Leonhard Euler, who published nearly 900 books.
A pair of perpendicular lines would be line CF and line AJ.
Line BC and line AJ are NOT perpendicular because when a pair of lines are perpendicular, all angles become 90 degrees. It is obvious, in the case, if you were to slide line BC on top of line AJ, the angles will not equal 90 degrees.
We obtain the joint PMF directly from the joint MGF:
![\implies\mathrm{Pr}[X=x,Y=y]=\begin{cases}0.1&\text{for }x=y=0\\0.2&\text{for }x=1,y=0\\0.3&\text{for }x=0,y=1\\0.4&\text{for }x=y=1\\0&\text{otherwise}\end{cases}](https://tex.z-dn.net/?f=%5Cimplies%5Cmathrm%7BPr%7D%5BX%3Dx%2CY%3Dy%5D%3D%5Cbegin%7Bcases%7D0.1%26%5Ctext%7Bfor%20%7Dx%3Dy%3D0%5C%5C0.2%26%5Ctext%7Bfor%20%7Dx%3D1%2Cy%3D0%5C%5C0.3%26%5Ctext%7Bfor%20%7Dx%3D0%2Cy%3D1%5C%5C0.4%26%5Ctext%7Bfor%20%7Dx%3Dy%3D1%5C%5C0%26%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
Then
![\mathrm{Pr}[X=Y]=\mathrm{Pr}[X=Y=0]+\mathrm{Pr}[X=Y=1]=0.1+0.4=\boxed{0.5}](https://tex.z-dn.net/?f=%5Cmathrm%7BPr%7D%5BX%3DY%5D%3D%5Cmathrm%7BPr%7D%5BX%3DY%3D0%5D%2B%5Cmathrm%7BPr%7D%5BX%3DY%3D1%5D%3D0.1%2B0.4%3D%5Cboxed%7B0.5%7D)
Multiply the -3 by what is inside the parentheses.
-3y + 15 =24
subtract 15 from both sides.
-3y=9
divide by -3 on both sides.
y = -3
<h3>
Answer: 6 cm^3</h3>
This is the same as saying 6 cubic cm
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Work Shown:
d = density = 4 g/cm^3
m = mass = 24 g
v = volume = unknown
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d = m/v
4 = 24/v
4v = 24 .... multiply both sides by v
v = 24/4 .... divide both sides by 4
v = 6 cm^3
