Question
When a snowstorm hit the town of Clarkesville, there already were 4 inches of snow on the ground. The storm lasted for 2 hours, and by the time it was over, there were at least 6 inches of snow on the ground. Which number line shows the solution set for the mean number of inches of snow per hour that could have fallen during the storm?
Answers
Answered by
GPT-4o mini
To determine the mean number of inches of snow per hour that fell during the storm, we first need to analyze the total snow accumulation.
1. **Initial Snow Accumulation:** 4 inches
2. **Final Snow Accumulation after the Storm:** At least 6 inches
3. **Snow Accumulation Due to the Storm:** The amount of snow that fell during the storm can be calculated by subtracting the initial snow from the final amount. Since the final amount is at least 6 inches, we can write this as:
\[
\text{Snow from storm} \geq 6 \text{ inches} - 4 \text{ inches} = 2 \text{ inches}
\]
4. **Duration of the Storm:** 2 hours.
Now we can find the mean number of inches of snow that fell per hour:
- Minimum snow during the storm: 2 inches
- Mean per hour = Total snow from the storm / Duration of the storm
Using the minimum amount:
\[
\text{Mean} \geq \frac{2 \text{ inches}}{2 \text{ hours}} = 1 \text{ inch per hour}
\]
However, since the storm could have dropped more than 2 inches, we express that the total snow from the storm can be for any amount greater than 2 inches. Let's denote the total snow from the storm as \( x \) (where \( x \geq 2 \)). Thus, we calculate:
\[
\text{Mean} = \frac{x}{2}
\]
As \( x \) can go up to \( 6 - 4 = 6 - 4 = 2 \text{ inches} \) maximum, we also know that \( x \) can be less than or equal to the total snow amount (6 inches):
So \( \text{Total} ≤ 6 - 4 = x \) then can be different possibilities from 2 to higher amounts so mean can go to at least 3 / 2 =1.5 inches/hour maximum (if x was precisely six).
Thus we can denote the mean inch of snow accumulation per hour must be at least 1 inch and can theoretically go above that 3 inch/hour max.
So the solution set for the mean amount of snow per hour can be shown as:
\[
\text{Mean} \in [1, 3]
\]
Therefore, the number line that represents this solution set would have a closed interval starting at 1 and ending at 3 with shading or indication of these points.
1. **Initial Snow Accumulation:** 4 inches
2. **Final Snow Accumulation after the Storm:** At least 6 inches
3. **Snow Accumulation Due to the Storm:** The amount of snow that fell during the storm can be calculated by subtracting the initial snow from the final amount. Since the final amount is at least 6 inches, we can write this as:
\[
\text{Snow from storm} \geq 6 \text{ inches} - 4 \text{ inches} = 2 \text{ inches}
\]
4. **Duration of the Storm:** 2 hours.
Now we can find the mean number of inches of snow that fell per hour:
- Minimum snow during the storm: 2 inches
- Mean per hour = Total snow from the storm / Duration of the storm
Using the minimum amount:
\[
\text{Mean} \geq \frac{2 \text{ inches}}{2 \text{ hours}} = 1 \text{ inch per hour}
\]
However, since the storm could have dropped more than 2 inches, we express that the total snow from the storm can be for any amount greater than 2 inches. Let's denote the total snow from the storm as \( x \) (where \( x \geq 2 \)). Thus, we calculate:
\[
\text{Mean} = \frac{x}{2}
\]
As \( x \) can go up to \( 6 - 4 = 6 - 4 = 2 \text{ inches} \) maximum, we also know that \( x \) can be less than or equal to the total snow amount (6 inches):
So \( \text{Total} ≤ 6 - 4 = x \) then can be different possibilities from 2 to higher amounts so mean can go to at least 3 / 2 =1.5 inches/hour maximum (if x was precisely six).
Thus we can denote the mean inch of snow accumulation per hour must be at least 1 inch and can theoretically go above that 3 inch/hour max.
So the solution set for the mean amount of snow per hour can be shown as:
\[
\text{Mean} \in [1, 3]
\]
Therefore, the number line that represents this solution set would have a closed interval starting at 1 and ending at 3 with shading or indication of these points.