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3 years ago

How many bit strings of length 12 are palindromes and contain 10 as sub string

1 answer:

4 0

There are as many palindromic 12-bit binary strings as there are permutations with repetition of 6-bit binary strings, which is equal to $2^6=64$ .

There are also only two permutations with repetition of 6-bit binary strings, that when each of them is mirrored and the result is "glued" to the right side of the original string, will give a palindromic string without 10 as a substring.
Those strings are 000000 and 111111.

Therefore there are $64-2=62$ palindromic 12-bit binary strings with 10 as substring.

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You want to go to graduate school, so you ask your math professor, Dr. Emmy Noether, for a letter of recommendation. You estimat

den301095 [7]

Answer:

$P(G) = 0.69$

$P(S | G) = 0.81$

$P(M|G') = 0.26$

Step-by-step explanation:

From the question we are told the

The probability of getting into getting into graduated school if you receive a strong recommendation is $P(G |S) = 0.80$

The probability of getting into getting into graduated school if you receive a moderately good recommendation is $P(G| M) = 0.60$

The probability of getting into getting into graduated school if you receive a weak recommendation is $P(G|W) = 0.05$

The probability of getting a strong recommendation is $P(S) = 0.7$

The probability of receiving a moderately good recommendation is $P(M) = 0.2$

The probability of receiving a weak recommendation is $P(W) = 0.1$

Generally the probability that you will get into a graduate program is mathematically represented as

$P(G) = P(S) * P(G|S) + P(M) * P(G|M) + P(W) * P(G|W)$

=> $P(G) = 0.7 * 0.8 + 0.2 * 0.6 + 0.1 * 0.05$

=> $P(G) = 0.69$

Generally given that you did receive an offer to attend a graduate program, what is the probability that you received a strong recommendation is mathematically represented as

$P( S|G) = \frac{ P(S) * P(G|S)}{ P(G)}$

=> $P(S|G) = \frac{ 0.7 * 0.8 }{0.69}$

=> $P(S | G) = 0.81$

Generally given that you didn't receive an offer to attend a graduate program the probability that you received a moderately good recommendation is mathematically represented as

$P(M|G') = \frac{ P(M) * (1- P(G|M))}{(1 - P(G))}$

$P(M| G') = \frac{ 0.2 * (1- 0.6)}{ (1 - 0.69)}$

$P(M|G') = 0.26$

3 0

3 years ago

Write 0.16666 as a fraction

olchik [2.2K]

This one you can do by multiplying the number by ten, getting 1.666, or 1+0.66. 0.66 is easy to put into a fraction form as 2/3. add the other 3/3 from the whole 1 to get 5/3. From here you either divide by 10 or multiply by 1/10, as KCF will do that anyways if you divide to get 5/30, or 1/6.

4 0

3 years ago

Read 2 more answers

The surface area of a cube is 328.56 square inches. How long are it’s sides?

gizmo_the_mogwai [7]

Answer:

7.4 in

Step-by-step explanation:

Surface area of a cube = 6s²

(where s is the side length)

Given: