.