Question
a leaky bucket contains 50ml of water and is losing water at a rate of 15 ml of water every 4 minutes. select the graph that shows how much water will be in the bucket over time.
1. A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 40 in increments of 10 and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Three unlabeled points are plotted as follows: left parenthesis 0 comma 50 right parenthesis, left parenthesis 20 comma 35 right parenthesis, and left parenthesis 40 comma 20 right parenthesis. A solid arrow passes through these points.
2. A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Four unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 2 comma 20 right parenthesis, left parenthesis 4 comma 30 right parenthesis, and left parenthesis 6 comma 40 right parenthesis. A solid arrow passes through these points.
3. A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 50 in increments of 10 and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Four unlabeled points are plotted as follows: left parenthesis 0 comma 0 right parenthesis, left parenthesis 10 comma 10 right parenthesis, left parenthesis 20 comma 20 right parenthesis, and left parenthesis 30 comma 30 right parenthesis. A solid arrow passes through these points.
4. A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Three unlabeled points are plotted as follows: left parenthesis 0 comma 50 right parenthesis, left parenthesis 4 comma 35 right parenthesis, and left parenthesis 8 comma 20 right parenthesis. A solid arrow passes through these points.
1. A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 40 in increments of 10 and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Three unlabeled points are plotted as follows: left parenthesis 0 comma 50 right parenthesis, left parenthesis 20 comma 35 right parenthesis, and left parenthesis 40 comma 20 right parenthesis. A solid arrow passes through these points.
2. A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Four unlabeled points are plotted as follows: left parenthesis 0 comma 10 right parenthesis, left parenthesis 2 comma 20 right parenthesis, left parenthesis 4 comma 30 right parenthesis, and left parenthesis 6 comma 40 right parenthesis. A solid arrow passes through these points.
3. A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 50 in increments of 10 and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Four unlabeled points are plotted as follows: left parenthesis 0 comma 0 right parenthesis, left parenthesis 10 comma 10 right parenthesis, left parenthesis 20 comma 20 right parenthesis, and left parenthesis 30 comma 30 right parenthesis. A solid arrow passes through these points.
4. A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Three unlabeled points are plotted as follows: left parenthesis 0 comma 50 right parenthesis, left parenthesis 4 comma 35 right parenthesis, and left parenthesis 8 comma 20 right parenthesis. A solid arrow passes through these points.
Answers
GPT-4o mini
Given the problem, we start with a leaky bucket containing 50 ml of water and losing water at a rate of 15 ml every 4 minutes.
First, we can determine the rate of loss per minute:
- Rate of loss: \( \frac{15 \, \text{ml}}{4 \, \text{minutes}} = 3.75 \, \text{ml/min} \)
To find out how much water is left in the bucket over time, we can create a function:
- Water remaining after \( t \) minutes: \( W(t) = 50 - 3.75t \)
Next, we'll calculate the amount of water in the bucket at specific intervals:
- At \( t = 0 \): \( W(0) = 50 - 3.75 \cdot 0 = 50 \, \text{ml} \)
- At \( t = 4 \): \( W(4) = 50 - 3.75 \cdot 4 = 50 - 15 = 35 \, \text{ml} \)
- At \( t = 8 \): \( W(8) = 50 - 3.75 \cdot 8 = 50 - 30 = 20 \, \text{ml} \)
- At \( t = 12 \): \( W(12) = 50 - 3.75 \cdot 12 = 50 - 45 = 5 \, \text{ml} \)
Now, we can check which graph matches our calculated points.
- From our calculations, we determined the points at key intervals:
- \( (0, 50) \)
- \( (4, 35) \)
- \( (8, 20) \)
- and we can assume a steady decrease to \( (12, 5) \), but that specific point is not plotted in any option.
Looking at the options provided:
1. The graph has points \( (0, 50) \), \( (20, 35) \), and \( (40, 20) \) which is inconsistent with our calculations.
2. The second graph matches none of our points.
3. The third graph shows \( (0, 0) \), which is incorrect.
4. The fourth graph matches our calculated points \( (0, 50) \), \( (4, 35) \), and \( (8, 20) \) correctly.
Thus, the correct graph that shows how much water will be in the bucket over time is:
**4. A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Three unlabeled points are plotted as follows: (0, 50), (4, 35), and (8, 20). A solid arrow passes through these points.**
First, we can determine the rate of loss per minute:
- Rate of loss: \( \frac{15 \, \text{ml}}{4 \, \text{minutes}} = 3.75 \, \text{ml/min} \)
To find out how much water is left in the bucket over time, we can create a function:
- Water remaining after \( t \) minutes: \( W(t) = 50 - 3.75t \)
Next, we'll calculate the amount of water in the bucket at specific intervals:
- At \( t = 0 \): \( W(0) = 50 - 3.75 \cdot 0 = 50 \, \text{ml} \)
- At \( t = 4 \): \( W(4) = 50 - 3.75 \cdot 4 = 50 - 15 = 35 \, \text{ml} \)
- At \( t = 8 \): \( W(8) = 50 - 3.75 \cdot 8 = 50 - 30 = 20 \, \text{ml} \)
- At \( t = 12 \): \( W(12) = 50 - 3.75 \cdot 12 = 50 - 45 = 5 \, \text{ml} \)
Now, we can check which graph matches our calculated points.
- From our calculations, we determined the points at key intervals:
- \( (0, 50) \)
- \( (4, 35) \)
- \( (8, 20) \)
- and we can assume a steady decrease to \( (12, 5) \), but that specific point is not plotted in any option.
Looking at the options provided:
1. The graph has points \( (0, 50) \), \( (20, 35) \), and \( (40, 20) \) which is inconsistent with our calculations.
2. The second graph matches none of our points.
3. The third graph shows \( (0, 0) \), which is incorrect.
4. The fourth graph matches our calculated points \( (0, 50) \), \( (4, 35) \), and \( (8, 20) \) correctly.
Thus, the correct graph that shows how much water will be in the bucket over time is:
**4. A coordinate graph shows the x-axis labeled as minutes ranging from 0 to 10 in 1 unit increments and the y-axis labeled as milliliters of water ranging from 0 to 50 in increments of 10. Three unlabeled points are plotted as follows: (0, 50), (4, 35), and (8, 20). A solid arrow passes through these points.**