Answer:
The area of the square as a function of the radius is given by 2r^2
Step-by-step explanation:
Check the attachment for solution
Answer:
Percent means per- amount
And the second one is dividing.
Step-by-step explanation:
The mean of a dataset is the average of the dataset.
- The mean is 1.5
- The standard deviation is 1.58
- The median remains unchanged, the mean increases, and the standard deviation decreases when <em>5 is increased to a larger value</em>
The given parameters are:
![\mathbf{x = 0, 0, 0, 1, 1, 1, 2, 2, 3, 5}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%20%3D%200%2C%200%2C%200%2C%201%2C%201%2C%201%2C%202%2C%202%2C%203%2C%205%7D)
<u>(a) Mean and Standard deviation</u>
The mean of the dataset is calculated using:
![\mathbf{\bar x = \frac{\sum x}{n}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cbar%20x%20%3D%20%5Cfrac%7B%5Csum%20x%7D%7Bn%7D%7D)
So, we have:
![\mathbf{\bar x = \frac{0+ 0+ 0+ 1+ 1+ 1+ 2+ 2+ 3+ 5}{10}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cbar%20x%20%3D%20%5Cfrac%7B0%2B%200%2B%200%2B%201%2B%201%2B%201%2B%202%2B%202%2B%203%2B%205%7D%7B10%7D%7D)
![\mathbf{\bar x = \frac{15}{10}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cbar%20x%20%3D%20%5Cfrac%7B15%7D%7B10%7D%7D)
![\mathbf{\bar x = 1.5}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cbar%20x%20%3D%201.5%7D)
Hence, the mean is 1.5
The standard deviation is calculated using:
![\mathbf{\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n - 1}}}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Csigma_x%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Csum%28x%20-%20%5Cbar%20x%29%5E2%7D%7Bn%20-%201%7D%7D%7D%7D)
So, we have:
![\mathbf{\sigma_x = \sqrt{\frac{(0 - 1.5)^2 + (0- 1.5)^2 + (0- 1.5)^2 + (1- 1.5)^2 + (1- 1.5)^2 + (1- 1.5)^2 + (2- 1.5)^2 + (2- 1.5)^2 + (3- 1.5)^2 + (5- 1.5)^2}{10 - 1}}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Csigma_x%20%3D%20%5Csqrt%7B%5Cfrac%7B%280%20-%201.5%29%5E2%20%2B%20%280-%201.5%29%5E2%20%2B%20%280-%201.5%29%5E2%20%2B%20%281-%201.5%29%5E2%20%2B%20%281-%201.5%29%5E2%20%2B%20%281-%201.5%29%5E2%20%2B%20%282-%201.5%29%5E2%20%2B%20%282-%201.5%29%5E2%20%2B%20%283-%201.5%29%5E2%20%2B%20%285-%201.5%29%5E2%7D%7B10%20-%201%7D%7D%7D)
![\mathbf{\sigma_x = \sqrt{\frac{22.5}{9}}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Csigma_x%20%3D%20%5Csqrt%7B%5Cfrac%7B22.5%7D%7B9%7D%7D%7D)
![\mathbf{\sigma_x = \sqrt{2.5}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Csigma_x%20%3D%20%5Csqrt%7B2.5%7D%7D)
![\mathbf{\sigma_x = 1.58}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Csigma_x%20%3D%201.58%7D)
Hence, the standard deviation is 1.58
<u />
<u>(b) When 5 is increased to a larger value</u>
When 5 is increased:
- The median remains unchanged
- The mean increases
- The standard deviation decreases
Read more about median, mean, and standard deviation at:
brainly.com/question/12598273
The answer to your question is 3