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Sample Response/Explanation:

The point that represents what the local business will donate is [tex]\((10,5)\)[/tex]. After testing the point in both equations, you can see that Student [tex]\(B\)[/tex] wrote the correct equation: [tex]\(5 = \frac{1}{2}(10)\)[/tex].

Which did you include in your answer? Select all that apply.

A. Student [tex]\(B\)[/tex] is correct because the tickets sold represent the input [tex]\((x)\)[/tex] and the amount donated represents the output [tex]\((y)\)[/tex].
B. Student [tex]\(B\)[/tex] is correct because the donated amount is represented by [tex]\(5 = \frac{1}{2}(10)\)[/tex].
C. Student [tex]\(B\)[/tex] is correct because Student [tex]\(A\)[/tex]'s equation [tex]\(y = 2x\)[/tex] represents [tex]\(5 = 2(10)\)[/tex], which is incorrect.

Sagot :

GinnyAnswer
Let's break down the question step by step and address the potential answers.

We need to provide a detailed solution for a given question related to calculating parking fees based on certain conditions. Here's the step-by-step breakdown:

### Given Information

1. Initial Fee for the First Two Hours: [tex]$8 2. Hourly Fee After the First Two Hours: $[/tex]2 per hour
3. Total Hours Parked: 14 hours

### Calculation Steps

1. Step 1: Calculating the Fee for the First Two Hours
- The fee for the first two hours of parking is fixed at [tex]$8. 2. Step 2: Determining the Remaining Hours - The total parking time is 14 hours. - Since we have already calculated the fee for the first 2 hours, we need to find the remaining hours by subtracting 2 from the total hours. - Remaining Hours = Total Hours - First Two Hours = 14 - 2 = 12 hours. 3. Step 3: Calculating the Fee for the Remaining Hours - The fee for each hour after the first two hours is $[/tex]2.
- Remaining Hours Fee = Remaining Hours Hourly Fee After Two Hours = 12 [tex]$2 = $[/tex]24.

4. Step 4: Calculating the Total Parking Fee
- The total parking fee is the sum of the fee for the first two hours and the fee for the remaining hours.
- Total Parking Fee = First Two Hours Fee + Remaining Hours Fee
- Total Parking Fee = [tex]$8 + $[/tex]24 = [tex]$32. ### Summary of Results - First Two Hours Fee: $[/tex]8
- Remaining Hours: 12 hours
- Remaining Hours Fee: [tex]$24 - Total Parking Fee: $[/tex]32

By following these steps, we have comprehensively determined how the total parking fee of [tex]$32 is calculated. ### Evaluating the Sample Response - Student B is correct. - Reasoning: The response correctly identifies that as per the calculations, tickets sold represent the input \((x)\) and the donation amount \(y\) is correctly represented by the equation $[/tex]5 = \frac{1}{2}(10)[tex]$, which aligns with the output of the valid `B` explanation provided in the example above. ### Select All That Apply 1. Student B is correct because the tickets sold represent the input \((x)\) and the amount donated represents the output \((y)\). 2. Student B is correct because the donated amount is represented by $[/tex]5 = \frac{1}{2}(10)$.
3. Student B is correct because Student A's equation [tex]\(y = 2x\)[/tex] represents [tex]\(5 = 2(10)\)[/tex], which is incorrect.

In summary, all mentioned points are relevant to the correctness of Student B's explanation.
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