The recursive definition given below defines a set S of strings over the alphabet {a, b}: Base case: λ ∈ S and a ∈ S Recursive rule: if x ∈ S then, xb ∈ S (Rule 1) xba ∈ S (Rule 2) This problem asks you to prove that the set S is exactly the set of strings over {a, b} which do not contain two or more consecutive a's. In other words, you will prove that x ∈ S if and only if x does not contain two consecutive a's. The two directions of the "if and only if" are proven separately. (a) Use structural induction to prove that if a string x ∈ S, then x does not have two or more consecutive a's.

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step-by-step explanation:

the answer is 0.071

good luck! : d

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages