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The relationship between Amanda’s distance from school and time since she left school is linear, as shown in the table below. T...Asked by dee
The relationship between Amanda’s distance from school and time since she left school is linear, as shown in the table below.The table shows time in hours as 0, 1, 3, and distance in miles as 3, 4.25, 6.75Based on the table, determine whether each statement is true or false.TrueFalseAmanda's initial distance from her school is 1.25 miles.Amanda's distance increases by 1.25 miles each hour.Amanda's distance from school after 4 hours is 9.75 miles.
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GPT-4o mini
Let's analyze the information given in the table to determine the truth of each statement.
1. The relationship is linear, and the data points provided are:
- At time 0 hours, distance is 3 miles.
- At time 1 hour, distance is 4.25 miles.
- At time 3 hours, distance is 6.75 miles.
We can determine the slope (rate of distance change) by calculating the difference in distance over the difference in time for known points.
- From 0 to 1 hour:
\( \text{Change} = 4.25 - 3 = 1.25 \text{ miles} \)
\( \text{Time} = 1 - 0 = 1 \text{ hour} \)
Rate = \( \frac{1.25 \text{ miles}}{1 \text{ hour}} = 1.25 \text{ miles/hour} \)
- From 1 to 3 hours:
\( \text{Change} = 6.75 - 4.25 = 2.5 \text{ miles} \)
\( \text{Time} = 3 - 1 = 2 \text{ hours} \)
Rate = \( \frac{2.5 \text{ miles}}{2 \text{ hours}} = 1.25 \text{ miles/hour} \)
Thus, Amanda's distance increases consistently by 1.25 miles each hour.
2. Let's evaluate each statement:
**Statement 1: Amanda's initial distance from her school is 1.25 miles.**
- **False**: According to the table, at time 0 hours, Amanda is 3 miles from school.
**Statement 2: Amanda's distance increases by 1.25 miles each hour.**
- **True**: As calculated, her distance does indeed increase by 1.25 miles for each hour.
**Statement 3: Amanda's distance from school after 4 hours is 9.75 miles.**
- To calculate Amanda's distance after 4 hours:
- Start distance: 3 miles
- Increase for 4 hours: \( 4 \times 1.25 = 5 \) miles
- Total distance after 4 hours: \( 3 + 5 = 8 \text{ miles} \)
- **False**: After 4 hours, Amanda's distance from school would be 8 miles, not 9.75 miles.
In summary:
1. False
2. True
3. False
1. The relationship is linear, and the data points provided are:
- At time 0 hours, distance is 3 miles.
- At time 1 hour, distance is 4.25 miles.
- At time 3 hours, distance is 6.75 miles.
We can determine the slope (rate of distance change) by calculating the difference in distance over the difference in time for known points.
- From 0 to 1 hour:
\( \text{Change} = 4.25 - 3 = 1.25 \text{ miles} \)
\( \text{Time} = 1 - 0 = 1 \text{ hour} \)
Rate = \( \frac{1.25 \text{ miles}}{1 \text{ hour}} = 1.25 \text{ miles/hour} \)
- From 1 to 3 hours:
\( \text{Change} = 6.75 - 4.25 = 2.5 \text{ miles} \)
\( \text{Time} = 3 - 1 = 2 \text{ hours} \)
Rate = \( \frac{2.5 \text{ miles}}{2 \text{ hours}} = 1.25 \text{ miles/hour} \)
Thus, Amanda's distance increases consistently by 1.25 miles each hour.
2. Let's evaluate each statement:
**Statement 1: Amanda's initial distance from her school is 1.25 miles.**
- **False**: According to the table, at time 0 hours, Amanda is 3 miles from school.
**Statement 2: Amanda's distance increases by 1.25 miles each hour.**
- **True**: As calculated, her distance does indeed increase by 1.25 miles for each hour.
**Statement 3: Amanda's distance from school after 4 hours is 9.75 miles.**
- To calculate Amanda's distance after 4 hours:
- Start distance: 3 miles
- Increase for 4 hours: \( 4 \times 1.25 = 5 \) miles
- Total distance after 4 hours: \( 3 + 5 = 8 \text{ miles} \)
- **False**: After 4 hours, Amanda's distance from school would be 8 miles, not 9.75 miles.
In summary:
1. False
2. True
3. False
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