Answer:
y = -1/3x + 6
Step-by-step explanation:
the slope is -1/3 because you find the the reciprocal and switch the sign. To find the y intercept you plug in the points to the equation.
5 = -1/3(3) + b
5 = -1 + b
6 = b
Answer:
The probability of failure of both the bulbs is 0.4323.
Step-by-step explanation:
For an exponential distribution the distribution is given by
![f(x,\lambda )=\int_{0}^{x }\lambda e^{-\lambda x}dx](https://tex.z-dn.net/?f=f%28x%2C%5Clambda%20%29%3D%5Cint_%7B0%7D%5E%7Bx%20%7D%5Clambda%20e%5E%7B-%5Clambda%20x%7Ddx)
The value of λ is related to the mean μ as λ=1/μ,
Let us denote the 2 bulbs by X and Y thus the probability distribution of the 2 bulbs is as under
![P(X)=\int_{0}^{x }\lambda _{X}e^{-\lambda _{X}x}dx](https://tex.z-dn.net/?f=P%28X%29%3D%5Cint_%7B0%7D%5E%7Bx%20%7D%5Clambda%20_%7BX%7De%5E%7B-%5Clambda%20_%7BX%7Dx%7Ddx)
Similarly for the bulb Y the distribution function is given by
Thus the probability for both the bulbs to fail within 1500 hours is
![P(E)=\int_{0}^{1500}\int_{0}^{1500}\frac{1}{1400}e^{\frac{-x}{1400}}\cdot \frac{1}{1400}e^{\frac{-y}{1400}}dxdy\\\\P(E)=\frac{1}{1400^2}(\int_{0}^{1500}\int_{0}^{1500}e^{\frac{-x}{1400}}\cdot e^{\frac{-y}{1400}}dxdy)\\\\P(E)=\frac{1}{1400^2}(\int_{0}^{1500}e^{\frac{-x}{1400}}dx)\cdot (\int_{0}^{1500}e^{\frac{-y}{1400}}dy)\\\\P(E)=\frac{1}{1400^{2}}\times 920.473\times 920.473\\\\\therefore P(E)=0.4323](https://tex.z-dn.net/?f=P%28E%29%3D%5Cint_%7B0%7D%5E%7B1500%7D%5Cint_%7B0%7D%5E%7B1500%7D%5Cfrac%7B1%7D%7B1400%7De%5E%7B%5Cfrac%7B-x%7D%7B1400%7D%7D%5Ccdot%20%5Cfrac%7B1%7D%7B1400%7De%5E%7B%5Cfrac%7B-y%7D%7B1400%7D%7Ddxdy%5C%5C%5C%5CP%28E%29%3D%5Cfrac%7B1%7D%7B1400%5E2%7D%28%5Cint_%7B0%7D%5E%7B1500%7D%5Cint_%7B0%7D%5E%7B1500%7De%5E%7B%5Cfrac%7B-x%7D%7B1400%7D%7D%5Ccdot%20e%5E%7B%5Cfrac%7B-y%7D%7B1400%7D%7Ddxdy%29%5C%5C%5C%5CP%28E%29%3D%5Cfrac%7B1%7D%7B1400%5E2%7D%28%5Cint_%7B0%7D%5E%7B1500%7De%5E%7B%5Cfrac%7B-x%7D%7B1400%7D%7Ddx%29%5Ccdot%20%28%5Cint_%7B0%7D%5E%7B1500%7De%5E%7B%5Cfrac%7B-y%7D%7B1400%7D%7Ddy%29%5C%5C%5C%5CP%28E%29%3D%5Cfrac%7B1%7D%7B1400%5E%7B2%7D%7D%5Ctimes%20920.473%5Ctimes%20920.473%5C%5C%5C%5C%5Ctherefore%20P%28E%29%3D0.4323)
Mrs.Mouth drove 360 miles on 25 gallons
360miles/25gallons=14.4 miles per gallon
Mr.Brain drove 480 miles on 32 gallons
480miles/32gallons=15 miles per gallon
Mr Brain can go further on one gallon of gas so he is getting the better gas mileage.
<span><span>Rate of interest is the percent charged or earned. Time that ... 1) How much interest will he pay if he pays the entire loan off at the end of the third year? 2) What is the total amount that she will repay? ... To buy a laptop computer, Elaine borrowed $2,000 for 3 years at an annual simple interest rate of 5%. ... Use 0.05 for 5%.</span><span>
</span></span>
Answer:
It should be greater i would think