Hey there!
The answer is C. teenagers across the country.
A population is the whole. It's every member of the group, which is pretty much the opposite of a sample. A sample is just a fraction or a percentage of the group.
The sample is the homeroom class, who is the group being surveyed. But the population the survey is determining data for overall is teenagers across the country.
We also know that they are across the country because we are told that the gym is a national franchise.
Hope this helps!
Always is the answer to the question
Answer:
B. Yes; the graph passes the vertical line test.
Step-by-step explanation:
If a vertical line can intersect the graph at more than one point the graph is not a function.
We have to determine the equation of the line passing through the point (2,-5) and parallel to the line ![5x = 6y+7](https://tex.z-dn.net/?f=5x%20%3D%206y%2B7)
When two lines are parallel, then the slopes of the two lines are equal.
Equation of line with point
and slope 'm' is given by:
![(y-y_1) = m(x-x_1)](https://tex.z-dn.net/?f=%28y-y_1%29%20%3D%20m%28x-x_1%29)
Since, we have to determine the equation of a line with point (2,-5).
So, the equation of the line is : ![(y-(-5)) = m(x-2)](https://tex.z-dn.net/?f=%28y-%28-5%29%29%20%3D%20m%28x-2%29)
![y+5 = m(x-2)](https://tex.z-dn.net/?f=y%2B5%20%3D%20m%28x-2%29)
Since, the line is parallel to the line ![5x = 6y+ 7](https://tex.z-dn.net/?f=5x%20%3D%206y%2B%207)
So, ![6y +7 = 5x](https://tex.z-dn.net/?f=6y%20%2B7%20%3D%205x)
![6y = 5x - 7](https://tex.z-dn.net/?f=6y%20%3D%205x%20-%207)
![y = \frac{5}{6}x - \frac{7}{6}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B5%7D%7B6%7Dx%20-%20%5Cfrac%7B7%7D%7B6%7D)
So, slope of the line 'm' is
.
Therefore, the equation of the line is:
![(y+5) = \frac{5}{6}(x-2)](https://tex.z-dn.net/?f=%28y%2B5%29%20%3D%20%5Cfrac%7B5%7D%7B6%7D%28x-2%29)
![6y + 30 = 5x - 10](https://tex.z-dn.net/?f=6y%20%2B%2030%20%3D%205x%20-%2010)
![6y - 5x = -10-30](https://tex.z-dn.net/?f=6y%20-%205x%20%3D%20-10-30)
![6y - 5x = -40](https://tex.z-dn.net/?f=6y%20-%205x%20%3D%20-40)
Therefore,
is the required equation of the line.