Answer: 
Center = (2, 3) radius = 
<u>Step-by-step explanation:</u>
When both the x² and y² values are equal and positive, the shape is a circle. Complete the square to put the equation in format:
(x-h)² + (y-k)² = r² where
- (h, k) is the vertex
- r is the radius
1) Group the x's and y's together and move the number to the right side
4x² - 16x + 4y² - 24y = -51
2) Factor out the 4 from the x² and y²
4(x² - 4x ) + 4(y² - 6y ) = -51
3) Complete the square (divide the x and y value by 2 and square it)
![4[x^2-4x+\bigg(\dfrac{-4}{2}\bigg)^2]+4[y^2-6y+\bigg(\dfrac{-6}{2}\bigg)^2]=-51+4\bigg(\dfrac{-4}{2}\bigg)^2+4\bigg(\dfrac{-6}{2}\bigg)^2](https://tex.z-dn.net/?f=4%5Bx%5E2-4x%2B%5Cbigg%28%5Cdfrac%7B-4%7D%7B2%7D%5Cbigg%29%5E2%5D%2B4%5By%5E2-6y%2B%5Cbigg%28%5Cdfrac%7B-6%7D%7B2%7D%5Cbigg%29%5E2%5D%3D-51%2B4%5Cbigg%28%5Cdfrac%7B-4%7D%7B2%7D%5Cbigg%29%5E2%2B4%5Cbigg%28%5Cdfrac%7B-6%7D%7B2%7D%5Cbigg%29%5E2)
= 4(x - 2)² + 4(y - 3)² = -51 + 4(-2)² + 4(-3)²
= 4(x - 2)² + 4(y - 3)² = -51 + 4(4) + 4(9)
= 4(x - 2)² + 4(y - 3)² = -51 + 16 + 36
= 4(x - 2)² + 4(y - 3)² = 1
4) Divide both sides by 4
- (h, k) = (2, 3)
Answer: a. 1.981 < μ < 2.18
b. Yes.
Step-by-step explanation:
A. For this sample, we will use t-distribution because we're estimating the standard deviation, i.e., we are calculating the standard deviation, and the sample is small, n = 12.
First, we calculate mean of the sample:
2.08
Now, we estimate standard deviation:
s = 0.1564
For t-score, we need to determine degree of freedom and 
:
df = 12 - 1
df = 11
= 1 - 0.95
α = 0.05
0.025
Then, t-score is
= 2.201
The interval will be
± 
2.08 ± 
2.08 ± 0.099
The 95% two-sided CI on the mean is 1.981 < μ < 2.18.
B. We are 95% confident that the true population mean for this clinic is between 1.981 and 2.18. Since the mean number performed by all clinics has been 1.95, and this mean is less than the interval, there is evidence that this particular clinic performs more scans than the overall system average.
Answer: 88º
Step-by-step explanation:
180-47=133-45=88
Answer:
formula = feet / 5280
=> 32750 / 5280
=> 6.20265.......
When rounded to the nearest tenth we get,
6.20 or simply 6.20
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