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The 'Shadow Cabinet' is a feature of which political system?
The Shadow Cabinet is a specialized group of opposition senior spokespeople in the Westminster (UK) system.
A satellite orbits Earth at constant speed $v$. A mass $m$ is ejected from it so that it just barely escapes Earth's gravitational pull. What additional kinetic energy must be given to mass $m$?
The satellite is in circular orbit at some radius $r$: $v = \sqrt{GM/r}$, so $v^2 = GM/r$.
Escape speed from radius $r$: $v_e = \sqrt{2GM/r} = v\sqrt{2}$
Extra KE needed $= \frac{1}{2}mv_e^2 - \frac{1}{2}mv^2 = \frac{1}{2}m(2v^2) - \frac{1}{2}mv^2 = \frac{1}{2}mv^2$
Use: $P(\text{exactly one of }X\text{ or }Y) = P(X)+P(Y)-2P(X\cap Y)$.
Adding all three equations:
$2[P(A)+P(B)+P(C)] - 2[P(A\cap B)+P(B\cap C)+P(C\cap A)] = \dfrac{3}{4}$
$\Rightarrow P(A)+P(B)+P(C) - [P(A\cap B)+P(B\cap C)+P(C\cap A)] = \dfrac{3}{8}$ ...(i)
Using inclusion-exclusion:
$P(A\cup B\cup C) = P(A)+P(B)+P(C)-P(A\cap B)-P(B\cap C)-P(C\cap A)+P(A\cap B\cap C)$
$= \dfrac{3}{8} + \dfrac{1}{16} = \dfrac{6}{16}+\dfrac{1}{16} = \dfrac{7}{16}$
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