Answer:
below :)
Step-by-step explanation:
1) 12
2}3/2
3)224.64
4)2 quarters
5)w=50
6)m=6y+7
7)42/6=7 x=6
We can divide 143.50 by 7. This gives us 20.5. This means that she works 20.5 hours a week or 21 hours if you round up.
Step-by-step explanation:
Mean:
E[Y] = E[3X₁ + X₂]
E[Y] = 3 E[X₁] + E[X₂]
E[Y] = 3µ + µ
E[Y] = 4µ
Variance:
Var[Y] = Var[3X₁ + X₂]
Var[Y] = 3² Var[X₁] + 2 Covar[X₁, X₂] + 1² Var[X₂]
(the covariance is 0 since X₁ and X₂ are independent)
Var[Y] = 9 Var[X₁] + Var[X₂]
Var[Y] = 9σ² + σ²
Var[Y] = 10σ²
identity used is
x³ + y³+ z³– 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx).
then use
(x+y+z)² = x²+y²+z²+2(xy+yz+xz)
225= 83 + 2(xy+yz+xz)
xy+yz+xz = (225-83)/2
xy+yz+xz= 142/2
xy+yz+xz= 71
ok
now use identity
x³ + y³+ z³– 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx).
now
x³ + y³+ z³– 3xyz = 15 (83 – xy – yz – zx).
= 15[83 - (71)]
= 15×12
=180
