Design a pda recognizing each of the following languages:
(1) {w | w = a nb n , n is odd}
(2) {w | w = w r and length of w is odd }
(3) {w | w = a nb 2n , n ≥ 1 }
(4) {w | w = a nb n+mc m, n ≥ 0, m ≥ 1 }
(5) {w | w = a 2nb 3n , n ≥ 0 }
(6) {w | w = a nb m, n ≥ 1, m ≥ 1 and n 6= m }

What are the related frequencies to the nearest hundredth of the columns of the two way table? group 1: a-102 b-34group 2: a-18 b-14edited: i don’t have all day to be waiting for an answer. i figured it out.

(05.03 mc) part a: explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−2 intersect are the solutions of the equation 4x = 2x−2. (4 points) part b: make tables to find the solution to 4x = 2x−2. take the integer values of x between −3 and 3. (4 points) part c: how can you solve the equation 4x = 2x−2 graphically? (2 points)

For the chance to be team captain, the numbers 1-30 are put in a hat and you get two chances to pick a number, without replacement. which formula correctly shows how to find the probability that you choose the number 1 and then 2?