9-8.2-(-1.9) =
9-8.2+1.9
.8+1.9
2.7
-8-(-5.4)-1.8 =
-8+5.4-1.8
-2.6-1.8
-4.4
Alex has a higher score by 7.1.
Answer:
![\large\boxed{\dfrac{5x\sqrt{x}}{8y^4}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Cdfrac%7B5x%5Csqrt%7Bx%7D%7D%7B8y%5E4%7D%7D)
Step-by-step explanation:
![\sqrt{\dfrac{25x^9y^3}{64x^6y^{11}}}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b},\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}};\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=\dfrac{\sqrt{25}}{\sqrt{64}}\cdot \sqrt{x^{9-6}y^{3-11}}=\dfrac{5}{8}\sqrt{x^3y^{-8}}=\dfrac{5}{8}\sqrt{x^3}\cdot\sqrt{y^{-8}}\\\\\text{use}\ a^na^m=a^{n+m},\ (a^n)^m=a^{nm}\\\\=\dfrac{5}{8}\sqrt{x^{2+1}}\cdot\sqrt{y^{(-4)(2)}}=\dfrac{5}{8}\sqrt{x^2x}\cdot\sqrt{(y^{-4})^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cdfrac%7B25x%5E9y%5E3%7D%7B64x%5E6y%5E%7B11%7D%7D%7D%5Cqquad%5Ctext%7Buse%7D%5C%20%5Csqrt%7Bab%7D%3D%5Csqrt%7Ba%7D%5Ccdot%5Csqrt%7Bb%7D%2C%5C%20%5Csqrt%7B%5Cdfrac%7Ba%7D%7Bb%7D%7D%3D%5Cdfrac%7B%5Csqrt%7Ba%7D%7D%7B%5Csqrt%7Bb%7D%7D%3B%5C%20%5Cdfrac%7Ba%5Em%7D%7Ba%5En%7D%3Da%5E%7Bm-n%7D%5C%5C%5C%5C%3D%5Cdfrac%7B%5Csqrt%7B25%7D%7D%7B%5Csqrt%7B64%7D%7D%5Ccdot%20%5Csqrt%7Bx%5E%7B9-6%7Dy%5E%7B3-11%7D%7D%3D%5Cdfrac%7B5%7D%7B8%7D%5Csqrt%7Bx%5E3y%5E%7B-8%7D%7D%3D%5Cdfrac%7B5%7D%7B8%7D%5Csqrt%7Bx%5E3%7D%5Ccdot%5Csqrt%7By%5E%7B-8%7D%7D%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%20a%5Ena%5Em%3Da%5E%7Bn%2Bm%7D%2C%5C%20%28a%5En%29%5Em%3Da%5E%7Bnm%7D%5C%5C%5C%5C%3D%5Cdfrac%7B5%7D%7B8%7D%5Csqrt%7Bx%5E%7B2%2B1%7D%7D%5Ccdot%5Csqrt%7By%5E%7B%28-4%29%282%29%7D%7D%3D%5Cdfrac%7B5%7D%7B8%7D%5Csqrt%7Bx%5E2x%7D%5Ccdot%5Csqrt%7B%28y%5E%7B-4%7D%29%5E2%7D)
![=\dfrac{5}{8}\sqrt{x^2}\cdot\sqrt{x}\cdot\sqrt{(y^{-4})^2}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=\dfrac{5}{8}x\sqrt{x}\cdot y^{-4}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{5x\sqrt{x}}{8y^4}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B5%7D%7B8%7D%5Csqrt%7Bx%5E2%7D%5Ccdot%5Csqrt%7Bx%7D%5Ccdot%5Csqrt%7B%28y%5E%7B-4%7D%29%5E2%7D%5Cqquad%5Ctext%7Buse%7D%5C%20%5Csqrt%7Ba%5E2%7D%3Da%5C%20%5Ctext%7Bfor%7D%5C%20a%5Cgeq0%5C%5C%5C%5C%3D%5Cdfrac%7B5%7D%7B8%7Dx%5Csqrt%7Bx%7D%5Ccdot%20y%5E%7B-4%7D%5Cqquad%5Ctext%7Buse%7D%5C%20a%5E%7B-n%7D%3D%5Cdfrac%7B1%7D%7Ba%5En%7D%5C%5C%5C%5C%3D%5Cdfrac%7B5x%5Csqrt%7Bx%7D%7D%7B8y%5E4%7D)
Answer:
Solution: { -29/3 , -10/3 }
Step-by-step explanation:
2y = x + 3 ---------> equ 1
5y = x - 7 equ 2
equ 1 - equ s ====> -3y = 10
y = -10/3
Put y = -10/3 in equ 1
2 * (-10/3) = x + 3
-20/3 = x + 3
(-20/3) - 3 = x
(-20/3) - (9/3) = x
(-20 - 9) / 3 =x
x = -29/3
Solution: { -29/3 , -10/3 }
The rise is 1 and the run is 2 so 1/2 since slope is rise over run.
Answer:
The mean and standard deviation of the number preferring the incumbent is mean = 330, standard deviation = 10.59.
Step-by-step explanation:
We are given that From previous polls, it is believed that 66% of likely voters prefer the incumbent.
A new poll of 500 likely voters will be conducted. In the new poll the proportion favoring the incumbent has not changed.
Let p = probability of voters preferring the incumbent = 66%
n = number of voters polled = 500
<u>So, the mean of the number preferring the incumbent is given by;</u>
Mean =
=
= 330 voters
<u>And, standard deviation of the number preferring the incumbent is given by;</u>
Variance =
=
= 112.2
So, Standard deviation =
=
= 10.59