Answer:
![10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}](https://tex.z-dn.net/?f=10x%5E4%5Csqrt%7B6%7D%2Bx%5E3%5Csqrt%7B30x%7D-10x%5E4%5Csqrt%7B3%7D-x%5E3%5Csqrt%7B15x%7D)
Step-by-step explanation:
Remove perfect squares from under the radicals.
![(\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})\\\\=(\sqrt{10x^4})(2\sqrt{15x^4}) +(\sqrt{10x^4})(\sqrt{3x^3}) -(x\sqrt{5x^2})(2\sqrt{15x^4}) -(x\sqrt{5x^2})(\sqrt{3x^3})\\\\=2\sqrt{150x^8}+\sqrt{30x^7}-2x\sqrt{75x^6}-x\sqrt{15x^5}\\\\=\boxed{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}](https://tex.z-dn.net/?f=%28%5Csqrt%7B10x%5E4%7D-x%5Csqrt%7B5x%5E2%7D%29%282%5Csqrt%7B15x%5E4%7D%2B%5Csqrt%7B3x%5E3%7D%29%5C%5C%5C%5C%3D%28%5Csqrt%7B10x%5E4%7D%29%282%5Csqrt%7B15x%5E4%7D%29%20%2B%28%5Csqrt%7B10x%5E4%7D%29%28%5Csqrt%7B3x%5E3%7D%29%20-%28x%5Csqrt%7B5x%5E2%7D%29%282%5Csqrt%7B15x%5E4%7D%29%20-%28x%5Csqrt%7B5x%5E2%7D%29%28%5Csqrt%7B3x%5E3%7D%29%5C%5C%5C%5C%3D2%5Csqrt%7B150x%5E8%7D%2B%5Csqrt%7B30x%5E7%7D-2x%5Csqrt%7B75x%5E6%7D-x%5Csqrt%7B15x%5E5%7D%5C%5C%5C%5C%3D%5Cboxed%7B10x%5E4%5Csqrt%7B6%7D%2Bx%5E3%5Csqrt%7B30x%7D-10x%5E4%5Csqrt%7B3%7D-x%5E3%5Csqrt%7B15x%7D%7D)
_____
The applicable rules of exponents are ...
(x^a)(x^b) = x^(a+b)
√(a^2) = a . . . . . . . for a > 0
(√a)(√b) = √(ab)
Answer:
7 sticks
Step-by-step explanation:
Answer:
The 99% confidence interval is between 62.36%(lower bound) and 89.64%(upper bound).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
![\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}](https://tex.z-dn.net/?f=%5Cpi%20%5Cpm%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D)
In which
z is the zscore that has a pvalue of
.
A sample of 65 students from the freshmen class is used and a mean score of 76% correct is obtained.
This means that ![n = 65, \pi = 0.76](https://tex.z-dn.net/?f=n%20%3D%2065%2C%20%5Cpi%20%3D%200.76)
99% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:
![\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.76 - 2.575\sqrt{\frac{0.76*0.24}{65}} = 0.6236](https://tex.z-dn.net/?f=%5Cpi%20-%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.76%20-%202.575%5Csqrt%7B%5Cfrac%7B0.76%2A0.24%7D%7B65%7D%7D%20%3D%200.6236)
The upper limit of this interval is:
![\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.76 + 2.575\sqrt{\frac{0.76*0.24}{65}} = 0.8964](https://tex.z-dn.net/?f=%5Cpi%20%2B%20z%5Csqrt%7B%5Cfrac%7B%5Cpi%281-%5Cpi%29%7D%7Bn%7D%7D%20%3D%200.76%20%2B%202.575%5Csqrt%7B%5Cfrac%7B0.76%2A0.24%7D%7B65%7D%7D%20%3D%200.8964)
0.6236*100 = 62.36%
0.8964*100 = 89.64%
The 99% confidence interval is between 62.36%(lower bound) and 89.64%(upper bound).
I don’t know what the question is, your just saying that
Answer: (2, -2)
Step-by-step explanation:
![\left(\frac{2+2}{2}, \frac{3-7}{2} \right)=(2,-2)](https://tex.z-dn.net/?f=%5Cleft%28%5Cfrac%7B2%2B2%7D%7B2%7D%2C%20%5Cfrac%7B3-7%7D%7B2%7D%20%5Cright%29%3D%282%2C-2%29)