Answer:
Option A) Inside the circle
Step-by-step explanation:
step 1
Find the radius of the circle
we know that
The radius is equal to the distance from the center to any point on the circle
the formula to calculate the distance between two points is equal to
![d\sqrt{(y2-y1)^2+(x2-x1)^2 }](https://tex.z-dn.net/?f=d%5Csqrt%7B%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%20%7D)
we have
A(-5,-8),M(-1,-3)
substitute the values
![r=\sqrt{(-3+8)^{2}+(-1+5)^{2}}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%28-3%2B8%29%5E%7B2%7D%2B%28-1%2B5%29%5E%7B2%7D%7D)
![r=\sqrt{(5)^{2}+(4)^{2}}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%285%29%5E%7B2%7D%2B%284%29%5E%7B2%7D%7D)
![r=\sqrt{41}\ units](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B41%7D%5C%20units)
step 2
Find the distance from the center to point V
we know that
If the distance from the center to point V is equal to the radius, then the point V lie on the circle
If the distance from the center to point V is less than the radius, then the point V lie inside the circle
If the distance from the center to point V is greater than the radius, then the point V lie outside the circle
we have
A(-5,-8),V(-11,-6)
substitute in the formula
![d=\sqrt{(-6+8)^{2}+(-11+5)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-6%2B8%29%5E%7B2%7D%2B%28-11%2B5%29%5E%7B2%7D%7D)
![d=\sqrt{(2)^{2}+(-6)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%282%29%5E%7B2%7D%2B%28-6%29%5E%7B2%7D%7D)
![d=\sqrt{40}\ units](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B40%7D%5C%20units)
so
![\sqrt{40}\ units< \sqrt{41}\ units](https://tex.z-dn.net/?f=%5Csqrt%7B40%7D%5C%20units%3C%20%5Csqrt%7B41%7D%5C%20units)
The distance from the center to point V is less than the radius
therefore
The point V lie inside the circle
Hope that helped :)
Answer: (110.22, 125.78)
Step-by-step explanation:
The confidence interval for the population mean is given by :-
![\mu\ \pm z_{\alpha/2}\times\dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Cmu%5C%20%5Cpm%20z_%7B%5Calpha%2F2%7D%5Ctimes%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
Given : Sample size = 463
![\mu=118\text{ minutes}](https://tex.z-dn.net/?f=%5Cmu%3D118%5Ctext%7B%20minutes%7D)
![\sigma=65\text{ minutes}](https://tex.z-dn.net/?f=%5Csigma%3D65%5Ctext%7B%20minutes%7D)
Significance level : ![\alpha=1-0.99=0.01](https://tex.z-dn.net/?f=%5Calpha%3D1-0.99%3D0.01)
Critical value : ![z_{\alpha/2}=z_{0.005}=\pm2.576](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3Dz_%7B0.005%7D%3D%5Cpm2.576)
We assume that the population is normally distributed.
Now, the 90% confidence interval for the population mean will be :-
![118\ \pm\ 2.576\times\dfrac{65}{\sqrt{463}} \\\\\approx118\pm7.78=(118-7.78\ ,\ 118+7.78)=(110.22,\ 125.78)](https://tex.z-dn.net/?f=118%5C%20%5Cpm%5C%202.576%5Ctimes%5Cdfrac%7B65%7D%7B%5Csqrt%7B463%7D%7D%20%5C%5C%5C%5C%5Capprox118%5Cpm7.78%3D%28118-7.78%5C%20%2C%5C%20118%2B7.78%29%3D%28110.22%2C%5C%20125.78%29)
Hence, 99% confidence interval for the mean study time of all first-year students = (110.22, 125.78)
Answer:
1. 21
2. -4
3. 20
4. 1
5. 4
6. -6
Step-by-step explanation:
Point D is the midpoint of the outer circle that we aim to find the area of
The circle has a diameter of WZ and radii of WC and CZ
We know that YZ=YD=10 cm
Let DC be
![x](https://tex.z-dn.net/?f=x)
and CY be
![10-x](https://tex.z-dn.net/?f=10-x)
The radius of the outer circle can be written as
![8+8+x](https://tex.z-dn.net/?f=8%2B8%2Bx)
or
![10+10-x](https://tex.z-dn.net/?f=10%2B10-x)
which we can equate to find the value of
![x](https://tex.z-dn.net/?f=x)
![8+8+x=10+10-x](https://tex.z-dn.net/?f=8%2B8%2Bx%3D10%2B10-x)
![16+x=20-x](https://tex.z-dn.net/?f=16%2Bx%3D20-x)
![2x=4](https://tex.z-dn.net/?f=2x%3D4)
![x=2](https://tex.z-dn.net/?f=x%3D2)
Therefore, the radius of the circle is
![8+8+2=18](https://tex.z-dn.net/?f=8%2B8%2B2%3D18)
And hence the area of the circle is
![\pi (18^{2})](https://tex.z-dn.net/?f=%20%20%5Cpi%20%2818%5E%7B2%7D%29)
=324