Question

state & sat practice aligned items: the cost of airing a commercial on television is modeled by the function c(n)=110n + 900, where n is the number of times the commercial is aired. based on this model, which statement is true? (1) the commercial costs $0 to produce and $110 per - airing up to $1000. (2) the commercial costs $110 to produce and $900 each time it is aired. (3) the commercial costs $900 to produce and $110 each time it is aired. (4) the commercial costs $1010 to produce and can air an unlimited number of times. the owner of a small computer repair business has one employee, who is paid an hourly rate of $22. the owner estimates his weekly profit using the function p(x)=8600 - 22x. in this function, x represents the number of 1 computers repaired per week 2 hours worked per week 3 customers served per week 4 days worked per week in air, the speed of sound s, in meters per second, is a linear function of the air temperature t, in degrees celsius, and is given by s(t)=0.6t + 331.4. which of the following statements is the best interpretation of the number 331.4 in this context? a. the speed of sound in meters per second at 0°c b. the speed of sound in meters per second at 1°c

Explanation:

First Problem

Step1: Analyze cost - function structure

The cost function for airing a commercial is $C(n)=110n + 900$, which is in the form of a linear function $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Here, the fixed cost (cost of production) is the y - intercept and the variable cost (cost per airing) is the slope.

Step2: Identify fixed and variable costs

The fixed cost of producing the commercial is $900$ (the value of $b$) and the variable cost per airing is $110$ (the value of $m$).

Step1: Understand the profit - function components

The profit function is $P(x)=8600−22x$. The employee is paid an hourly rate of $22$. In a profit - cost - revenue relationship, if we assume revenue is fixed (represented by the constant term $8600$) and cost is variable, and the cost is related to the employee's pay. Since the employee is paid $22$ per hour, $x$ must represent the number of hours worked per week as the cost component in the profit function is $22x$.

Step1: Recall the form of a linear function

The speed of sound in air is given by the linear function $S(T)=0.6T + 331.4$, which is in the form $y=mx + b$. In the context of a linear relationship between speed of sound $S$ and temperature $T$, when $T = 0$ (substitute $T = 0$ into the function), we get $S(0)=0.6\times0+331.4=331.4$.

Answer:

(3) The commercial costs $900$ to produce and $110$ each time it is aired.

Second Problem