Answer:
a) x=12
b) x=8.71
c) x=10.95
d) x=3.92
e) x=5.152
Step-by-step explanation:
a) x=12.
To have a probability of 0.5, x must be the mean of X.
b) x=8.71
![z=-1.6449\\\\x=\mu+z\sigma=12-1.6449*2=8.71](https://tex.z-dn.net/?f=z%3D-1.6449%5C%5C%5C%5Cx%3D%5Cmu%2Bz%5Csigma%3D12-1.6449%2A2%3D8.71)
c) x=10.95
![P(X](https://tex.z-dn.net/?f=P%28X%3C12%29%3D0.5%5C%5C%5C%5CP%28X%3Cx%29%3D0.5-P%28X%3C12%29%3D0.5-0.2%3D0.3%5C%5C%5C%5Cz%3D-0.5244%5C%5C%5C%5Cx%3D12-0.5244%2A2%3D10.95)
d) x=3.92
If we define Y=X-12, then
![\mu_Y=\mu_X-12\\\\\sigma_Y=\sigma_X](https://tex.z-dn.net/?f=%5Cmu_Y%3D%5Cmu_X-12%5C%5C%5C%5C%5Csigma_Y%3D%5Csigma_X)
For z=1.96, the probability around the mean is 0.95. Then:
![x=(12-12)+1.96*2=0+3.92=3.92](https://tex.z-dn.net/?f=x%3D%2812-12%29%2B1.96%2A2%3D0%2B3.92%3D3.92)
e) x=5.152
As in the question d, the area around the mean now is 0.99. This happens when z=2.576. Then:
![x=(12-12)+2.576*2=0+5.152=5.152](https://tex.z-dn.net/?f=x%3D%2812-12%29%2B2.576%2A2%3D0%2B5.152%3D5.152)
Answer:
Square
Step-by-step explanation:
Area of triangle = 1/2 * b * h
= 1/2 * 15 * 25
= 187.5 ft²
Area of square = side * side
= 14 * 14
= 196 ft²
Comparing both areas, it is clear that square have a larger area.
Answer:
D if i'm wrong i'm so sorry
Step-by-step explanation:
Answer:
I think you would use the distributive property
Hello,
r=5(1+cos t)
r'=5(-sin t)
r²+r'²= 25[(1+cos t)²+(-sin t)²]=50(1-cos t)=50 sin² (t/2)
Between 0 and π, sin x>0 ==>|sin x|=sin x
![l= 2*5* \int\limits^{\pi}_0{sin( \frac{t}{2} )} \, dt= 5[-cos (t/2)]_0^{\pi}\\\\ =5(0+1)=5](https://tex.z-dn.net/?f=l%3D%202%2A5%2A%20%5Cint%5Climits%5E%7B%5Cpi%7D_0%7Bsin%28%20%5Cfrac%7Bt%7D%7B2%7D%20%29%7D%20%5C%2C%20dt%3D%205%5B-cos%20%28t%2F2%29%5D_0%5E%7B%5Cpi%7D%5C%5C%5C%5C%0A%3D5%280%2B1%29%3D5)
Here is the method but i may have make some mistakes.