In a state legislature the elected representatives include 19 Democrats, 14 Republicans, and 3 Independents. What's the probability that a random selection of 6 legislators would include 2 of each?

Create and solve a linear equation that represents the model, where squares and triangles are shown evenly balanced on a balance beam. assume the weight of a square is 1 unit and the weight of a triangle is unknown.

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?