To evaluate the statements based on Amanda's distance from school as given in the table, let’s first look at the provided data points:
- At \( t = 0 \) hours, distance = 3 miles
- At \( t = 1 \) hour, distance = 4.25 miles
- At \( t = 3 \) hours, distance = 6.75 miles
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Amanda's initial distance from her school is 1.25 miles.
- False. The initial distance from school at \( t = 0 \) hours is 3 miles.
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Amanda's distance increases by 1.25 miles each hour.
- To determine the increase in distance, we can compare the distance at \( t = 0 \) and \( t = 1 \):
- From 3 miles (at \( t = 0 \)) to 4.25 miles (at \( t = 1 \)): Increase = \( 4.25 - 3 = 1.25 \) miles.
- From 4.25 miles (at \( t = 1 \)) to 6.75 miles (at \( t = 3 \)): Increase = \( 6.75 - 4.25 = 2.5 \) miles (for 2 hours).
- This shows that the increase is not consistent each hour (1.25 miles for the first hour, and an average of 1.25 miles over the next 2 hours). However, the relationship is linear, but not with a constant 1.25 mile/hour increase.
- False. The increase in distance is not consistent at 1.25 miles/hour over every hour.
- To determine the increase in distance, we can compare the distance at \( t = 0 \) and \( t = 1 \):
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Amanda's distance from school after 4 hours is 9.75 miles.
- To find the distance after 4 hours, we need to determine the linear equation based on the data points we have:
- Using points \( (0, 3) \) and \( (1, 4.25) \):
- The slope (m) = \( \frac{4.25 - 3}{1 - 0} = 1.25 \).
- The equation of the line (distance \( d \) as a function of time \( t \)) can be written as: \[ d(t) = 1.25t + 3 \]
- Plugging in \( t = 4 \): \[ d(4) = 1.25(4) + 3 = 5 + 3 = 8 \] miles.
- False. The distance after 4 hours is 8 miles, not 9.75 miles.
In summary:
- Amanda's initial distance from her school is 1.25 miles: False
- Amanda's distance increases by 1.25 miles each hour: False
- Amanda's distance from school after 4 hours is 9.75 miles: False
17 answers