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2 months ago

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The table below shows the linear relationship between the number of people at a picnic and the total cost of the picnic. Which s

tatements about the function described by the table are true? Check all that apply. The independent variable is the number of people. The initial value (initial fee) for the picnic is $40. The rate of change is $8.67 per person. As the number of people increases, the total cost of the picnic increases. If 4 people attended the picnic, the total cost would be $46.

2 answers:

Zina [12.3K]2 months ago

7 0

The count of people serves as the independent variable. The picnic's starting cost (initial fee) is $40. When more people attend, the picnic's overall expense rises.

Svet_ta [12.7K]2 months ago

3 0

Answer:

The accurate selections include:

The independent variable represents the number of people.
The picnic begins with a base cost of $40.
The total expense increases as the number of attendees goes up.

Detailed explanation:

The provided table displays a linear connection between the attendee count and the picnic's total expense as follows:

Number of people Total Cost ($)

6 52

9 58

12 64

15 70

The total cost depends directly on the number of people present.

This means the number of people is the independent variable, while total cost is dependent.

Since the relationship is linear, we can derive a function describing cost by using any two points.

Let f(n) represent cost for n attendees.

Using points (6,52) and (9,58),

we formulate:

$f(n)-52=\dfrac{58-52}{9-6}\times (n-6)\\\\f(n)-52=\dfrac{6}{3}\times (n-6)\\\\f(n)-52=2(n-6)\\\\f(n)-52=2n-12\\\\f(n)=2n-12+52\\\\f(n)=2n+40$

The initial fee equals the cost when no one attends, so at n=0:

f(0)=40

Thus, the starting cost is $40.

The slope, or rate of change, is $2 per person based on the function.

(Because f(n) = 2n + 40)

It is clear from the data that total cost rises alongside number of people.
If 4 people attend (n=4),

Calculate cost:

f(4) = 2×4 + 40 = 8 + 40 = 48

Therefore, total expenses for 4 attendees amount to $48.

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