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3 years ago

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Suppose S is a recursively defined set, defined by - the number 1 is in S - if n is in S, then so is 3n + 2 - if n is in S, then

so is 5n - 1 - if n is in S, then so is n + 7. Suppose you want to prove using structural induction that all members of S have a certain property. What do you have to prove in the base step?

1 answer:

Tatiana [17]3 years ago

8 0

Answer:

See answer below

Step-by-step explanation:

Using structural induction, we would have to prove that 1 and all the numbers derived from this fact, have the property.

That is to say, we would have to prove that

1, 3*1+2, 5*1-1 and 1+7 = {1, 4, 5, 8} have the property we want to prove S has.

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Every time I use a piece of scrap paper, I crumple it up and try to shoot it inside the recycling bin across the room. I'm prett

valentinak56 [21]

Using the binomial distribution, it is found that there is a 0.0012 = 0.12% probability at least two of them make it inside the recycling bin.

<h3>What is the binomial distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

With 5 shoots, the probability of making at least one is $\frac{211}{243}$ , hence the probability of making none, P(X = 0), is $\frac{232}{243}$ , hence:

$(1 - p)^5 = \frac{232}{243}$

$\sqrt[5]{(1 - p)^5} = \sqrt[5]{\frac{232}{243}}$

1 - p = 0.9908

p = 0.0092

Then, with 6 shoots, the parameters are:

n = 6, p = 0.0092.

The probability that at least two of them make it inside the recycling bin is:

$P(X \geq 2) = 1 - P(X < 2)$

In which:

[P(X < 2) = P(X = 0) + P(X = 1)

Then:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{6,0}.(0.0092)^{0}.(0.9908)^{6} = 0.9461$

$P(X = 1) = C_{6,1}.(0.0092)^{1}.(0.9908)^{5} = 0.0527$

Then:

P(X < 2) = P(X = 0) + P(X = 1) = 0.9461 + 0.0527 = 0.9988

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9988 = 0.0012$

0.0012 = 0.12% probability at least two of them make it inside the recycling bin.

More can be learned about the binomial distribution at brainly.com/question/24863377

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2 years ago

Anya wanted a book that cost $34.99 regularly at the bookstore. If Anya had a coupon for 20% off any regularly priced item at th

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Answer:

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Step-by-step explanation:

34.99*.20 = 6.998

34.99-6.998 = 27.992

the answer rounded would be $27.99

Hope this helps

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3 years ago

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victus00 [196]

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Answer:

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Step-by-step explanation:

Refer to attachment.

<em>Hope</em><em> </em><em>it</em><em> </em><em>helps</em><em>.</em>

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2 years ago