Answer :
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
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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
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