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3 years ago

A relay team of 4 swimmers is to be formed from a swim team with 20 member. How many different relay teams are possible?

1 answer:

5 0

<span>When order does not matter you use what is called n choose k formula

n!/(k!(n-k)!) where n is the number of things to choose from and k is the number of choices made, in this case:

20!/(4!(20-4)!)=4845</span>

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Find the percentage change from the first quantity to the second quantity: from 60 km/h to 45 km/h

stiks02 [169]

Answer:

75%

Step-by-step explanation:

6 0

3 years ago

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 $n = 20$

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

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

$P(X = 16) = C_{20,16}.(0.75)^{16}.(0.25)^{4} = 0.1897$

$P(X = 17) = C_{20,17}.(0.75)^{17}.(0.25)^{3} = 0.1339$

$P(X = 18) = C_{20,18}.(0.75)^{18}.(0.25)^{2} = 0.0669$

$P(X = 19) = C_{20,19}.(0.75)^{19}.(0.25)^{1} = 0.0211$

$P(X = 20) = C_{20,20}.(0.75)^{20}.(0.25)^{0} = 0.0032$

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1897 + 0.1339 + 0.0669 + 0.0211 + 0.0032 = 0.4148$

c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

$E(X) = 22*0.75 = 16.5$

The closest integer to 16.5 is 17.

7 0

3 years ago

Write the expression 5³⋅5⁴ using a single base

Mnenie [13.5K]

Answer:

Step-by-step explanation:

If two numbers have the same base, add the powers

5³ * 5⁴ = 5⁽³⁺⁴⁾ = 5⁷

6 0

4 years ago

Read 2 more answers

What is the slope of the line that passes through the points

Oksana_A [137]

The slope is ∞ , line is a vertical line parallel to y axis.

<h3>What is a Straight Line Function ?</h3>

A straight line function is a function that can be represented by y = mx +c , where m is the slope of the line and c is the intercept on the y axis.

There are two points given for a line ,

The slope is represented by

$\rm m = \dfrac{y_2 -y_1}{x_2 -x_1}\\\\m = \dfrac{31-6}{1-1}$

m = ∞

which means the line is a vertical line parallel to y axis.

To know more about Straight Line Function

brainly.com/question/21145944

#SPJ1

4 0

2 years ago

Please Help With this question!<br> There are 3 pictures!

Likurg_2 [28]

Corresponding Angles postulate is ur answer mate

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3 years ago