Answer:
823.7 m^2
Step-by-step explanation:
The ratio of the side lengths is 6/5.
The ratio of the areas is the square of the ratio of the side lengths, 36/25.
572 m^2 * 36/25 = 823.7 m^2
Answer:
First answer: 3
Second answer: 6
Each square you see on the cube you add +1 to get 3
But in total the cube has 6 faces
Answer:
a) ![p = 0.5](https://tex.z-dn.net/?f=%20p%20%3D%200.5)
b) ![\hat p= \frac{X}{n}= \frac{154}{329}= 0.468](https://tex.z-dn.net/?f=%20%5Chat%20p%3D%20%5Cfrac%7BX%7D%7Bn%7D%3D%20%5Cfrac%7B154%7D%7B329%7D%3D%200.468)
c) ![0.468 - 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.423](https://tex.z-dn.net/?f=0.468%20-%201.64%20%5Csqrt%7B%5Cfrac%7B0.468%281-0.468%29%7D%7B329%7D%7D%3D0.423)
![0.468 + 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.513](https://tex.z-dn.net/?f=0.468%20%2B%201.64%20%5Csqrt%7B%5Cfrac%7B0.468%281-0.468%29%7D%7B329%7D%7D%3D0.513)
And the 90% confidence interval for the true proportion is given by (0.527;0.593).
Step-by-step explanation:
Part a
For this case we don't have any prior info given so then the probability assumed for this case is:
![p = 0.5](https://tex.z-dn.net/?f=%20p%20%3D%200.5)
Part b
For this case the proportion of success is given by:
![\hat p= \frac{X}{n}= \frac{154}{329}= 0.468](https://tex.z-dn.net/?f=%20%5Chat%20p%3D%20%5Cfrac%7BX%7D%7Bn%7D%3D%20%5Cfrac%7B154%7D%7B329%7D%3D%200.468)
Part c
The confidence interval for the true proportion would be given by this formula
![\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}](https://tex.z-dn.net/?f=%5Chat%20p%20%5Cpm%20z_%7B%5Calpha%2F2%7D%20%5Csqrt%7B%5Cfrac%7B%5Chat%20p%281-%5Chat%20p%29%7D%7Bn%7D%7D)
For the 90% confidence interval the value of and , and the critical value would be given by:
![z_{\alpha/2}=1.64](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D1.64)
The confidence interval is given by:
![0.468 - 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.423](https://tex.z-dn.net/?f=0.468%20-%201.64%20%5Csqrt%7B%5Cfrac%7B0.468%281-0.468%29%7D%7B329%7D%7D%3D0.423)
![0.468 + 1.64 \sqrt{\frac{0.468(1-0.468)}{329}}=0.513](https://tex.z-dn.net/?f=0.468%20%2B%201.64%20%5Csqrt%7B%5Cfrac%7B0.468%281-0.468%29%7D%7B329%7D%7D%3D0.513)
And the 90% confidence interval for the true proportion is given by (0.527;0.593).
Answer:
Reference angle will be ![60^{\circ}](https://tex.z-dn.net/?f=60%5E%7B%5Ccirc%7D)
![cos(1680)=\frac{-1}{2}](https://tex.z-dn.net/?f=cos%281680%29%3D%5Cfrac%7B-1%7D%7B2%7D)
![sin(1680)=-0.866](https://tex.z-dn.net/?f=sin%281680%29%3D-0.866)
Step-by-step explanation:
We have given
It can be written as
As 240° is lie in the third quadrant
And we know that for third quadrant
Reference angle is given by ![angle-180^{\circ}](https://tex.z-dn.net/?f=angle-180%5E%7B%5Ccirc%7D)
So reference angle will be ![240^{\circ}-180^{\circ}=60^{\circ}](https://tex.z-dn.net/?f=240%5E%7B%5Ccirc%7D-180%5E%7B%5Ccirc%7D%3D60%5E%7B%5Ccirc%7D)
Now ![cos(1640)=cos(9\pi +60)=-cos60=\frac{-1}{2}](https://tex.z-dn.net/?f=cos%281640%29%3Dcos%289%5Cpi%20%2B60%29%3D-cos60%3D%5Cfrac%7B-1%7D%7B2%7D)
![sin(1640)=cos(9\pi +60)=-sin60=-0.866](https://tex.z-dn.net/?f=sin%281640%29%3Dcos%289%5Cpi%20%2B60%29%3D-sin60%3D-0.866)
2 > x > -1 is the inequality.