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3 years ago

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Wilson’s theorem says that a number N is prime if and only if (N − 1)! ≡ −1 (mod N). (a) If p is prime, then every number 1 ≤ x

< p is invertible (has an inverse) modulo p. Which of these numbers are their own inverse?

1 answer:

olga2289 [7]3 years ago

6 0

Answer:

The answer to this question can be explained below as:

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At a 20th high school reunion, all the classmates were asked the number of children they had. The probability of having a partic

finlep [7]

Answer:

a) We need to check two conditions:

1) $\sum_{i=1}^n P_i = 1$

$0.05+0.14+0.34+0.24+0.11+0.07+0.02+0.02+0.01= 1$

2) $P_i \geq 0 , \forall i=1,2,...,n$

So we satisfy the two conditions so then we have a probability distribution

b) $P(C \geq 1)$

And we can use the complement rule and we got:

$P(C \geq 1)= 1-P(C$

c) $P(C=0) = 0.05$

d) For this case we see that the result from part b use the probability calculated from part c using the complement rule.

Step-by-step explanation:

For this case we have the following probability distribution given:

C 0 1 2 3 4 5 6 7 8

P 0.05 0.14 0.34 0.24 0.11 0.07 0.02 0.02 0.01

And we assume the following questions:

a) Verify that this is a probability distribution

We need to check two conditions:

1) $\sum_{i=1}^n P_i = 1$

$0.05+0.14+0.34+0.24+0.11+0.07+0.02+0.02+0.01= 1$

2) $P_i \geq 0 , \forall i=1,2,...,n$

So we satisfy the two conditions so then we have a probability distribution

b) What is the probability one randonmly chosen classmate has at least one child

For this case we want this probability:

$P(C \geq 1)$

And we can use the complement rule and we got:

$P(C \geq 1)= 1-P(C$

c) What is the probability one randonmly chosen classmate has no children

For this case we want this probability:

$P(C=0) = 0.05$

d) Look at the answers for parts b and c and explain their relationship

For this case we see that the result from part b use the probability calculated from part c using the complement rule.

5 0

3 years ago

3) Consider a triangle with side lengths 5 and 13. What are the possibilities for the third side if the

mars1129 [50]

Answer:

find the square of both numbers

13²=169

5²=25

minus the square

169-25 to get 144

find the square root of 144

✓144=12 the third side is 12

7 0

2 years ago

Read 2 more answers

You invest $12,000 at 3.8% annual interest compounded annually. How much will you have at the end of 5 years?

Serjik [45]

Answer:

The answer is 60,000.

Step-by-step explanation:

If you invest 12,000 at 3.8 annual interest. Annual means yearly, so that's every year. 12,000 x 5 is 60,000 that's why the answer is 60,000. If the answer is incorrect or correct let me know. If it's correct, mark me as brainlest, give me a rating, or say thank you! Have A Great Day.

3 0

2 years ago

Test for the commutative property of union and intersection of the sets P = { x : x is all real numbers between 2 and 7} and Q =

In-s [12.5K]

Answer:

Step-by-step explanation:

P = {x : x is a real number between 2 and 7}

{x: 3,4,5,6}

Q = {x : x is all rational number between 2 and 7}

{4 }

We know that P contains all the rational numbers between 2 and 7.

And P ∪ Q and Q ∪ P each of them contain all the real numbers which are between 2 and 7.

{3,4,5,6}

Here Q is the proper subset of P

P ∩ Q = Q ∩ P = Q= {4}

4 0

2 years ago

Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the requirements that

masha68 [24]

Answer:

This procedure does not result in a binomial distribution because in each trial there are more than two possible outcomes, that is, this problem cannot be simplified as a yes or no question.

Step-by-step explanation:

For the binomial probability distribution being satisfied, two things are necessary:

1) The answer can only be two outcomes, two possibilities, for example, yes/no questions.

2) The probability of a success(an answer) on each trial must be the same. That is, if we are going to survey 100 people if they are Buffalo Bills fans, they will answer yes or no, and each of those 100 people will have the same probability of being a Buffalo Bills fans.

In this problem, we have that:

Surveying 20 college students and recording their favorite TV show.

There is infinite possibilities for each answer. One can answer Narcos, other Monday Night Football, other Sportscentre, and so it goes.

So this procedure does not result in a binomial distribution because in each trial there are more than two possible answers, that is, this problem cannot be simplified as a yes or no question.

If for example, we asked the 20 students if Monday Night Football was their favorite show, then they could answer only yes or no, so it would be a binomial procedure.

3 0

3 years ago