Answer:
![\frac{7\sqrt{6}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B7%5Csqrt%7B6%7D%7D%7B2%7D)
Step-by-step explanation:
To rationalize the denominator, all you have to do is multiply the top and bottom by √6:
![\frac{21}{\sqrt{6}}\cdot\frac{\sqrt{6}}{\sqrt{6}} = \frac{21\sqrt{6}}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B21%7D%7B%5Csqrt%7B6%7D%7D%5Ccdot%5Cfrac%7B%5Csqrt%7B6%7D%7D%7B%5Csqrt%7B6%7D%7D%20%3D%20%5Cfrac%7B21%5Csqrt%7B6%7D%7D%7B6%7D)
You can further simplify by dividing the top and bottom by 3:
![\frac{7\sqrt{6}}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B7%5Csqrt%7B6%7D%7D%7B2%7D)
I hope this helped.
A model house that runs completely on renewable energy uses 2windmills and 3 solar panels. Each windmill generates M kilowatt-hours (kWh) of energy per year, ad each solar panel generates S kWh per year. Which expressions can we use to describe how many kWh of energy the model house will output in 10years?
9514 1404 393
Answer:
0.296
Step-by-step explanation:
8/27 is the repeating decimal 0.296296296...(3-digit repeat)
The ten-thousandths digit is 2, so rounding the number simply truncates it at the thousandths place.
8/27 ≈ 0.296
Answer:
The following lines is perpendicular, y=-x+6 and y=x+1
Step-by-step explanation:
- Slope of parallel lines are equal
(ex. slope of 2 stays 2 )
- Slope of perpendicular lines to another is the negative reciprocal
(ex. slope of 2 becomes -1/2)
y = -x + 6 and y = x + 1
the slope for y = -x + 6 is <em>-1 (-1/1)</em>
the slope for y = x + 1 is <em>1</em>
the slope -1 is the negative reciprocal of 1
hence, the definition of perpendicular fits the given
Learn more about Perpendicular and Parallel Lines here: brainly.com/question/1202004
Answer:
a
![\mu = 127](https://tex.z-dn.net/?f=%5Cmu%20%20%3D%20%20127)
b
c
![z-score = 3.18](https://tex.z-dn.net/?f=z-score%20%20%3D%20%203.18%20)
d
Yes, 158 players out of 508 is an unusual number of men born in the first 3 months of the year because the z score of 158 is greater than 3( Note :the probability of z-score = 3 is 97%)
e
The correct option is option 3
Step-by-step explanation:
From the question we are told that
The population proportion is p = 0.25
The sample size is n = 508
Generally the mean is mathematically represented as
![\mu = np](https://tex.z-dn.net/?f=%5Cmu%20%20%3D%20%20np)
=> ![\mu = 508 * 0.25](https://tex.z-dn.net/?f=%5Cmu%20%20%3D%20%20508%20%2A%200.25)
=> ![\mu = 127](https://tex.z-dn.net/?f=%5Cmu%20%20%3D%20%20127)
Generally the standard deviation is mathematically represented as
![\sigma = \sqrt{ np (1-p)}](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%20%5Csqrt%7B%20np%20%281-p%29%7D)
=>
=>
Generally the z-score of 158 is mathematically represented as
![z-score = \frac{158 - 127}{9.76}](https://tex.z-dn.net/?f=z-score%20%20%3D%20%20%5Cfrac%7B158%20-%20127%7D%7B9.76%7D)
=> ![z-score = \frac{158 - 127}{9.76}](https://tex.z-dn.net/?f=z-score%20%20%3D%20%20%5Cfrac%7B158%20-%20127%7D%7B9.76%7D)
=> ![z-score = 3.18](https://tex.z-dn.net/?f=z-score%20%20%3D%20%203.18%20)
Yes, 158 players out of 508 is an unusual number of men born in the first 3 months of the year because the z score of 158 is greater than 3( Note :the probability of z-score = 3 is 97%)
What this means is that the almost the whole professional hockey league player are born in the first month which is unusual