Answer:
x = 55
y = 70
Step-by-step explanation:
since it's all sides are equal its an equilateral triangle
each angle of an equilateral triangle is 60°
therefore,
y - 10 = 60 => y = 60 + 10
y = 70
x + 5 = 60 => x = 60 - 5
x = 55
Answer:
Step-by-step explanation:
<u><em>( 8 ).</em></u> m∠1 = m∠ 4 = m∠ 5 = <em>m∠6 = 52°</em>
<em><u>( 9 ).</u></em> m∠ 2 = m∠ 3 = <em>m∠ 7</em> = m∠ 8 = 180° - 52° <em>= 128°</em>
Answer:
You need more information to graaph this.
Step-by-step explanation:
By definition of covariance,
![\mathrm{Cov}(U,V)=E[(U-E[U])(V-E[V])]=E[UV-E[U]V-UE[V]+E[U]E[V]]=E[UV]-E[U]E[V]](https://tex.z-dn.net/?f=%5Cmathrm%7BCov%7D%28U%2CV%29%3DE%5B%28U-E%5BU%5D%29%28V-E%5BV%5D%29%5D%3DE%5BUV-E%5BU%5DV-UE%5BV%5D%2BE%5BU%5DE%5BV%5D%5D%3DE%5BUV%5D-E%5BU%5DE%5BV%5D)
Since
and
, we have
![E[U]=2E[X]+E[Y]-1](https://tex.z-dn.net/?f=E%5BU%5D%3D2E%5BX%5D%2BE%5BY%5D-1)
![E[V]=2E[X]-E[Y]+1](https://tex.z-dn.net/?f=E%5BV%5D%3D2E%5BX%5D-E%5BY%5D%2B1)
![\implies E[U]E[V]=(2E[X]+E[Y]-1)(2E[X]-(E[Y]-1))=4E[X]^2-(E[Y]-1)^2=4E[X]^2-E[Y]^2+2E[Y]-1](https://tex.z-dn.net/?f=%5Cimplies%20E%5BU%5DE%5BV%5D%3D%282E%5BX%5D%2BE%5BY%5D-1%29%282E%5BX%5D-%28E%5BY%5D-1%29%29%3D4E%5BX%5D%5E2-%28E%5BY%5D-1%29%5E2%3D4E%5BX%5D%5E2-E%5BY%5D%5E2%2B2E%5BY%5D-1)
and

![\implies E[UV]=4E[X^2]-E[Y^2]+2E[Y]-1](https://tex.z-dn.net/?f=%5Cimplies%20E%5BUV%5D%3D4E%5BX%5E2%5D-E%5BY%5E2%5D%2B2E%5BY%5D-1)
Putting everything together, we have
![\mathrm{Cov}(U,V)=(4E[X^2]-E[Y^2]+2E[Y]-1)-(4E[X]^2-E[Y]^2+2E[Y]-1)](https://tex.z-dn.net/?f=%5Cmathrm%7BCov%7D%28U%2CV%29%3D%284E%5BX%5E2%5D-E%5BY%5E2%5D%2B2E%5BY%5D-1%29-%284E%5BX%5D%5E2-E%5BY%5D%5E2%2B2E%5BY%5D-1%29)
![\mathrm{Cov}(U,V)=4(E[X^2]-E[X]^2)-(E[Y^2]-E[Y]^2)](https://tex.z-dn.net/?f=%5Cmathrm%7BCov%7D%28U%2CV%29%3D4%28E%5BX%5E2%5D-E%5BX%5D%5E2%29-%28E%5BY%5E2%5D-E%5BY%5D%5E2%29)
![\mathrm{Cov}(U,V)=4V[X]-V[Y]=4a-a=\boxed{3a}](https://tex.z-dn.net/?f=%5Cmathrm%7BCov%7D%28U%2CV%29%3D4V%5BX%5D-V%5BY%5D%3D4a-a%3D%5Cboxed%7B3a%7D)
Answer:240
Step-by-step explanation:
80 divided by 1/3