The formula for volume of a sphere is V = 4
/3 x π x r3 (cubed).
The original radius of the balloon is 10 ft, so when we plug that value into the equation we get 4188.79. When the balloon deflated, the new radius was 5 ft, so the new volume is 523.6. The question asks how much volume was lost, so we need to subtract 4188.79 - 523.6 and get approximately 3665.
Hope this helps! I hate taking usa test prep quizzes too haha.
Answer:
0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
In a given region, the number of tornadoes in a one-week period is modeled by a Poisson distribution with mean 2
Three weeks, so ![\mu = 2*3 = 6](https://tex.z-dn.net/?f=%5Cmu%20%3D%202%2A3%20%3D%206)
Calculate the probability that fewer than four tornadoes occur in a three-week period.
This is:
![P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)](https://tex.z-dn.net/?f=P%28X%20%3C%204%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29%20%2B%20P%28X%20%3D%203%29)
In which
![P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5Cfrac%7Be%5E%7B-%5Cmu%7D%2A%5Cmu%5E%7Bx%7D%7D%7B%28x%29%21%7D)
![P(X = 0) = \frac{e^{-6}*6^{0}}{(0)!} = 0.0025](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20%5Cfrac%7Be%5E%7B-6%7D%2A6%5E%7B0%7D%7D%7B%280%29%21%7D%20%3D%200.0025)
![P(X = 1) = \frac{e^{-6}*6^{1}}{(1)!} = 0.0149](https://tex.z-dn.net/?f=P%28X%20%3D%201%29%20%3D%20%5Cfrac%7Be%5E%7B-6%7D%2A6%5E%7B1%7D%7D%7B%281%29%21%7D%20%3D%200.0149)
![P(X = 2) = \frac{e^{-6}*6^{2}}{(2)!} = 0.0446](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20%5Cfrac%7Be%5E%7B-6%7D%2A6%5E%7B2%7D%7D%7B%282%29%21%7D%20%3D%200.0446)
![P(X = 3) = \frac{e^{-6}*6^{3}}{(3)!} = 0.0892](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20%5Cfrac%7Be%5E%7B-6%7D%2A6%5E%7B3%7D%7D%7B%283%29%21%7D%20%3D%200.0892)
Then
![P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0025 + 0.0149 + 0.0446 + 0.0892 = 0.1512](https://tex.z-dn.net/?f=P%28X%20%3C%204%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29%20%2B%20P%28X%20%3D%203%29%20%3D%200.0025%20%2B%200.0149%20%2B%200.0446%20%2B%200.0892%20%3D%200.1512)
0.1512 = 15.12% probability that fewer than four tornadoes occur in a three-week period.
More info. I can't really answer this. Sorry
Answer:
x=0.5
Step-by-step explanation:
32x+16=32
-16 -16
32x=16
÷32 ÷32
x=0.5 or x=1/2