This problem concerns languages over the alphabet Σ = {1}. For any two integers q, r ≥0, define the language Lr, q over Σ as
Lr, q ={1mq+r : m ≥0}={1q,1q+r,12q+r,...}.
For instance, L1,3 ={1,1111,1111111,...}.
(a) Show that for every q and r, the language Lr, q is regular.
(b) Show that if L is a regular language over Σ, then L can be written as
L = Lr1,q ∪ Lr2,q ∪···∪ Lrk, q ∪ L0,
where 0 ≤ r1 < ··· < rk are integers and L0 is a finite set.

Write a function that draws a pool ball. this function should take as parameters, the color, the number that should go on the pool ball, and the location of the center of the pool ball. the radius of the pool balls should be pool_ball_radius, and the font of the number should be pool_ball_font. the text of the pool ball font should be white. drawpoolball(color.orange, 5, 100, 100); drawpoolball(color.green, 6, 50, 200); drawpoolball(color.red, 3, 150, 350); drawpoolball(color.blue, 2, 250, 140); to center the numbers on the pool ball, you should use the getwidth() and getheight() methods. you are allowed to call these methods on your text object, such as txt.

In cell b18, enter a formula to calculate the amount budgeted for meals. this amount is based on the daily meal allowance and the total travel days (# of nights+1).

All of these are true about using adhesive except: a. dissimilar materials can be joined. b. mixing tips are product and material specific. c. a specific application gun may be required. d. two-part adhesives are dispensed using two mixing tips