PartialMathematician

The volume of a cylinder: \(\pi r^2 \cdot h\). h = height

The radius is 6 cm, and the height is 4*12 = 48 cm. The volume of the cylinder is \(36\pi \cdot 48 = 1728\pi\). 

The volume of a sphere: \(\dfrac{4}{3} \pi r^3\). 

The radius is 6 cm, and \(6^3 \) is 216. \(\dfrac{4}{3} \cdot 216 = 288\). The volume of one sphere is \(288\pi\). If we multiply by 4, the volume of the four spheres is \(1152\pi\). 

We can calculate the empty cylinder space by subtracting 4 VolumeSphere from VolumeCylinder. We have \(1728\pi - 1152\pi\), which simplifies into \(\boxed{576\pi}\).

Here is a graph:

https://www.desmos.com/calculator/8tbu0ownp3

- PM

The line is parallel to x = 8. Since the point is (4, -2), the x-coordinate is 4. The line parallel to x = 8 is the line x = 4. 

Hope this helps,

- PM

P(B | A), the conditional probability that the student... Out of 210 students, 90 have at least one sister. There are 45 who have at least one sister and one brother. \(\dfrac{45}{90}\) simplifies to \(\dfrac{1}{2}\). 

- PM

Across Quadrants I and II. 

You are very welcome!

:P

According to desmos, the best fit line is \(y = 12.7288x + 24.678\), which you can round to \(y = 12.73x + 24.68\) or \(y = 13x + 25\) .

Hope this helps,

- PM

Here is a graph:

https://www.desmos.com/calculator/vgvpzwtqbr

- PM

Why are they duplicates of the same point in the question?

Exponential Growth. When X increases, Y increases. When X decreases, Y decreases.