Answer:
Step-by-step explanation:
tan 0 = 1/ cot 0
so, tan 0=11/60,
cot 0= 1/ (11/60)
cot 0= 60/ 11
Answer:
50 degrees
Step-by-step explanation:
vertical angles are the same
angle LPM = 180-60-70
angle LPM = 180-130 = 50
angle LPM = angle KPN
50=angle KPN
8 = 2^x + 4
2^x = 8 - 4
2^x = 4
as you know 4 = 2^2 so now you have:
2^x = 2^2
x = 2
54 days!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answer:
![P(X>8)=e^{-1}](https://tex.z-dn.net/?f=P%28X%3E8%29%3De%5E%7B-1%7D)
Step-by-step explanation:
The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:
![P(X=x)=\lambda e^{-\lambda x}, x>0](https://tex.z-dn.net/?f=P%28X%3Dx%29%3D%5Clambda%20e%5E%7B-%5Clambda%20x%7D%2C%20x%3E0)
And 0 for other case. Let X the random variable that represent "The number of years a radio functions" and we know that the distribution is given by:
![X \sim Exp(\lambda=\frac{1}{8})](https://tex.z-dn.net/?f=X%20%5Csim%20Exp%28%5Clambda%3D%5Cfrac%7B1%7D%7B8%7D%29)
We can assume that the random variable t represent the number of years that the radio is already here. So the interest is find this probability:
![P(X>8|X>t)](https://tex.z-dn.net/?f=P%28X%3E8%7CX%3Et%29)
We have an important property on the exponential distribution called "Memoryless" property and says this:
![P(X>a+t| X>t)=P(X>a)](https://tex.z-dn.net/?f=P%28X%3Ea%2Bt%7C%20X%3Et%29%3DP%28X%3Ea%29)
Where a represent a shift and t the time of interest.
On this case then ![P(X>8|X>t)=P(X>8+t|X>t)=P(X>8)](https://tex.z-dn.net/?f=P%28X%3E8%7CX%3Et%29%3DP%28X%3E8%2Bt%7CX%3Et%29%3DP%28X%3E8%29)
We can use the definition of the density function and find this probability:
![P(X>8)=\int_{8}^{\infty} \frac{1}{8}e^{-\frac{1}{8}x}dx](https://tex.z-dn.net/?f=P%28X%3E8%29%3D%5Cint_%7B8%7D%5E%7B%5Cinfty%7D%20%5Cfrac%7B1%7D%7B8%7De%5E%7B-%5Cfrac%7B1%7D%7B8%7Dx%7Ddx)
![=\frac{1}{8} \int_{8}^{\infty} e^{-\frac{1}{8}x}dx](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B8%7D%20%5Cint_%7B8%7D%5E%7B%5Cinfty%7D%20e%5E%7B-%5Cfrac%7B1%7D%7B8%7Dx%7Ddx)
![=[lim_{x\to\infty} (-e^{-\frac{1}{8}x})+e^{-1}]=0+e^{-1}=e^{-1}](https://tex.z-dn.net/?f=%3D%5Blim_%7Bx%5Cto%5Cinfty%7D%20%28-e%5E%7B-%5Cfrac%7B1%7D%7B8%7Dx%7D%29%2Be%5E%7B-1%7D%5D%3D0%2Be%5E%7B-1%7D%3De%5E%7B-1%7D)