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A water pump moves 330 gallons of water in 22 minutes. What is the unit rate of gallons per minute?(1 point) gallons per minuteQuestion
a water pump moves 330 gallons of water in 22 minuets. What is the unit rate of gallons per minute?
___ gallons per minutes
___ gallons per minutes
Answers
Answer
a processing machine crushes 3 1/3 kilograms of dried fruits in 3/4 minute. determine the kilograms of fruit crushed in one minute. what processes will you use to solve this problem?
a. 3/4 ÷3 1/4
b. 3 1/4 - 3/4
c. 3 1/4 x 3/4
d. 3 1/4 ÷ 3/4
enter your solution as a mixed number
__ kilograms per minute
a. 3/4 ÷3 1/4
b. 3 1/4 - 3/4
c. 3 1/4 x 3/4
d. 3 1/4 ÷ 3/4
enter your solution as a mixed number
__ kilograms per minute
Answer
it takes 76 gallons of water to produce 4 ounces of oatmeal. complete the table
_______________________________________________
| Ounces of oatmeal | Gallons of water |
|________________________|______________________ |
| 2 | 38 |
|________________________|_____________________ |
| 4 | 76 |
|________________________|______________________ |
| 10 | __ |
|________________________|______________________ |
| __ | 304 |
|________________________|_____________________ |
_______________________________________________
| Ounces of oatmeal | Gallons of water |
|________________________|______________________ |
| 2 | 38 |
|________________________|_____________________ |
| 4 | 76 |
|________________________|______________________ |
| 10 | __ |
|________________________|______________________ |
| __ | 304 |
|________________________|_____________________ |
Answer
y________________________________ .
12 |_____|_____|_____|_____|_____|___C |
|_____|_____|_____|_____|_____|_____|
8 |_____|_____|_____|_____•B_____|_____|
|_____|_____|_____|_____|_____|_____|
4 |_____|_____•A_____|_____|_____|_____|
|_____|_____|_____|_____|_____|_____| x
0 12 24 36
12 |_____|_____|_____|_____|_____|___C |
|_____|_____|_____|_____|_____|_____|
8 |_____|_____|_____|_____•B_____|_____|
|_____|_____|_____|_____|_____|_____|
4 |_____|_____•A_____|_____|_____|_____|
|_____|_____|_____|_____|_____|_____| x
0 12 24 36
Answer
a is coordinated at (4,12) b is at (8,24) and c (12,36)
Answer
y________________________________ .
12 |_____|_____|_____|_____|_____|___C |
|_____|_____|_____|_____|_____|_____|
8 |_____|_____|____|____•B_____|____|
downloads |_____|_____|_____|_____|_____|_____|
of 4 |_____|____•A_____|_____|____|_____|
number |_____|_____|_____|_____|_____|_____| x
0 ..................12..................24...................36
number of web visits
the simplified form of the ratio of downloads to web visits is:
__to__
__:__
__ as a fraction
12 |_____|_____|_____|_____|_____|___C |
|_____|_____|_____|_____|_____|_____|
8 |_____|_____|____|____•B_____|____|
downloads |_____|_____|_____|_____|_____|_____|
of 4 |_____|____•A_____|_____|____|_____|
number |_____|_____|_____|_____|_____|_____| x
0 ..................12..................24...................36
number of web visits
the simplified form of the ratio of downloads to web visits is:
__to__
__:__
__ as a fraction
Answered by
GPT-4o mini
To find the unit rate of gallons per minute, divide the total gallons of water by the total minutes.
\[
\text{Unit rate} = \frac{\text{Total gallons}}{\text{Total minutes}} = \frac{330 \text{ gallons}}{22 \text{ minutes}} = 15 \text{ gallons per minute}.
\]
So, the unit rate is **15 gallons per minute**.
\[
\text{Unit rate} = \frac{\text{Total gallons}}{\text{Total minutes}} = \frac{330 \text{ gallons}}{22 \text{ minutes}} = 15 \text{ gallons per minute}.
\]
So, the unit rate is **15 gallons per minute**.
Answered by
GPT-4o mini
To determine the kilograms of fruit crushed in one minute, you will divide the total kilograms of fruit by the time in minutes.
### Given:
- Total weight of fruit = \( 3 \frac{1}{3} \) kilograms
- Time = \( \frac{3}{4} \) minutes
### Step 1: Convert the mixed number to an improper fraction
First, convert \( 3 \frac{1}{3} \) to an improper fraction:
\[
3 \frac{1}{3} = \frac{10}{3} \text{ kilograms}
\]
### Step 2: Set up the division
Now we need to find out how many kilograms are crushed in one minute, which is given by:
\[
\text{Kilograms per minute} = \frac{\text{Total kilograms}}{\text{Time in minutes}} = \frac{\frac{10}{3}}{\frac{3}{4}}
\]
### Step 3: Dividing fractions
To divide fractions, multiply by the reciprocal of the second fraction:
\[
\frac{\frac{10}{3}}{\frac{3}{4}} = \frac{10}{3} \times \frac{4}{3} = \frac{10 \times 4}{3 \times 3} = \frac{40}{9}
\]
### Step 4: Convert the improper fraction back to a mixed number
To convert \( \frac{40}{9} \) to a mixed number:
1. Divide 40 by 9, which goes 4 times (because \( 9 \times 4 = 36 \)).
2. The remainder is \( 40 - 36 = 4 \).
So,
\[
\frac{40}{9} = 4 \frac{4}{9}
\]
### Conclusion
The answer in kilograms per minute is
\[
\boxed{4 \frac{4}{9}} \text{ kilograms per minute}
\]
### Process Used
The most appropriate process from your options is:
**d. \( 3 \frac{1}{4} \div \frac{3}{4} \)** (though remember we actually computed it as \( \frac{10}{3} \div \frac{3}{4} \)).
### Given:
- Total weight of fruit = \( 3 \frac{1}{3} \) kilograms
- Time = \( \frac{3}{4} \) minutes
### Step 1: Convert the mixed number to an improper fraction
First, convert \( 3 \frac{1}{3} \) to an improper fraction:
\[
3 \frac{1}{3} = \frac{10}{3} \text{ kilograms}
\]
### Step 2: Set up the division
Now we need to find out how many kilograms are crushed in one minute, which is given by:
\[
\text{Kilograms per minute} = \frac{\text{Total kilograms}}{\text{Time in minutes}} = \frac{\frac{10}{3}}{\frac{3}{4}}
\]
### Step 3: Dividing fractions
To divide fractions, multiply by the reciprocal of the second fraction:
\[
\frac{\frac{10}{3}}{\frac{3}{4}} = \frac{10}{3} \times \frac{4}{3} = \frac{10 \times 4}{3 \times 3} = \frac{40}{9}
\]
### Step 4: Convert the improper fraction back to a mixed number
To convert \( \frac{40}{9} \) to a mixed number:
1. Divide 40 by 9, which goes 4 times (because \( 9 \times 4 = 36 \)).
2. The remainder is \( 40 - 36 = 4 \).
So,
\[
\frac{40}{9} = 4 \frac{4}{9}
\]
### Conclusion
The answer in kilograms per minute is
\[
\boxed{4 \frac{4}{9}} \text{ kilograms per minute}
\]
### Process Used
The most appropriate process from your options is:
**d. \( 3 \frac{1}{4} \div \frac{3}{4} \)** (though remember we actually computed it as \( \frac{10}{3} \div \frac{3}{4} \)).
Answered by
GPT-4o mini
To complete the table with the given information (76 gallons of water for 4 ounces of oatmeal), we can first determine the relationship between ounces of oatmeal and gallons of water.
### Step 1: Find the unit rate
From the data, we know:
- 4 ounces of oatmeal requires 76 gallons of water.
To find the amount of water needed for one ounce of oatmeal, divide the gallons of water by the ounces of oatmeal:
\[
\text{Gallons per ounce} = \frac{76 \text{ gallons}}{4 \text{ ounces}} = 19 \text{ gallons per ounce}
\]
### Step 2: Fill in the table
#### For 10 ounces of oatmeal
Using the unit rate:
\[
\text{Gallons for 10 ounces} = 10 \text{ ounces} \times 19 \text{ gallons per ounce} = 190 \text{ gallons}
\]
#### For 304 gallons of water
Using the unit rate in the reverse direction:
\[
\text{Ounces for 304 gallons} = \frac{304 \text{ gallons}}{19 \text{ gallons per ounce}} = 16 \text{ ounces}
\]
### Final Completed Table
Here’s the completed table:
| Ounces of oatmeal | Gallons of water |
|--------------------|------------------|
| 2 | 38 |
| 4 | 76 |
| 10 | 190 |
| 16 | 304 |
So, the missing values are:
- **For 10 ounces:** 190 gallons
- **For 304 gallons:** 16 ounces
### Step 1: Find the unit rate
From the data, we know:
- 4 ounces of oatmeal requires 76 gallons of water.
To find the amount of water needed for one ounce of oatmeal, divide the gallons of water by the ounces of oatmeal:
\[
\text{Gallons per ounce} = \frac{76 \text{ gallons}}{4 \text{ ounces}} = 19 \text{ gallons per ounce}
\]
### Step 2: Fill in the table
#### For 10 ounces of oatmeal
Using the unit rate:
\[
\text{Gallons for 10 ounces} = 10 \text{ ounces} \times 19 \text{ gallons per ounce} = 190 \text{ gallons}
\]
#### For 304 gallons of water
Using the unit rate in the reverse direction:
\[
\text{Ounces for 304 gallons} = \frac{304 \text{ gallons}}{19 \text{ gallons per ounce}} = 16 \text{ ounces}
\]
### Final Completed Table
Here’s the completed table:
| Ounces of oatmeal | Gallons of water |
|--------------------|------------------|
| 2 | 38 |
| 4 | 76 |
| 10 | 190 |
| 16 | 304 |
So, the missing values are:
- **For 10 ounces:** 190 gallons
- **For 304 gallons:** 16 ounces
Answered by
GPT-4o mini
It appears that you are presenting a coordinate grid with certain points marked on it. Let's denote the points given:
- Point A is represented at coordinates \( (x_1, 4) \)
- Point B is represented at coordinates \( (x_2, 8) \)
- Point C is located at the top right end of the graph, likely at \( (12, y) \)
### Step 1: Identify Coordinates of A, B, and C
From the grid for Points A, B, and C:
- **Point A (marked at y = 4)**: It appears that Point A is not explicitly stated but is along the y-axis at \( y = 4 \). It's not clear from the grid where Point A is on the x-axis based on how you’ve described it.
- **Point B (marked at y = 8)**: Similarly to Point A, we would also need the x-coordinate of point B to define it completely.
- **Point C**: It is at \( y = 12\) but requires the x-axis coordinate as well.
### Step 2: Determine Specific Coordinates
In order to discuss the coordinates properly, we need to infer or define specific x-values for A, B, and C. Here's how you could theoretically extract their coordinates assuming it was formatted in a way that follows a standard grid:
- If Point A is halfway to the left on the grid, it could, for example, be at \( (6, 4) \).
- If Point B is somewhere near the middle, it might be at \( (6, 8) \).
- If Point C is at the upper right end of the graph, it could be at \( (12, 12) \).
### Conclusion
Assuming the points you provided can be indicated in more detail:
- Point A \((x_1, 4)\) where \(x_1\) is determined from the graph
- Point B \((x_2, 8)\) where \(x_2\) is determined from the graph
- Point C \((12, 12)\)
If you can specify the x-coordinates for Points A, B, and C or provide additional context, we can calculate slopes, distances, or any other necessary information related to these points on the Cartesian coordinate system!
- Point A is represented at coordinates \( (x_1, 4) \)
- Point B is represented at coordinates \( (x_2, 8) \)
- Point C is located at the top right end of the graph, likely at \( (12, y) \)
### Step 1: Identify Coordinates of A, B, and C
From the grid for Points A, B, and C:
- **Point A (marked at y = 4)**: It appears that Point A is not explicitly stated but is along the y-axis at \( y = 4 \). It's not clear from the grid where Point A is on the x-axis based on how you’ve described it.
- **Point B (marked at y = 8)**: Similarly to Point A, we would also need the x-coordinate of point B to define it completely.
- **Point C**: It is at \( y = 12\) but requires the x-axis coordinate as well.
### Step 2: Determine Specific Coordinates
In order to discuss the coordinates properly, we need to infer or define specific x-values for A, B, and C. Here's how you could theoretically extract their coordinates assuming it was formatted in a way that follows a standard grid:
- If Point A is halfway to the left on the grid, it could, for example, be at \( (6, 4) \).
- If Point B is somewhere near the middle, it might be at \( (6, 8) \).
- If Point C is at the upper right end of the graph, it could be at \( (12, 12) \).
### Conclusion
Assuming the points you provided can be indicated in more detail:
- Point A \((x_1, 4)\) where \(x_1\) is determined from the graph
- Point B \((x_2, 8)\) where \(x_2\) is determined from the graph
- Point C \((12, 12)\)
If you can specify the x-coordinates for Points A, B, and C or provide additional context, we can calculate slopes, distances, or any other necessary information related to these points on the Cartesian coordinate system!
Answered by
GPT-4o mini
Thank you for providing the coordinates for points A, B, and C.
- Point A: \( (4, 12) \)
- Point B: \( (8, 24) \)
- Point C: \( (12, 36) \)
### 1. **Finding the Slope Between Points A and B:**
To find the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\), you use the formula:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
For points A and B:
- \( (x_1, y_1) = (4, 12) \)
- \( (x_2, y_2) = (8, 24) \)
Calculating the slope:
\[
\text{slope}_{AB} = \frac{24 - 12}{8 - 4} = \frac{12}{4} = 3
\]
### 2. **Finding the Slope Between Points B and C:**
For points B and C:
- \( (x_1, y_1) = (8, 24) \)
- \( (x_2, y_2) = (12, 36) \)
Calculating the slope:
\[
\text{slope}_{BC} = \frac{36 - 24}{12 - 8} = \frac{12}{4} = 3
\]
### 3. **Finding the Equation of the Line:**
Since both slopes are equal, points A, B, and C are collinear. We can also derive the equation of the line formed by these points using the point-slope form of a linear equation:
\[
y - y_1 = m(x - x_1)
\]
You can use point A \((4, 12)\) for this purpose, with a slope \(m = 3\):
\[
y - 12 = 3(x - 4)
\]
Expanding this:
\[
y - 12 = 3x - 12
\]
Adding 12 to both sides leads to:
\[
y = 3x
\]
### 4. **Verification:**
- For Point A \((4, 12)\):
\[
y = 3(4) = 12 \quad \text{(Correct)}
\]
- For Point B \((8, 24)\):
\[
y = 3(8) = 24 \quad \text{(Correct)}
\]
- For Point C \((12, 36)\):
\[
y = 3(12) = 36 \quad \text{(Correct)}
\]
### Conclusion:
The coordinates of the points are \((4, 12)\), \((8, 24)\), and \((12, 36)\). The equation of the line passing through these points is:
\[
\boxed{y = 3x}
\]
You can apply this information in various contexts such as finding points on the line or verifying points if presented with new coordinates!
- Point A: \( (4, 12) \)
- Point B: \( (8, 24) \)
- Point C: \( (12, 36) \)
### 1. **Finding the Slope Between Points A and B:**
To find the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\), you use the formula:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
For points A and B:
- \( (x_1, y_1) = (4, 12) \)
- \( (x_2, y_2) = (8, 24) \)
Calculating the slope:
\[
\text{slope}_{AB} = \frac{24 - 12}{8 - 4} = \frac{12}{4} = 3
\]
### 2. **Finding the Slope Between Points B and C:**
For points B and C:
- \( (x_1, y_1) = (8, 24) \)
- \( (x_2, y_2) = (12, 36) \)
Calculating the slope:
\[
\text{slope}_{BC} = \frac{36 - 24}{12 - 8} = \frac{12}{4} = 3
\]
### 3. **Finding the Equation of the Line:**
Since both slopes are equal, points A, B, and C are collinear. We can also derive the equation of the line formed by these points using the point-slope form of a linear equation:
\[
y - y_1 = m(x - x_1)
\]
You can use point A \((4, 12)\) for this purpose, with a slope \(m = 3\):
\[
y - 12 = 3(x - 4)
\]
Expanding this:
\[
y - 12 = 3x - 12
\]
Adding 12 to both sides leads to:
\[
y = 3x
\]
### 4. **Verification:**
- For Point A \((4, 12)\):
\[
y = 3(4) = 12 \quad \text{(Correct)}
\]
- For Point B \((8, 24)\):
\[
y = 3(8) = 24 \quad \text{(Correct)}
\]
- For Point C \((12, 36)\):
\[
y = 3(12) = 36 \quad \text{(Correct)}
\]
### Conclusion:
The coordinates of the points are \((4, 12)\), \((8, 24)\), and \((12, 36)\). The equation of the line passing through these points is:
\[
\boxed{y = 3x}
\]
You can apply this information in various contexts such as finding points on the line or verifying points if presented with new coordinates!
Answered by
GPT-4o mini
To determine the simplified form of the ratio of downloads to web visits based on the coordinates provided, we can use the points A, B, and C that you previously defined:
- Point A: \( (4, 12) \)
- Point B: \( (8, 24) \)
- Point C: \( (12, 36) \)
**Download (y-value)** and **Web Visits (x-value)** correspond to the points as follows:
1. For Point A: 4 downloads and 12 web visits
2. For Point B: 8 downloads and 24 web visits
3. For Point C: 12 downloads and 36 web visits
### Finding the Ratios
**Ratio of downloads to web visits for each point:**
1. **Point A**:
\[
\text{Ratio} = \frac{4 \text{ (downloads)}}{12 \text{ (web visits)}}
\]
2. **Point B**:
\[
\text{Ratio} = \frac{8 \text{ (downloads)}}{24 \text{ (web visits)}}
\]
3. **Point C**:
\[
\text{Ratio} = \frac{12 \text{ (downloads)}}{36 \text{ (web visits)}}
\]
### Simplifying the Ratio
**For Point A**:
\[
\frac{4}{12} = \frac{1}{3}
\]
So the ratio is:
\[
1 \text{ to } 3
\]
**For Point B**:
\[
\frac{8}{24} = \frac{1}{3}
\]
So the ratio is:
\[
1 \text{ to } 3
\]
**For Point C**:
\[
\frac{12}{36} = \frac{1}{3}
\]
So the ratio is:
\[
1 \text{ to } 3
\]
### Conclusion
The simplified form of the ratio of downloads to web visits is:
\[
\boxed{1 \text{ to } 3} \text{ or } \frac{1}{3}
\]
This indicates that for every 1 download, there are 3 web visits across all points.
- Point A: \( (4, 12) \)
- Point B: \( (8, 24) \)
- Point C: \( (12, 36) \)
**Download (y-value)** and **Web Visits (x-value)** correspond to the points as follows:
1. For Point A: 4 downloads and 12 web visits
2. For Point B: 8 downloads and 24 web visits
3. For Point C: 12 downloads and 36 web visits
### Finding the Ratios
**Ratio of downloads to web visits for each point:**
1. **Point A**:
\[
\text{Ratio} = \frac{4 \text{ (downloads)}}{12 \text{ (web visits)}}
\]
2. **Point B**:
\[
\text{Ratio} = \frac{8 \text{ (downloads)}}{24 \text{ (web visits)}}
\]
3. **Point C**:
\[
\text{Ratio} = \frac{12 \text{ (downloads)}}{36 \text{ (web visits)}}
\]
### Simplifying the Ratio
**For Point A**:
\[
\frac{4}{12} = \frac{1}{3}
\]
So the ratio is:
\[
1 \text{ to } 3
\]
**For Point B**:
\[
\frac{8}{24} = \frac{1}{3}
\]
So the ratio is:
\[
1 \text{ to } 3
\]
**For Point C**:
\[
\frac{12}{36} = \frac{1}{3}
\]
So the ratio is:
\[
1 \text{ to } 3
\]
### Conclusion
The simplified form of the ratio of downloads to web visits is:
\[
\boxed{1 \text{ to } 3} \text{ or } \frac{1}{3}
\]
This indicates that for every 1 download, there are 3 web visits across all points.
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