answer:The proof can be extended by considering the cumulative distribution functions (CDFs) of X and Y. Let F_X(x) and F_Y(y) be the CDFs of X and Y, respectively. Since X leq Y, we have that F_X(x) geq F_Y(x) for all x. Now, let x^* = VaR_alpha(X). By definition, F_X(x^*) = alpha. Since F_Y(x^*) leq F_X(x^*), we have that F_Y(x^*) leq alpha. Therefore, x^* is also an upper bound for the set {y: F_Y(y) leq alpha}, which implies that VaR_alpha(Y) leq x^* = VaR_alpha(X). Hence, VaR is monotonic even when Y is not a scaled version of X.

answer:To solve the equation, follow these steps: 1. Add 14 to both sides to isolate the term with ( x ): [ frac{x}{2} - 12 + 14 = -14 + 14 ] [ frac{x}{2} + 2 = 0 ] 2. Subtract 2 from both sides to prepare for multiplication: [ frac{x}{2} = -2 ] 3. Multiply both sides by 2 to solve for ( x ): [ 2 cdot frac{x}{2} = -2 cdot 2 ] [ x = -4 ] So, the solution to the equation is ( x = -4 ).

answer:Malcolm X married Betty Shabazz (formerly Betty Sanders) on January 12, 1958, in Lansing, Michigan. Born in 1934, Betty Shabazz grew up in Detroit and attended Tuskegee Institute before transferring to Brooklyn State College School of Nursing, from which she graduated in 1956. Together, Malcolm and Betty had six daughters.

answer:We have the following given data {eq}begin{align} x+y+z &=3 P & (4,1,9) end{align} {/eq} Solution The equation of a plane parallel to another plane {eq}ax+by+cz=d_1{/eq} is given as {eq}ax+by+cz=d_2{/eq} The value of {eq}d_2{/eq} can be determined by plugging in the values of x, y, z corresponding to a point through which this plane is passing. Plugging in our values, we have: {eq}begin{align} x+y+z &=d_2 Rightarrow 4+1+9 &=d_2 Rightarrow d_2 &=14 text{ So, } ~~ x+y+z &=14 & left[ text{This is the equation of the plane which is parallel to the given plane } right] end{align} {/eq} Therefore, the equation of the parallel plane is {eq}displaystyle boxed{color{blue} { x+y+z =14 }} {/eq}