Question
leaky bucket contains 50 ml 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 point)
Responses
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.
Image with alt text: 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.
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.
Image with alt text: 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.
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.
Image with alt text: 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.
Responses
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.
Image with alt text: 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.
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.
Image with alt text: 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.
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.
Image with alt text: 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
To determine which graph accurately represents the scenario described, let's calculate the amount of water left in the leaky bucket over time.
1. **Initial amount of water**: 50 ml
2. **Rate of loss**: 15 ml every 4 minutes
To find the rate of loss per minute, we can calculate:
- Loss rate = 15 ml / 4 min = 3.75 ml per minute.
Now, we will calculate how much water will be in the bucket at different time intervals:
- **At 0 minutes**: 50 ml
- **At 4 minutes**: 50 ml - 15 ml = 35 ml
- **At 8 minutes**: 35 ml - 15 ml = 20 ml
- **At 12 minutes**: 20 ml - 15 ml = 5 ml
- **At 16 minutes**: 5 ml - (15 ml if possible) = 0 ml (assuming it can't go negative, it remains at 0 ml).
Now we create a table of values:
| Time (minutes) | Water (ml) |
|----------------|-------------|
| 0 | 50 |
| 4 | 35 |
| 8 | 20 |
| 12 | 5 |
| 16 | 0 |
Now, let's evaluate the graphs based on these points:
- The first graph plots points (0, 50), (20, 35), and (40, 20), which doesn't match the calculated values as it has a point at 20 ml when it should be at about 15 ml.
- The second graph plots points starting from (0, 0), which is incorrect because we start with 50 ml.
- The third graph plots points (0, 50), (4, 35), and (8, 20), which precisely matches the calculated values.
Based on these observations, the third graph is the correct representation of the water level in the leaky bucket over time.
1. **Initial amount of water**: 50 ml
2. **Rate of loss**: 15 ml every 4 minutes
To find the rate of loss per minute, we can calculate:
- Loss rate = 15 ml / 4 min = 3.75 ml per minute.
Now, we will calculate how much water will be in the bucket at different time intervals:
- **At 0 minutes**: 50 ml
- **At 4 minutes**: 50 ml - 15 ml = 35 ml
- **At 8 minutes**: 35 ml - 15 ml = 20 ml
- **At 12 minutes**: 20 ml - 15 ml = 5 ml
- **At 16 minutes**: 5 ml - (15 ml if possible) = 0 ml (assuming it can't go negative, it remains at 0 ml).
Now we create a table of values:
| Time (minutes) | Water (ml) |
|----------------|-------------|
| 0 | 50 |
| 4 | 35 |
| 8 | 20 |
| 12 | 5 |
| 16 | 0 |
Now, let's evaluate the graphs based on these points:
- The first graph plots points (0, 50), (20, 35), and (40, 20), which doesn't match the calculated values as it has a point at 20 ml when it should be at about 15 ml.
- The second graph plots points starting from (0, 0), which is incorrect because we start with 50 ml.
- The third graph plots points (0, 50), (4, 35), and (8, 20), which precisely matches the calculated values.
Based on these observations, the third graph is the correct representation of the water level in the leaky bucket over time.