The answer to that is A) 1
Answer:
(a) P-value = 0.074, α = 0.05 do not reject H0
(b) P-value = 0.006, α = 0.001 do not reject H0
(c) P-value = 0.494, α = 0.05 do not reject H0
(d) P-value = 0.074, α = 0.10 reject H0
(e) P-value = 0.028, α = 0.01 do not reject H0
(f) P-value = 0.296, α = 0.10 do not reject H0
Step-by-step explanation:
The p-value is used to determine the statistical significance of the results of a statistical test. The p-value is the probability that the null hypothesis is correct. Smaller the p-value, higher is the probability that the alternate hypothesis is correct. On the other hand, the significance level (α) is the probability of rejecting the null hypothesis when it is true. It is the risk that you are willing to take in saying that there are differences between groups when there are not.
In order to reject the null hypothesis, the p-value should be lower than the significance level (α).
Question:
Simplify the radical expressions

![10.\ \sqrt[3]{135}](https://tex.z-dn.net/?f=10.%5C%20%5Csqrt%5B3%5D%7B135%7D)
Answer:





![\sqrt[3]{24} = 2 \sqrt[3]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B24%7D%20%3D%202%20%5Csqrt%5B3%5D%7B3%7D)
![\sqrt[3]{81} =3\sqrt[3]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B81%7D%20%3D3%5Csqrt%5B3%5D%7B3%7D)

![\sqrt[3]{40} = 2 \sqrt[3]{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B40%7D%20%3D%202%20%5Csqrt%5B3%5D%7B5%7D)
![\sqrt[3]{135} =3\sqrt[3]{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B135%7D%20%3D3%5Csqrt%5B3%5D%7B5%7D)
Step-by-step explanation:
Express 63 as 9 * 7

Split:



Express 48 as 16 * 3

Split



Express 75 as 25 * 3

Split


Express 99 as 9 * 11

Split


Express 92 as 4 * 23



Express 24 as 8 * 3
![\sqrt[3]{24} = \sqrt[3]{8} * \sqrt[3]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B24%7D%20%3D%20%5Csqrt%5B3%5D%7B8%7D%20%2A%20%5Csqrt%5B3%5D%7B3%7D)
Express 8 as 2^3
![\sqrt[3]{24} = \sqrt[3]{2^3} * \sqrt[3]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B24%7D%20%3D%20%5Csqrt%5B3%5D%7B2%5E3%7D%20%2A%20%5Csqrt%5B3%5D%7B3%7D)
![\sqrt[3]{24} = 2 \sqrt[3]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B24%7D%20%3D%202%20%5Csqrt%5B3%5D%7B3%7D)
![7.\ \sqrt[3]{81}](https://tex.z-dn.net/?f=7.%5C%20%5Csqrt%5B3%5D%7B81%7D)
Express 81 as 27 * 3
![\sqrt[3]{81} =\sqrt[3]{27}*\sqrt[3]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B81%7D%20%3D%5Csqrt%5B3%5D%7B27%7D%2A%5Csqrt%5B3%5D%7B3%7D)
Express 27 as 3^3
![\sqrt[3]{81} =\sqrt[3]{3^3}*\sqrt[3]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B81%7D%20%3D%5Csqrt%5B3%5D%7B3%5E3%7D%2A%5Csqrt%5B3%5D%7B3%7D)
![\sqrt[3]{81} =3\sqrt[3]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B81%7D%20%3D3%5Csqrt%5B3%5D%7B3%7D)
Express 128 as 64 * 2


![9.\sqrt[3]{40}](https://tex.z-dn.net/?f=9.%5Csqrt%5B3%5D%7B40%7D)
Express 40 as 8 * 5
![\sqrt[3]{40} = \sqrt[3]{8} * \sqrt[3]{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B40%7D%20%3D%20%5Csqrt%5B3%5D%7B8%7D%20%2A%20%5Csqrt%5B3%5D%7B5%7D)
![\sqrt[3]{40} = \sqrt[3]{2^3} * \sqrt[3]{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B40%7D%20%3D%20%5Csqrt%5B3%5D%7B2%5E3%7D%20%2A%20%5Csqrt%5B3%5D%7B5%7D)
![\sqrt[3]{40} = 2 \sqrt[3]{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B40%7D%20%3D%202%20%5Csqrt%5B3%5D%7B5%7D)
![10.\ \sqrt[3]{135}](https://tex.z-dn.net/?f=10.%5C%20%5Csqrt%5B3%5D%7B135%7D)
Express 135 as 27 * 5
![\sqrt[3]{135} =\sqrt[3]{27}*\sqrt[3]{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B135%7D%20%3D%5Csqrt%5B3%5D%7B27%7D%2A%5Csqrt%5B3%5D%7B5%7D)
Express 27 as 3^3
![\sqrt[3]{135} =\sqrt[3]{27}*\sqrt[3]{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B135%7D%20%3D%5Csqrt%5B3%5D%7B27%7D%2A%5Csqrt%5B3%5D%7B5%7D)
![\sqrt[3]{135} =3\sqrt[3]{5}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B135%7D%20%3D3%5Csqrt%5B3%5D%7B5%7D)