Answer: Not rounded: 39.6 Rounded: 40
Step-by-step explanation:
Answer:
2.25
Step-by-step explanation:
The computation of the number c that satisfied is shown below:
Given that
![f(x) = \sqrt{x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%7Bx%7D)
Interval = (0,9)
According to the Rolle's mean value theorem,
If f(x) is continuous in {a,b) and it is distinct also
And, f(a) ≠ f(b) so its existance should be at least one value
i.e
![f^i(c) = \frac{f(b) - f(a)}{b -a }](https://tex.z-dn.net/?f=f%5Ei%28c%29%20%3D%20%5Cfrac%7Bf%28b%29%20-%20f%28a%29%7D%7Bb%20-a%20%7D)
After this,
![f(x) = \sqrt{x} \\\\ f^i(x) = \frac{1}{2}x ^{\frac{1}{2} - 1} \\\\ = \frac{1}{2}x ^{\frac{-1}{2}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csqrt%7Bx%7D%20%5C%5C%5C%5C%20f%5Ei%28x%29%20%3D%20%5Cfrac%7B1%7D%7B2%7Dx%20%5E%7B%5Cfrac%7B1%7D%7B2%7D%20-%201%7D%20%5C%5C%5C%5C%20%3D%20%20%5Cfrac%7B1%7D%7B2%7Dx%20%5E%7B%5Cfrac%7B-1%7D%7B2%7D)
![f^i(x) = \frac{1}{{2}\sqrt{x} } = f^i(c) = \frac{1}{{2}\sqrt{c} } \\\\\a = 0, f (a) = f(o) = \sqrt{0} = 0 \\\\\ b = 9 , f (b) = f(a) = \sqrt{9} = 3\\](https://tex.z-dn.net/?f=f%5Ei%28x%29%20%3D%20%5Cfrac%7B1%7D%7B%7B2%7D%5Csqrt%7Bx%7D%20%7D%20%3D%20f%5Ei%28c%29%20%3D%20%5Cfrac%7B1%7D%7B%7B2%7D%5Csqrt%7Bc%7D%20%7D%20%5C%5C%5C%5C%5Ca%20%3D%200%2C%20f%20%28a%29%20%3D%20f%28o%29%20%3D%20%5Csqrt%7B0%7D%20%3D%200%20%5C%5C%5C%5C%5C%20b%20%3D%209%20%2C%20f%20%28b%29%20%3D%20f%28a%29%20%3D%20%5Csqrt%7B9%7D%20%3D%203%5C%5C)
After this,
Put the values of a and b to the above equation
![f^i(c) = \frac{f(b) - f(a)}{b - a} \\\\ \frac{1}{{2}\sqrt{c} } = \frac{3 -0}{9-0} \\\\ \frac{1}{\sqrt[2]{c} } = \frac{3}{9} \\\\ \frac{1}{\sqrt[2]{c} } = \frac{1}{3} \\\\ \sqrt[2]{c} = 3\\\\\sqrt{c} = \frac{3}{2} \\\\ c = \frac{9}{4}](https://tex.z-dn.net/?f=f%5Ei%28c%29%20%3D%20%5Cfrac%7Bf%28b%29%20-%20f%28a%29%7D%7Bb%20-%20a%7D%20%20%5C%5C%5C%5C%20%5Cfrac%7B1%7D%7B%7B2%7D%5Csqrt%7Bc%7D%20%7D%20%3D%20%5Cfrac%7B3%20-0%7D%7B9-0%7D%20%20%5C%5C%5C%5C%20%5Cfrac%7B1%7D%7B%5Csqrt%5B2%5D%7Bc%7D%20%7D%20%3D%20%5Cfrac%7B3%7D%7B9%7D%20%5C%5C%5C%5C%20%5Cfrac%7B1%7D%7B%5Csqrt%5B2%5D%7Bc%7D%20%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5C%5C%5C%5C%20%5Csqrt%5B2%5D%7Bc%7D%20%3D%203%5C%5C%5C%5C%5Csqrt%7Bc%7D%20%3D%20%5Cfrac%7B3%7D%7B2%7D%20%5C%5C%5C%5C%20c%20%3D%20%5Cfrac%7B9%7D%7B4%7D)
= 2.25
Your answer would be 11.4
Hope it helps
(5,1) is the function of the given equation
Answer:
0.47 is the probability it rains at least 2 out of any randomly selected 5 days during the given time of year
Step-by-step explanation:
We are given the following information:
We treat training as a success.
P(Rain) = 30% = 0.30
Then the chances of rain on each day follows a binomial distribution, where
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 5
We have to evaluate:
0.47 is the probability it rains at least 2 out of any randomly selected 5 days during the given time of year