What is the prime factorization of 65

Mathematics

2 answers:

Juliette [100K]3 years ago

6 0

<u>Answer: </u>

Prime factorization of 65 is $5 \times 13$

<u>Solution: </u>

Need to find the prime factorization of 65.

Prime factorization is finding all the prime factors of 65.

Method is to take prime number one by one . check whether the given number is divisible by the prime number till you get all the prime factors of given number.

In our case number is 65 . since given number 65 is not divisible by first two prime number that are 2 and 3 , divide 65 by third prime number = 5

$\frac{65}{5} = 13$

That means 65 = $5 \times 13$

Now if you see, both factors that are 5 and 13 are prime numbers.

So prime factorization of 65 is $5 \times 13$

Gnoma [55]3 years ago

5 0

65 has factors of 5 and 13

5•13

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The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

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

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

In this problem we have that:

$p = 0.75$

a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ . So

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

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$