Consider idealized versions of two U. S. professional sports. In football, a team can score 2,3, or 6 points at a time. Having scored 6 points, it can then score an additional 0, 1, or 2 points. In baseball, runs (points) occur one at a time. However, if a game ends with each team having the same number of runs, an additional inning is played to resolve the tie. (This rule is applied recursively.) We assume, somewhat unrealistically, that there is no upper limit to the scores for either game. Required:
a. Give a regular expression for the set of possible football scores: m–n, with m and n in unary notation.
b. Give an NFA for the same language.
c. Same as b), but now give a DFA.
d. Show that the set of possible baseball scores is not regular.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation:

∡ eia and ∡ kij are congruent

step-by-step explanation: