The answer
is 85 gallons
in a day
answer
14 inches
explanation
the area of a square is A = s^2 where s is the side length
A = s^2
196 = s^2
s = ![\sqrt{196}](https://tex.z-dn.net/?f=%5Csqrt%7B196%7D)
s = 14 inches
A.
![\mathbb P(X>1000)=\mathbb P\left(\dfrac{X-1200}{100}>\dfrac{1000-1200}{100}\right)=\mathbb P(Z>-2)](https://tex.z-dn.net/?f=%5Cmathbb%20P%28X%3E1000%29%3D%5Cmathbb%20P%5Cleft%28%5Cdfrac%7BX-1200%7D%7B100%7D%3E%5Cdfrac%7B1000-1200%7D%7B100%7D%5Cright%29%3D%5Cmathbb%20P%28Z%3E-2%29)
Since about 95% of a normal distribution falls within two standard deviations of the mean, that leaves 5% that lie without, with 2.5% lying to either side.
![\mathbb P(Z>-2)=\mathbb P(|Z|2)=0.95+0.025=0.975](https://tex.z-dn.net/?f=%5Cmathbb%20P%28Z%3E-2%29%3D%5Cmathbb%20P%28%7CZ%7C%3C2%29%2B%5Cmathbb%20P%28Z%3E2%29%3D0.95%2B0.025%3D0.975)
b.
![\mathbb P(1100](https://tex.z-dn.net/?f=%5Cmathbb%20P%281100%3CX%3C1300%29%3D%5Cmathbb%20P%5Cleft%28%5Cdfrac%7B1100-1200%7D%7B100%7D%3C%5Cdfrac%7BX-1200%7D%7B100%7D%3C%5Cdfrac%7B1300-1200%7D%7B100%7D%5Cright%29%3D%5Cmathbb%20P%28-1%3CZ%3C1%29)
About 68% of a normal distribution lies within one standard deviation of the mean, so this probability is about 0.68.
c. You're looking for
![k](https://tex.z-dn.net/?f=k)
such that
![\mathbb P(X>k)=0.10](https://tex.z-dn.net/?f=%5Cmathbb%20P%28X%3Ek%29%3D0.10)
Since
![\mathbb P(X>k)=\mathbb P\left(\dfrac{X-1200}{100}>\dfrac{k-1200}{100}\right)=\mathbb P(Z>k^*)=0.10](https://tex.z-dn.net/?f=%5Cmathbb%20P%28X%3Ek%29%3D%5Cmathbb%20P%5Cleft%28%5Cdfrac%7BX-1200%7D%7B100%7D%3E%5Cdfrac%7Bk-1200%7D%7B100%7D%5Cright%29%3D%5Cmathbb%20P%28Z%3Ek%5E%2A%29%3D0.10)
occurs for
![k^*\approx1.2816](https://tex.z-dn.net/?f=k%5E%2A%5Capprox1.2816)
, it follows that
![\dfrac{k-1200}{100}=1.2816\implies k\approx1328](https://tex.z-dn.net/?f=%5Cdfrac%7Bk-1200%7D%7B100%7D%3D1.2816%5Cimplies%20k%5Capprox1328)
So there's a probability of 0.10 for having a demand exceeding about 1328 pounds.
25,236 I don’t if it’s reasonable or not sorry
Answer:
Step-by-step explanation:
Line PU is transversal and lines QR and ST are parallels
Angle PRQ and UST add up to 180 degrees
- 15(x+2) = 180 - 135
- 15x + 30 = 45
- 15x = 15
- x = 1