Dab on them haters brobro
Answer:
x = 0.25 or 1/4
Step-by-step explanation:
"If a=b and b=c, then a=c" is a statement of the transitive property of equality. The same property applies to the congruence relation.
Your appropriate choice is
• transitive property
Answer:
If a Poisson process applies, we have the probability that k potholes are find in t miles as:
![P(x=k)=\frac{(rt)^ke^{-rt}}{k!}](https://tex.z-dn.net/?f=P%28x%3Dk%29%3D%5Cfrac%7B%28rt%29%5Eke%5E%7B-rt%7D%7D%7Bk%21%7D)
The probability that no more that one pothole will appear in a section of one mile is P=0.1353.
The probability that no more that 4 potholes will occur in a given section of 5 miles is P=0.0293.
Step-by-step explanation:
We have the rate of potholes:
![r=2\,pothole/mile](https://tex.z-dn.net/?f=r%3D2%5C%2Cpothole%2Fmile)
If a Poisson process applies, we have the probability that k potholes are find in t miles as:
![P(x=k)=\frac{(rt)^ke^{-rt}}{k!}](https://tex.z-dn.net/?f=P%28x%3Dk%29%3D%5Cfrac%7B%28rt%29%5Eke%5E%7B-rt%7D%7D%7Bk%21%7D)
The probability that no more that one pothole will appear in a section of one mile is P=0.1353:
![t=1\\\\P(x](https://tex.z-dn.net/?f=t%3D1%5C%5C%5C%5CP%28x%3C1%29%3DP%280%29%3D%5Cfrac%7B%282%2A1%29%5E0e%5E%7B-2%2A1%7D%7D%7B0%21%7D%3D%5Cfrac%7B1%2Ae%5E%7B-2%7D%7D%7B1%7D%3D%200.1353)
The probability that no more that 4 potholes will occur in a given section of 5 miles is P=0.0293:
![t=5\\\\P(x\leq4)=P(0)+P(1)+P(2)+P(4)\\\\P(0)=\frac{(2*5)^0e^{-2*5}}{0!}= 0.000045 \\\\P(1)= \frac{(2*5)^1e^{-2*5}}{1!}= 0.000454 \\\\ P(2)= \frac{(2*5)^2e^{-2*5}}{2!}= 0.002270 \\\\P(3)= \frac{(2*5)^3e^{-2*5}}{3!}= 0.007567 \\\\P(4)= \frac{(2*5)^4e^{-2*5}}{4!}= 0.018917 \\\\\\P(x\leq4)=P(0)+P(1)+P(2)+P(4)\\\\P(x\leq4)=0.000045+0.000454+0.00227+0.007567+0.018917\\\\P(x\leq 4)= 0.029253](https://tex.z-dn.net/?f=t%3D5%5C%5C%5C%5CP%28x%5Cleq4%29%3DP%280%29%2BP%281%29%2BP%282%29%2BP%284%29%5C%5C%5C%5CP%280%29%3D%5Cfrac%7B%282%2A5%29%5E0e%5E%7B-2%2A5%7D%7D%7B0%21%7D%3D%200.000045%20%5C%5C%5C%5CP%281%29%3D%20%5Cfrac%7B%282%2A5%29%5E1e%5E%7B-2%2A5%7D%7D%7B1%21%7D%3D%200.000454%20%5C%5C%5C%5C%20P%282%29%3D%20%5Cfrac%7B%282%2A5%29%5E2e%5E%7B-2%2A5%7D%7D%7B2%21%7D%3D%200.002270%20%5C%5C%5C%5CP%283%29%3D%20%5Cfrac%7B%282%2A5%29%5E3e%5E%7B-2%2A5%7D%7D%7B3%21%7D%3D%200.007567%20%5C%5C%5C%5CP%284%29%3D%20%5Cfrac%7B%282%2A5%29%5E4e%5E%7B-2%2A5%7D%7D%7B4%21%7D%3D%200.018917%20%5C%5C%5C%5C%5C%5CP%28x%5Cleq4%29%3DP%280%29%2BP%281%29%2BP%282%29%2BP%284%29%5C%5C%5C%5CP%28x%5Cleq4%29%3D0.000045%2B0.000454%2B0.00227%2B0.007567%2B0.018917%5C%5C%5C%5CP%28x%5Cleq%204%29%3D%200.029253)
Answer:
15
Step-by-step explanation:
Use Pythagorean theorem.
c² = a² + b²
c² = 9² + 12²
c² = 225
c = 15