Answer:
![{9}^ {\frac{1}{8}x}](https://tex.z-dn.net/?f=%7B9%7D%5E%20%7B%5Cfrac%7B1%7D%7B8%7Dx%7D)
Step-by-step explanation:
We want to find an equivalent expression for
![(\sqrt[4]{9})^{ \frac{1}{2}x}](https://tex.z-dn.net/?f=%20%28%5Csqrt%5B4%5D%7B9%7D%29%5E%7B%20%5Cfrac%7B1%7D%7B2%7Dx%7D%20%20)
To find an equivalent expression, we need to apply the following property of exponents:
![{a}^{ \frac{m}{n}}=( \sqrt[n]{ {a}} )^{m}](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B%20%5Cfrac%7Bm%7D%7Bn%7D%7D%3D%28%20%5Csqrt%5Bn%5D%7B%20%7Ba%7D%7D%20%20%29%5E%7Bm%7D%20)
We let a=9, n=4 and m=½x
Then :
![{9}^{ \frac{ \frac{1}{2}x}{4}}=( \sqrt[4]{ {9}} )^{ \frac{1}{2}x}](https://tex.z-dn.net/?f=%20%7B9%7D%5E%7B%20%5Cfrac%7B%20%5Cfrac%7B1%7D%7B2%7Dx%7D%7B4%7D%7D%3D%28%20%5Csqrt%5B4%5D%7B%20%7B9%7D%7D%20%20%29%5E%7B%20%5Cfrac%7B1%7D%7B2%7Dx%7D%20)
Simplify the left hand side to get:
![{9}^ {\frac{1}{8}x} =( \sqrt[4]{ {9}} )^{ \frac{1}{2}x}](https://tex.z-dn.net/?f=%7B9%7D%5E%20%7B%5Cfrac%7B1%7D%7B8%7Dx%7D%20%3D%28%20%5Csqrt%5B4%5D%7B%20%7B9%7D%7D%20%20%29%5E%7B%20%5Cfrac%7B1%7D%7B2%7Dx%7D%20)
Therefore the correct answer is:
![{9}^ {\frac{1}{8}x}](https://tex.z-dn.net/?f=%7B9%7D%5E%20%7B%5Cfrac%7B1%7D%7B8%7Dx%7D)
Answer: 14
Step-by-step explanation:
- Degrees of freedom is the number of values in the evaluation of a test statistic that are free to vary.
For t-statistic , the degree of freedom for a sample with sample size 'n' is given by :-
![df=n-1](https://tex.z-dn.net/?f=df%3Dn-1)
Given : Sample size : n-1
Then, the number of degrees of freedom the t-value will have :-
![df=15-1=14](https://tex.z-dn.net/?f=df%3D15-1%3D14)
Hence, the t-value will have 14 degrees of freedom.
Total Marbles = 8 + 6 + 12 + 10 = 36
Probability the marble is blue = 8/36
Inverse this to get the probability of the marble not being blue
Probability of the marble not being blue = 28/36 = 7/9
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Answer:
b
Step-by-step explanation: