Consider the single-input single-output LTI system x_ = 2 4 1 1 1 0 1 1 0 0 1 3 5 | {z } T 2 4 1 1 0 0 1 0 0 0 1 3 5 2 4 1 1 0 0 1 1 0 0 1 3 5 | {z } T1 x + 2 4 b1 b2 b3 3 5u: What conditions should b1; b2; b3 satisfy for the system to be controllable? You will need to simplify the conditions to the simplest possible form to get the full credit. 4

Solve each quadratic equation by factoring and using the zero product property. [tex]x^2+6x+8=0[/tex]

Data from 2005 for various age groups show that for each $100 increase in the median weekly income for whites, the median weekly income of blacks increases by $105. also, for workers of ages 25 to 54 the median weekly income for whites was $676 and for blacks was $527. (a) let w represent the median weekly income for whites and b the median weekly income for blacks, and write the equation of the line that gives b as a linear function of w. b = (b) when the median weekly income for whites is $760, what does the equation in (a) predict for the median weekly income for blacks?

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