Scenario 1: Which states would get you to 270 the fastest? List the states and the number of votes you used in this scenario

Alex drew a circle with right triangle prq inscribed in it, as shown below: the figure shows a circle with points p, q, and r on it forming an inscribed triangle. side pq is a chord through the center and angle r is a right angle. arc qr measures 80 degrees.

There are three bags: a (contains 2 white and 4 red balls), b (8 white, 4 red) and c (1 white 3 red). you select one ball at random from each bag, observe that exactly two are white, but forget which ball came from which bag. what is the probability that you selected a white ball from bag a?

If tan2a=cot(a+60), find the value of a, where 2a is an acute angle