I think is OB, I’m not too sure tho
Answer:
0.25
Step-by-step explanation:
outcomes painted in blue: {3, 4, 5, 6}
number of even outcomes painted in blue: 2
number of total outcomes: 8
Therefore, the probability that the roll will show an even number and a face that is painted blue is: 2/8 = 0.25
Slope formula:
m = (y2-y1)/(x2-x1)
m = (13-19)/(-3-(-8))
m = (13-19)/(-3+8)
m = -6/5
The slope is therefore -6/5
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If you do in fact mean
(as opposed to one of these being the derivative of
at some point), then integrating twice gives
![f''(x) = -\dfrac1{x^2}](https://tex.z-dn.net/?f=f%27%27%28x%29%20%3D%20-%5Cdfrac1%7Bx%5E2%7D)
![f'(x) = \displaystyle -\int \frac{dx}{x^2} = \frac1x + C_1](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cdisplaystyle%20-%5Cint%20%5Cfrac%7Bdx%7D%7Bx%5E2%7D%20%3D%20%5Cfrac1x%20%2B%20C_1)
![f(x) = \displaystyle \int \left(\frac1x + C_1\right) \, dx = \ln|x| + C_1x + C_2](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cdisplaystyle%20%5Cint%20%5Cleft%28%5Cfrac1x%20%2B%20C_1%5Cright%29%20%5C%2C%20dx%20%3D%20%5Cln%7Cx%7C%20%2B%20C_1x%20%2B%20C_2)
From the initial conditions, we find
![f(1) = \ln|1| + C_1 + C_2 = 0 \implies C_1 + C_2 = 0](https://tex.z-dn.net/?f=f%281%29%20%3D%20%5Cln%7C1%7C%20%2B%20C_1%20%2B%20C_2%20%3D%200%20%5Cimplies%20C_1%20%2B%20C_2%20%3D%200)
![f(6) = \ln|6| + 6C_1 + C_2 = 0 \implies 6C_1 + C_2 = -\ln(6)](https://tex.z-dn.net/?f=f%286%29%20%3D%20%5Cln%7C6%7C%20%2B%206C_1%20%2B%20C_2%20%3D%200%20%5Cimplies%206C_1%20%2B%20C_2%20%3D%20-%5Cln%286%29)
Eliminating
, we get
![(C_1 + C_2) - (6C_1 + C_2) = 0 - (-\ln(6))](https://tex.z-dn.net/?f=%28C_1%20%2B%20C_2%29%20-%20%286C_1%20%2B%20C_2%29%20%3D%200%20-%20%28-%5Cln%286%29%29)
![-5C_1 = \ln(6)](https://tex.z-dn.net/?f=-5C_1%20%3D%20%5Cln%286%29)
![C_1 = -\dfrac{\ln(6)}5 = -\ln\left(\sqrt[5]{6}\right) \implies C_2 = \ln\left(\sqrt[5]{6}\right)](https://tex.z-dn.net/?f=C_1%20%3D%20-%5Cdfrac%7B%5Cln%286%29%7D5%20%3D%20-%5Cln%5Cleft%28%5Csqrt%5B5%5D%7B6%7D%5Cright%29%20%5Cimplies%20C_2%20%3D%20%5Cln%5Cleft%28%5Csqrt%5B5%5D%7B6%7D%5Cright%29)
Then
![\boxed{f(x) = \ln|x| - \ln\left(\sqrt[5]{6}\right)\,x + \ln\left(\sqrt[5]{6}\right)}](https://tex.z-dn.net/?f=%5Cboxed%7Bf%28x%29%20%3D%20%5Cln%7Cx%7C%20-%20%5Cln%5Cleft%28%5Csqrt%5B5%5D%7B6%7D%5Cright%29%5C%2Cx%20%2B%20%5Cln%5Cleft%28%5Csqrt%5B5%5D%7B6%7D%5Cright%29%7D)