Answer:
A
Step-by-step explanation:
A and D are your answers.
They have an Infinite number of solutions because when the equations are put into slope-intercept form (y=mx+b), they end up having the same slope (m) and the same y-intercept (b).
The answer is 6. Hopefully this helped!!
Answer:
P(0≤T≤400)=0.3296
Step-by-step explanation:
we know probability density function is
![f(x;\lambda)= \left\{\begin{matrix} \lambda e^{-\lambda x}& x\geq 0 \\0 & x< 0\end{matrix}\right.](https://tex.z-dn.net/?f=f%28x%3B%5Clambda%29%3D%20%5Cleft%5C%7B%5Cbegin%7Bmatrix%7D%20%5Clambda%20e%5E%7B-%5Clambda%20x%7D%26%20x%5Cgeq%200%20%5C%5C0%20%26%20x%3C%200%5Cend%7Bmatrix%7D%5Cright.)
![\lambda=\frac{1}{\mu}](https://tex.z-dn.net/?f=%5Clambda%3D%5Cfrac%7B1%7D%7B%5Cmu%7D)
![\lambda=\frac{1}{1000}](https://tex.z-dn.net/?f=%5Clambda%3D%5Cfrac%7B1%7D%7B1000%7D)
probability that bulb will fail within first 400 hours
P(0≤T≤400)= ![\int\limits^{400}_0 {f(x)} \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B400%7D_0%20%7Bf%28x%29%7D%20%5C%2C%20dx)
P(0≤T≤400)= ![\int\limits^{400}_0 {\frac{e^{-\frac{t}{1000}}}{1000}} \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B400%7D_0%20%7B%5Cfrac%7Be%5E%7B-%5Cfrac%7Bt%7D%7B1000%7D%7D%7D%7B1000%7D%7D%20%5C%2C%20dx)
=![(1000)^{-1}[\frac{e^{\frac{-t}{1000}}}{-(1000^{-1})}]^{400}_0](https://tex.z-dn.net/?f=%281000%29%5E%7B-1%7D%5B%5Cfrac%7Be%5E%7B%5Cfrac%7B-t%7D%7B1000%7D%7D%7D%7B-%281000%5E%7B-1%7D%29%7D%5D%5E%7B400%7D_0)
=![-[e^{\frac{-400}{1000}}-e^0]](https://tex.z-dn.net/?f=-%5Be%5E%7B%5Cfrac%7B-400%7D%7B1000%7D%7D-e%5E0%5D)
=1-0.67032 = 0.3296
so about 32.96 % bulb will fail within 400 hrs.
I think that would be 100 million pounds of coal.