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 9.6 millimeters, width of 5 millimeters, and height of 7 millimeters.
What is the volume of the rectangular prism?
The volume of a right rectangular prism is given as:
V = l × w × h
where
l = length of the prism
w = width of the prism
h = height of the prism
Plugging in the given values, we get:
V = 9.6 mm × 5 mm × 7 mm
V = 336 mm³
Therefore, the volume of the rectangular prism is 336 cubic millimeters.
Since A rectangular prism has a length of 10.4 millimeters, a width of 5 millimeters, and a height of 8 millimeters.
So here the volume is
= (10.4) (5) (8)
= 416\ mm^3
Here we multiplied all three things to get the volume
hence, The volume of the rectangular prism is 416\ mm^3
Yes, that is correct. The volume formula for a rectangular prism is V = l × w × h, where l is the length, w is the width, and h is the height. Plugging in the given values, we get:
V = 10.4 mm × 5 mm × 8 mm
V = 416 mm³
Therefore, the volume of the rectangular prism is 416 cubic millimeters.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The stem-and-leaf plot shows the heights in centimeters of Teddy Bear sunflowers grown in two different types of soil.
Soil A Soil B
5 9
5 2 1 1 6 3 9
5 1 0 7 0 2 3 6 7 8
2 1 8 3
0 9
Key: 9|6 means 69 Key: 5|8 means 58
Calculate the mean of each data set.
Calculate the mean absolute deviation (MAD) of each data set.
Which set is more variable? How do you know?
First, we need to find the mean of each data set:
For Soil A:
- We have a total of 8 data points.
- To find the mean, we add up all the heights and divide by the total number of data points:
(50 + 51 + 51 + 52 + 55 + 57 + 59 + 59) / 8 = 54.25 cm
For Soil B:
- We have a total of 15 data points.
- To find the mean, we add up all the heights and divide by the total number of data points:
(36 + 37 + 38 + 39 + 60 + 63 + 67 + 68 + 68 + 68 + 70 + 72 + 73 + 78 + 89) / 15 = 63.867 cm
Next, we need to find the mean absolute deviation (MAD) of each data set:
For Soil A:
- To find the MAD, we first find the absolute deviation of each data point by subtracting the mean from each height and taking the absolute value:
|50 - 54.25| = 4.25
|51 - 54.25| = 3.25
|51 - 54.25| = 3.25
|52 - 54.25| = 2.25
|55 - 54.25| = 0.75
|57 - 54.25| = 2.75
|59 - 54.25| = 4.75
|59 - 54.25| = 4.75
- Next, we find the average of these absolute deviations:
(4.25 + 3.25 + 3.25 + 2.25 + 0.75 + 2.75 + 4.75 + 4.75) / 8 = 3.4375 cm
For Soil B:
- To find the MAD, we first find the absolute deviation of each data point by subtracting the mean from each height and taking the absolute value:
|36 - 63.867| = 27.867
|37 - 63.867| = 26.867
|38 - 63.867| = 25.867
|39 - 63.867| = 24.867
|60 - 63.867| = 3.867
|63 - 63.867| = 0.867
|67 - 63.867| = 3.133
|68 - 63.867| = 4.133
|68 - 63.867| = 4.133
|68 - 63.867| = 4.133
|70 - 63.867| = 6.133
|72 - 63.867| = 8.133
|73 - 63.867| = 9.133
|78 - 63.867| = 14.133
|89 - 63.867| = 25.133
- Next, we find the average of these absolute deviations:
(27.867 + 26.867 + 25.867 + 24.867 + 3.867 + 0.867 + 3.133 + 4.133 + 4.133 + 4.133 + 6.133 + 8.133 + 9.133 + 14.133 + 25.133) / 15 = 10.0718 cm
Finally, we can compare the MAD of each data set to determine which one is more variable. A larger MAD indicates more variability in the data set. Here, we can see that the MAD for Soil B is much larger than the MAD for Soil A. Therefore, we can say that Soil B is more variable than Soil A.
I'm confused
I apologize for any confusion. Let me clarify the solution:
The stem-and-leaf plot shows the heights in centimeters of Teddy Bear sunflowers grown in two different types of soil. We are asked to calculate the mean of each data set and the mean absolute deviation (MAD) of each data set and determine which set is more variable.
Here is the stem-and-leaf plot for Soil A:
Soil A
5 9
5 2 1 1
5 1 0
2 1
0
To calculate the mean of Soil A, we need to add up all the values in the data set and then divide by the total number of values. There are 8 data points in Soil A. Adding up the values, we get:
50 + 51 + 51 + 52 + 55 + 57 + 59 + 59 = 434
Dividing by the total number of values, we get:
434 ÷ 8 = 54.25 cm
So, the mean of Soil A is 54.25 cm.
To calculate the MAD of Soil A, we need to find the absolute deviation of each value from the mean. The absolute deviation is the difference between each value and the mean, ignoring the negative sign. For example, if the value is 50 and the mean is 54.25, the absolute deviation is |50 - 54.25| = 4.25. We then find the average of all the absolute deviations.
Here are the absolute deviations for each value in Soil A:
|50 - 54.25| = 4.25
|51 - 54.25| = 3.25
|51 - 54.25| = 3.25
|52 - 54.25| = 2.25
|55 - 54.25| = 0.75
|57 - 54.25| = 2.75
|59 - 54.25| = 4.75
|59 - 54.25| = 4.75
Adding up the absolute deviations, we get:
4.25 + 3.25 + 3.25 + 2.25 + 0.75 + 2.75 + 4.75 + 4.75 = 26.25
Dividing by the total number of values, we get:
26.25 ÷ 8 = 3.28125 cm
So, the MAD of Soil A is 3.28125 cm.
Here is the stem-and-leaf plot for Soil B:
Soil B
6 3 9
7 0 2 3 6 7 8
8 3
9
To calculate the mean of Soil B, we need to add up all the values in the data set and then divide by the total number of values. There are 15 data points in Soil B. Adding up the values, we get:
36 + 37 + 38 + 39 + 60 + 63 + 67 + 68 + 68 + 68 + 70 + 72 + 73 + 78 + 89 = 978
Dividing by the total number of values, we get:
978 ÷ 15 = 65.2 cm
So, the mean of Soil B is 65.2 cm.
To calculate the MAD of Soil B, we need to find the absolute deviation of each value from the mean, and then find the average of all the absolute deviations. Here are the absolute deviations for each value in Soil B:
|36 - 65.2| = 29.2
|37 - 65.2| = 28.2
|38 - 65.2| = 27.2
|39 - 65.2| = 26.2
|60 - 65.2| = 5.2
|63 - 65.2| = 2.2
|67 - 65.2| = 1.8
|68 - 65.2| = 2.8
|68 - 65.2| = 2.8
|68 - 65.2| = 2.8
|70 - 65.2| = 4.8
|72 - 65.2| = 6.8
|73 - 65.2| = 7.8
|78 - 65.2| = 12.8
|89 - 65.2| = 23.8
Adding up the absolute deviations, we get:
29.2 + 28.2 + 27.2 + 26.2 + 5.2 + 2.2 + 1.8 + 2.8 + 2.8 + 2.8 + 4.8 + 6.8 + 7.8 + 12.8 + 23.8 = 182.4
Dividing by the total number of values, we get:
182.4 ÷ 15 = 12.16 cm
So, the MAD of Soil B is 12.16 cm.
To determine which set is more variable, we compare the MADs. The larger the MAD, the more variable the data set. Here, we can see that the MAD for Soil B (12.16 cm) is much larger than the MAD for Soil A (3.28125 cm). Therefore, we can conclude that Soil B is more variable than Soil A.
I hope this explanation clears up any confusion. Let me know if you have any further questions!
?
Please let me know if you have any questions or if there is anything that is unclear. I would be happy to clarify any part of the solution.
To find the volume of a rectangular prism, you multiply its length, width, and height. In this case, the length is 9.6 millimeters, the width is 5 millimeters, and the height is 7 millimeters.
The formula to calculate the volume of a rectangular prism is:
Volume = Length × Width × Height
So, plugging in the given values:
Volume = 9.6 mm × 5 mm × 7 mm
To calculate this, we can follow the steps:
1. Multiply the length and width: 9.6 mm × 5 mm = 48 mm²
2. Multiply the result by the height: 48 mm² × 7 mm = 336 mm³
Therefore, the volume of the rectangular prism is 336 cubic millimeters.