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3 years ago

In how many ways can 7 people line if A needs to be first or last and B needs to be in the middle

Mathematics

1 answer:

12345 [234]3 years ago

8 0

Answer:

<em>Assuming person A and person B are part of the 7 people</em>, there are 10 ways the 7 people can line up if A needs to be first or last and B needs to be in the middle.

Step-by-step explanation:

There are 2 places for A (first, last) and 5 places for B (anywhere but first or last). 2 x 5 = 10.

You might be interested in

How much power is used if a force of 35 newtons is used to push a box a distance of 20 meters in 5 seconds

Umnica [9.8K]

Answer:

140 W

Step-by-step explanation:

Power is measured in joules per second, or watts. A joule is a measure of energy equal to 1 newton-meter. These unit relationships tell you how to combine the numbers:

power = (35 N)(20 m)/(5 s) = (35·20/5) N·m/s = 140 J/s = 140 W

6 0

3 years ago

Consider this expression.(The square root of a to the power of 3 - 7 )+ lbl When a = 2 and b = -4, the value of the expression i

lesya692 [45]

Given that: a = 2, b = -4

$\sqrt{a^3-7}\text{ + |b| = }\sqrt{2^3-7}\text{ + |-4| = }\sqrt{8-7}\text{ }+\text{ 4 = }\sqrt{1}+\text{ 4 = 1 + 4 = 5}$

3 0

1 year ago

Find the slope of the line that passes through the points (2.1) and (-1.-1).

sp2606 [1]

Answer: The slope is $\frac{2}{3}$

Step-by-step explanation:

The slope can be calculated with the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Then, knowing that the line passes through the points (2,1) and (-1,-1), we can substitute the coordinates into the formula.

In this case:

$y_2=-1\\y_1=1\\x_2=-1\\x_1=2$

Therefore, the slope of the line that passes through the points (2,1) and (-1,-1) is:

$m=\frac{-1-1}{-1-2}\\\\m=\frac{-2}{-3}\\\\m=\frac{2}{3}$

6 0

3 years ago

Critical Thinking: Empirical/Quantitative Skills

aliya0001 [1]

Answer:

1. 0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.

2. 0.4522 = 45.22% probability that at most 180 passengers show up for the flight.

3. 0.5478 = 54.78% probability that more than 180 passengers show up for the flight.

Step-by-step explanation:

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.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .