___ gallons per minutes
11 answers
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.
To determine the kilograms of fruit crushed in one minute, you will divide the total kilograms of fruit by the time in minutes.
First, convert \( 3 \frac{1}{3} \) to an improper fraction:
\[ 3 \frac{1}{3} = \frac{10}{3} \text{ kilograms} \]
Now we need to find out how many kilograms are crushed in one minute, which is given by:
\[ \text{Kilograms per minute} = \frac{\text{Total kilograms}}{\text{Time in minutes}} = \frac{\frac{10}{3}}{\frac{3}{4}} \]
To divide fractions, multiply by the reciprocal of the second fraction:
\[ \frac{\frac{10}{3}}{\frac{3}{4}} = \frac{10}{3} \times \frac{4}{3} = \frac{10 \times 4}{3 \times 3} = \frac{40}{9} \]
To convert \( \frac{40}{9} \) to a mixed number:
So,
\[ \frac{40}{9} = 4 \frac{4}{9} \]
The answer in kilograms per minute is
\[ \boxed{4 \frac{4}{9}} \text{ kilograms per minute} \]
The most appropriate process from your options is: d. \( 3 \frac{1}{4} \div \frac{3}{4} \) (though remember we actually computed it as \( \frac{10}{3} \div \frac{3}{4} \)).
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.
From the data, we know:
To find the amount of water needed for one ounce of oatmeal, divide the gallons of water by the ounces of oatmeal:
\[ \text{Gallons per ounce} = \frac{76 \text{ gallons}}{4 \text{ ounces}} = 19 \text{ gallons per ounce} \]
Using the unit rate: \[ \text{Gallons for 10 ounces} = 10 \text{ ounces} \times 19 \text{ gallons per ounce} = 190 \text{ gallons} \]
Using the unit rate in the reverse direction: \[ \text{Ounces for 304 gallons} = \frac{304 \text{ gallons}}{19 \text{ gallons per ounce}} = 16 \text{ ounces} \]
Here’s the completed table:
| Ounces of oatmeal | Gallons of water | |--------------------|------------------| | 2 | 38 | | 4 | 76 | | 10 | 190 | | 16 | 304 |
So, the missing values are:
It appears that you are presenting a coordinate grid with certain points marked on it. Let's denote the points given:
From the grid for Points A, B, and C:
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:
Assuming the points you provided can be indicated in more detail:
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!
Thank you for providing the coordinates for points A, B, and C.
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:
Calculating the slope:
\[ \text{slope}_{AB} = \frac{24 - 12}{8 - 4} = \frac{12}{4} = 3 \]
For points B and C:
Calculating the slope:
\[ \text{slope}_{BC} = \frac{36 - 24}{12 - 8} = \frac{12}{4} = 3 \]
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:
\[ y = 3x \]
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 \((12, 36)\): \[ y = 3(12) = 36 \quad \text{(Correct)} \]
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!
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:
Download (y-value) and Web Visits (x-value) correspond to the points as follows:
Ratio of downloads to web visits for each point:
Point A: \[ \text{Ratio} = \frac{4 \text{ (downloads)}}{12 \text{ (web visits)}} \]
Point B: \[ \text{Ratio} = \frac{8 \text{ (downloads)}}{24 \text{ (web visits)}} \]
Point C: \[ \text{Ratio} = \frac{12 \text{ (downloads)}}{36 \text{ (web visits)}} \]
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: \[ 1 \text{ to } 3 \]
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.
