Question

sung-hi is filling a sandbox with sand at the rate shown in the table below. which statement must be true regarding the linear function that represents this situation?

\

$$\begin{tabular}{|l|c|c|c|c|c|} \\hline \\multicolumn{6}{|c|}{amount of sand in the sandbox} \\\\ \\hline number of minutes since sung-hi started & 0 & 1 & 2 & 3 & 4 \\\\ \\hline amount of sand in the sandbox (pounds) & 200 & 220 & 240 & 260 & 280 \\\\ \\hline \\end{tabular}$$

• the initial value must be 0 pounds.
• the initial value must be 20 pounds.
• the rate of change must be 0 pounds per minute.
• the rate of change must be 20 pounds per minute.

Explanation:

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"concepts_used": [
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"new_concepts": [
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"Rate of Change"
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"Rate of Change"
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<reasoning>

Determine the initial value

\[
\text{Initial Value} = y(0) = 200\text{ pounds}
\]

Calculate the rate of change

\[
\text{Rate of Change} = \frac{220 - 200}{1 - 0} = 20\text{ pounds per minute}
\]

Evaluate the given statements

\[

$$\begin{aligned} &\text{Initial value is } 200 \implies \text{First and second options are false.} \\ &\text{Rate of change is } 20 \implies \text{Third option is false, fourth option is true.} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>The initial value must be 0 pounds.</mcq-option>
<mcq-option>The initial value must be 20 pounds.</mcq-option>
<mcq-option>The rate of change must be 0 pounds per minute.</mcq-option>
<mcq-correct>The rate of change must be 20 pounds per minute.</mcq-correct>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Equations"
]
}
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Answer:

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"step_cot",
"multiple_choice_formatter",
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"Rate of Change"
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"Initial Value",
"Rate of Change"
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</pre_analysis>

<reasoning>

Determine the initial value

\[
\text{Initial Value} = y(0) = 200\text{ pounds}
\]

Calculate the rate of change

\[
\text{Rate of Change} = \frac{220 - 200}{1 - 0} = 20\text{ pounds per minute}
\]

Evaluate the given statements

\[

$$\begin{aligned} &\text{Initial value is } 200 \implies \text{First and second options are false.} \\ &\text{Rate of change is } 20 \implies \text{Third option is false, fourth option is true.} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>The initial value must be 0 pounds.</mcq-option>
<mcq-option>The initial value must be 20 pounds.</mcq-option>
<mcq-option>The rate of change must be 0 pounds per minute.</mcq-option>
<mcq-correct>The rate of change must be 20 pounds per minute.</mcq-correct>
</answer>

<post_analysis>
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"subject": "Mathematics",
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"Mathematics",
"Algebra",
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