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Given the data below, determine which function has the greater slope and what it indicates.

Broccoli

\begin{tabular}{|l|c|c|c|c|}
\hline
Amount (lbs) & 2.5 & 3 & 3.25 & 4.15 \\
\hline
Cost (\[tex]$) & 3.00 & 3.60 & 3.90 & 4.98 \\
\hline
\end{tabular}

\ \textless \ strong\ \textgreater \ Cauliflower\ \textless \ /strong\ \textgreater \

\begin{tabular}{|l|c|c|c|c|}
\hline
Amount (lbs) & 2.75 & 3.2 & 3.85 & 4.5 \\
\hline
Cost (\$[/tex]) & 2.75 & 3.20 & 3.85 & 4.50 \\
\hline
\end{tabular}

Which function has the greater slope and what does it indicate?

A. The broccoli function has the greater slope, which shows that the cost per pound of broccoli is less than the cost per pound of cauliflower.

B. The broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower.

C. The cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is less than the cost per pound of broccoli.

D. The cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is greater than the cost per pound of broccoli.

Sagot :

GinnyAnswer
Let's analyze the given data and determine the correct interpretation.

### Step-by-Step Solution:

1. We have data for both broccoli and cauliflower in terms of their amounts (in pounds) and costs (in dollars).

2. To understand which function has the greater slope and what it indicates, we need to calculate the slope for the cost per pound for each vegetable. The slope here represents the rate of change of cost with respect to the amount.

3. For Broccoli:
- Data points for amount: [2.5, 3, 3.25, 4.15]
- Data points for cost: [3.00, 3.60, 3.90, 4.98]

The slope for the broccoli data is approximately 1.2.

4. For Cauliflower:
- Data points for amount: [2.75, 3.2, 3.85, 4.5]
- Data points for cost: [2.75, 3.20, 3.85, 4.50]

The slope for the cauliflower data is approximately 1.0.

5. Comparing the slopes:
- The slope for broccoli is 1.2.
- The slope for cauliflower is 1.0.

6. Based on the slopes calculated:
- The slope of the broccoli function ([tex]\(1.2\)[/tex]) is greater than the slope of the cauliflower function ([tex]\(1.0\)[/tex]).
- Greater slope indicates a higher cost per pound. Therefore, the cost per pound of broccoli is greater than the cost per pound of cauliflower.

Therefore, the correct statement is:

The broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower.
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