A technical analyst is modeling a system's output by multiplying two input functions: $f(x) = 3x - 2$ and $g(x) = 5x + 1$. To compute $(f \cdot g)(x)$, the analyst uses the FOIL method to expand the expression $(3x - 2)(5x + 1)$. Match each specific step of the FOIL process with the correct mathematical term it produces in the expansion.

A production manager is modeling total revenue by finding the product of two functions: $f(x) = 3x - 2$ and $g(x) = 5x + 1$. According to the definition of function multiplication, which of the following is the correctly simplified expression for $(f \cdot g)(x)$?

A project manager is estimating total labor costs by multiplying the number of active work crews, $f(x) = 3x - 2$, by the average daily rate per crew, $g(x) = 5x + 1$. Arrange the following steps in the correct order to recall the derivation of the total cost function $(f \cdot g)(x)$.

A corporate data analyst is combining two performance models, $f(x) = 3x - 2$ and $g(x) = 5x + 1$, to create a master output function $(f \cdot g)(x)$. According to the definition of function multiplication, the simplified polynomial for this output function is ${}15x^2 - 7x - 2$. Is this statement true or false?

Recalling the Multiplication of Two Linear Functions

Recalling the Steps of Function Multiplication

An office operations manager uses two linear models to estimate monthly paper supplies: the number of active administrative departments is modeled by $f(x) = 3x - 2$, and the average boxes of paper used per department is modeled by $g(x) = 5x + 1$. To construct the total supply function $(f \cdot g)(x)$, the manager multiplies the two functions: $(f \cdot g)(x) = (3x - 2)(5x + 1)$. After expanding this product to ${}15x^2 + 3x - 10x - 2$ and combining the like terms, the coefficient of the linear $x$ term in the final simplified polynomial is ____.