(automata theory) problem statement:

let l be any regular language over an alphabet σ. using l, we define

chop(l) = {w : ∃ x, y, z ∈ σ∗ , xyz ∈ l, w = xz}.

show that chop(l) is regular or give a counter-example.

Aswim teacher sells lesson packages. the best deal has the highest ratio of lessons to total cost.swim lesson packagesnumber of lessons total cost$10$4010 1 $8015$80which package is the best deal? l lesson for $105 lessons for $4010 lessons for $8015 lessons for $80mark this and returnsave and exit

(i really need ) read the story problem, and then answer the questions that follow. gordon works for a graphic design firm and is creating a label for a food truck vendor. the vendor specializes in finger food and wants to sell food in right conical containers so that they are easy for people to hold. to complete his label, gordon needs to collect several different measurements to ensure that the label he designs will fit the surface of the container. gordon has been told that the containers have a diameter of 4 inches and a height of 6 inches. part a: find the slant height of the cone. the slant height is the distance from the apex, or tip, to the base along the cone’s lateral surface. show your work. part b: find the measure of the angle formed between the base of the cone and a line segment that represents the slant height. part c: imagine two line segments where each represents a slant height of the cone. the segments are on opposite sides of the cone and meet at the apex. find the measurement of the angle formed between the line segments.

One cell phone plan charges $20 per month plus $0.15 per minute used. a second cell phone plan charges $35 per month plus $0.10 per minute used. write and solve an equation to find the number of minutes you must talk to have the same cost for both calling plans.