Answer:
Radius: 

Step-by-step explanation:
Given

Solving (a): The radius of the circle
First, we express the equation as:

Where


So, we have:

Divide through by 9

Rewrite as:

Group the expression into 2
![[x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%5D%20%2B%20%5By%5E2%2B%20%5Cfrac%7B12%7D%7B9%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D)
![[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%5D%20%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D)
Next, we complete the square on each group.
For ![[x^2 + 3x]](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%5D)
1: Divide the 
2: Take the 
3: Add this 
So, we have:
![[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%5D%20%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D)
![[x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%20%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2%5D%20%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2)
Factorize
![[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2)
Apply the same to y
![[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%20%2B%28%5Cfrac%7B4%7D%7B6%7D%29%5E2%20%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2%20%2B%28%5Cfrac%7B4%7D%7B6%7D%29%5E2)
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2%20%2B%28%5Cfrac%7B4%7D%7B6%7D%29%5E2)
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%5Cfrac%7B9%7D%7B4%7D%20%2B%5Cfrac%7B16%7D%7B36%7D)
Add the fractions
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D%5Cfrac%7B-19%20%2A%204%20%2B%209%20%2A%209%20%2B%2016%20%2A%201%7D%7B36%7D)
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D%5Cfrac%7B21%7D%7B36%7D)
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D%5Cfrac%7B7%7D%7B12%7D)
![[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B2%7D%7B3%7D%5D%5E2%20%3D%5Cfrac%7B7%7D%7B12%7D)
Recall that:

By comparison:

Take square roots of both sides

Split

Rationalize





Solving (b): The center
Recall that:

Where


From:
![[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B2%7D%7B3%7D%5D%5E2%20%3D%5Cfrac%7B7%7D%7B12%7D)
and 
Solve for h and k
and 
Hence, the center is:

Answer:

Step-by-step explanation:




Final Answer: 
Answer:
Between 15.95 ounces and 16.15 ounces.
Step-by-step explanation:
We have the following value m, being the mean, sd, being the standard deviation and n, the sample size:
m = 16.05
sd = 0.1005
n = 4
We apply the formula of this case, which would be:
m + - 2 * sd / (n ^ 1/2)
In this way we create a range, replacing we have:
16.05 + 2 * 0.1005 / (4 ^ 1/2) = 16.1505
16.05 - 2 * 0.1005 / (4 ^ 1/2) = 15.9495
Which means that 95% of all samples are between 15.95 ounces and 16.15 ounces.
Mr. Webster is buying a carpet for an exercise room in his basement the room will an area of 230 ft