Answer:
They both owe each other
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
-10 + 10
-10 and 10 are additive inverses, so when we add them, it is equal to zero
-10 + 10 = 0
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:
Vertical angles are angles opposite of each other. hope it helps
Answer:
4 miles to the nearest mile.
Step-by-step explanation:
Circumference of the track = 2 pi r
= 2*pi*0.2 = 1.257 miles
Ellie ran 3 times around the track so
the distance she ran is 3* 1.257
= 4 miles
