Consider the set defined by the following inequalities: (x1 ≥ x2 − 1 and x2 ≥ 0) or (x1 ≤ x2 − 1 and x2 ≤ 0). 1. draw the set. is it convex? 2. show that it can be described as a single quadratic inequality of the form q( x) = x ⊤ ax + 2b ⊤ x + c ≤ 0, for a matrix a = a ⊤ ∈ r2,2, b ∈ r2 and c ∈ r which you will determine. 3. what is the convex hull of this set?

What are the relative frequencies to the nearest hundredth of the columns of the two-way table?

If f(x) = x+8 and g(x) = 4x- 3, find (f+g)(x)

Consider the following estimates from the early 2010s of shares of income to each group. country poorest 40% next 30% richest 30% bolivia 10 25 65 chile 10 20 70 uruguay 20 30 50 1.) using the 4-point curved line drawing tool, plot the lorenz curve for bolivia. properly label your curve. 2.) using the 4-point curved line drawing tool, plot the lorenz curve for uruguay. properly label your curve.