9514 1404 393
Answer:
4
Step-by-step explanation:
∛64 = ∛(4³) = 4
_____
The real root when the root index is odd will have the same sign as the value whose root it is. 64 is positive, so the real cube root will be positive.
Answer:
20%
Step-by-step explanation:
![\displaystyle\lim_{n\to\infty}\sqrt[n]{\left|\left(\frac{5n+15}{2n-1}\right)^n\right|}=\lim_{n\to\infty}\frac{5n+15}{2n-1}=\dfrac52](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bn%5Cto%5Cinfty%7D%5Csqrt%5Bn%5D%7B%5Cleft%7C%5Cleft%28%5Cfrac%7B5n%2B15%7D%7B2n-1%7D%5Cright%29%5En%5Cright%7C%7D%3D%5Clim_%7Bn%5Cto%5Cinfty%7D%5Cfrac%7B5n%2B15%7D%7B2n-1%7D%3D%5Cdfrac52)
Since this limit exceeds 1, the series diverges.
The first answer because (3,0) is the point that crosses the x-axis.
Answer:
The estimate is ![P__{hat}} \pm E = 0.37 \pm 0.0348](https://tex.z-dn.net/?f=P__%7Bhat%7D%7D%20%5Cpm%20E%20%20%3D%200.37%20%5Cpm%200.0348)
Step-by-step explanation:
From the question we are told that
The sample size is n = 522
The sample proportion of students would like to talk about school is ![\r p__{hat}} = 0.37](https://tex.z-dn.net/?f=%5Cr%20p__%7Bhat%7D%7D%20%3D%20%200.37)
Given that the confidence level is 90 % then the level of significance can be mathematically evaluated as
![\alpha = 100 - 90](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%20100%20-%2090)
![\alpha = 10\%](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%2010%5C%25)
![\alpha = 0.10](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%200.10)
Next we obtain the critical value of
from the normal distribution table, the value is
![Z_{\frac{\alpha }{2} } =Z_{\frac{0.10}{2} } = 1.645](https://tex.z-dn.net/?f=Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%3DZ_%7B%5Cfrac%7B0.10%7D%7B2%7D%20%7D%20%3D%20%201.645)
Generally the margin of error can be mathematically represented as
![E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r P_{hat}(1- \r P_{hat} )}{n } }](https://tex.z-dn.net/?f=E%20%3D%20%20Z_%7B%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%7D%20%2A%20%20%5Csqrt%7B%5Cfrac%7B%5Cr%20P_%7Bhat%7D%281-%20%5Cr%20P_%7Bhat%7D%20%29%7D%7Bn%20%7D%20%7D)
=> ![E = 1.645 * \sqrt{\frac{0.37 (1- 0.37 )}{522 } }](https://tex.z-dn.net/?f=E%20%3D%201.645%20%2A%20%20%5Csqrt%7B%5Cfrac%7B0.37%20%281-%200.37%20%20%29%7D%7B522%20%7D%20%7D)
=> ![E = 0.0348](https://tex.z-dn.net/?f=E%20%3D%200.0348)
Generally the estimate the proportion of all teenagers who want more family discussions about school at 90% confidence level is
![P__{hat}} \pm E](https://tex.z-dn.net/?f=P__%7Bhat%7D%7D%20%5Cpm%20%20E)
substituting values
![0.37 \pm 0.0348](https://tex.z-dn.net/?f=0.37%20%5Cpm%200.0348)