Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
What is the volume of the rectangular prism?
There is no given information or measurements to solve for the volume of the rectangular prism. Additional information is needed such as the length, width, and height of the prism in order to calculate its volume.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Using the following set of data, calculate the lower quartile, the upper quartile, and the interquartile range.
20, 22, 25, 28, 29, 30, 32, 33, 34
Be sure to show your work for finding:
the lower quartile
the upper quartile
the interquartile range
To find the lower quartile:
1. Put the data in order from smallest to largest:
20, 22, 25, 28, 29, 30, 32, 33, 34
2. Find the median of the lower half of the data set:
20, 22, 25, 28
The median of this set is 23.5, which is the lower quartile.
To find the upper quartile:
1. Put the data in order from smallest to largest:
20, 22, 25, 28, 29, 30, 32, 33, 34
2. Find the median of the upper half of the data set:
30, 32, 33, 34
The median of this set is 32.5, which is the upper quartile.
To find the interquartile range:
1. Subtract the lower quartile from the upper quartile:
32.5 - 23.5 = 9
The interquartile range is 9.
Therefore, the lower quartile is 23.5, the upper quartile is 32.5, and the interquartile range is 9.
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Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday
Temperature (degrees F) 49 55 52 46 47 42 38
Julia measured the high temperature in her town for one week. Using the chart above, find the mean absolute deviation for the high temperatures. Round your answer to the nearest tenth.
Be sure to show your work for finding:
the mean of the set of data
the distance of each number from the mean
the mean absolute deviation
To find the mean of the set of data:
1. Add up all the temperature values:
49 + 55 + 52 + 46 + 47 + 42 + 38 = 329
2. Divide the sum by the number of values (in this case, 7):
329 ÷ 7 = 47
The mean temperature for the week is 47 degrees F.
To find the distance of each temperature from the mean:
1. Subtract the mean from each temperature value:
49 - 47 = 2
55 - 47 = 8
52 - 47 = 5
46 - 47 = -1
47 - 47 = 0
42 - 47 = -5
38 - 47 = -9
2. Take the absolute value of each difference (so that negative values become positive):
|2| = 2
|8| = 8
|5| = 5
|-1| = 1
|0| = 0
|-5| = 5
|-9| = 9
The distances from the mean are 2, 8, 5, 1, 0, 5, and 9.
To find the mean absolute deviation:
1. Add up all the distances:
2 + 8 + 5 + 1 + 0 + 5 + 9 = 30
2. Divide the sum by the number of values (in this case, 7):
30 ÷ 7 = 4.3
The mean absolute deviation for the high temperatures is 4.3 (rounded to the nearest tenth).
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What is the volume of the rectangular prisms?
There is no given information or measurements to solve for the volume of the rectangular prisms. Additional information is needed such as the length, width, and height of the prism in order to calculate its volume.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A right rectangular prism has a length of 15 millimeters, width of 3 millimeters, and height of 4 millimeters.
What is the surface area of the prism?
To find the surface area of a rectangular prism, you need to find the area of each face and add them together.
1. The top and bottom faces each have an area of:
15 mm x 3 mm = 45 mm²
2. The front and back faces each have an area of:
15 mm x 4 mm = 60 mm²
3. The left and right faces each have an area of:
3 mm x 4 mm = 12 mm²
4. Add up all the areas:
45 mm² + 45 mm² + 60 mm² + 60 mm² + 12 mm² + 12 mm² = 234 mm²
The surface area of the prism is 234 square millimeters.
To find the volume of a rectangular prism, you need to know the length, width, and height of the prism.
The formula to calculate the volume of a rectangular prism is V = l × w × h, where V is the volume, l is the length, w is the width, and h is the height.
To find the volume, simply multiply the length, width, and height together.
For example, if the length is 5 cm, the width is 3 cm, and the height is 2 cm, the volume can be calculated as follows:
V = 5 cm × 3 cm × 2 cm
V = 30 cm³
Thus, the volume of the rectangular prism in this example is 30 cm³.