Let's analyze the information given in the table to determine the truth of each statement.
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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.
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From 0 to 1 hour: \( \text{Change} = 4.25 - 3 = 1.25 \text{ miles} \) \( \text{Time} = 1 - 0 = 1 \text{ hour} \) Rate = \( \frac{1.25 \text{ miles}}{1 \text{ hour}} = 1.25 \text{ miles/hour} \)
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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.
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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:
- False
- True
- False
17 answers