To solve this problem, let's break it down step-by-step.
First, we need to determine the cost per pound for ordering 20.75 pounds of almonds based on the given pricing structure:
1. Identify the appropriate price bracket:
- From the chart:
- For up to 10 pounds, the cost per pound is [tex]$20.
- For more than 10, and up to 20 pounds, the cost per pound is $[/tex]15.
- For more than 20, and up to 30 pounds, the cost per pound is [tex]$10.
- For more than 30 pounds, the cost per pound is $[/tex]5.
Since 20.75 pounds falls into the "more than 20, and up to 30" category, the cost per pound will be [tex]$10.
2. Calculate the total cost:
- Multiply the number of pounds by the cost per pound to get the total cost:
\[
\text{Total cost} = \text{Weight} \times \text{Cost per pound} = 20.75 \, \text{pounds} \times 10 \, \text{dollars per pound} = 207.5 \, \text{dollars}
\]
3. Describe the step function for the graph:
- The step function represents the cost per pound for varying quantities of almonds.
- For the interval "more than 20, and up to 30 pounds":
- At \(x = 20\), the price changes from the previous interval, so it will be an open circle.
- At \(x = 30\), the interval ends, so it will be a closed circle.
- The y-value (cost per pound) for this interval is 10 dollars.
So, the graph will have a horizontal segment at y = 10 with an open circle at (20, 10) indicating the transition to this segment, and a closed circle at (30, 10) indicating the continuation of the segment up to 30 pounds.
Putting it all together, based on the steps outlined, the correct answer is:
```
a horizontal segment with an open circle at (20,10) and a closed circle at (30,10) ; \$[/tex] 207.50
```
