A restaurant sells three sizes of shakes. The small, medium and large sizes each cost $2.00, $3.00, and $3.50 respectively. Let X represent the restaurant's income on a randomly selected shake purchase. Based on previous data, here's the probability distribution of X along with summary statistics. Express the cost of making x small boxes, y medium boxes, and z large boxes as a function of three variables: C = f(x, y, z)

In math, function means that the values of the dependent variable (C) are determined by independent variables.

The cost of making different sized boxes as a function can be expressed as: C = 2x + 3y + 3.5z

This can be shown by:

This can be shown in the function C = f(x, y, z) as:

C = 2x + 3y + 3.5z

In this question, the mathematical expression depicts the value of the variable C and is determined by the independent variables x, y, and z.

Therefore, the cost can be shown as C = 2x + 3y + 3.5z

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C = 2x + 3y + 3.5z

Explanation:

a) Data and Calculations:

Let x = small boxes

y = medium boxes

z = large boxes

Cost of x = $2.00

Cost of y = $3.00

Cost of z = $3.50

The cost of making x small boxes, y medium boxes, and z large boxes as a function of three variables: C = f(x, y, z)

C = 2x + 3y + 3.5z

b) In this function, the mathematical relationship expresses the value of a single dependent variable, C, as determined by the values of the independent variables x, y, and z, which are the number of the small, medium, and large sizes of shakes that the restaurant sells.  Mathematically, a function means that the dependent variable is determined by the independent variable(s).