Find the value of the variable in the polygon.

Mathematics

1 answer:

galben [10]2 years ago

7 0

Answer:

103

Step-by-step explanation:

This shape is pentagon.

Note : -

Sum of interior angles of a pentagon is 540.

115 + 105 + 117 + 100 + x = 540

437 + x = 540

x = 540 - 437

x = 103

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6 men and 8 women are going to be assigned to a specific row of seats in a theater. If the 14 tickets for the numbered seats are

Sedbober [7]

If exactly one woman is to sit in one of the first 5 seats, then it means that 4 men completes the first 5 seats.
No of ways 4 men can be selected from 6 men = 6C4 = 15
No of ways 4 men can sit on 5 seats = 5P4 = 120
No of ways 1 woman can be selected fom 8 women = 8C1 = 8
No of ways 1 woman can sit on 5 seats = 5P1 = 5

No of ways <span>that exactly one woman is in one of the first 5 seats = 15 * 120 * 8 * 5 = 72,000

No of ways 14 people can be arranged in 14 seats = 14!

Probability that exactly one woman is in one of the first 5 seats = 72,000 / 14! = 0.0000008259 = 0.000083%
</span>

8 0

2 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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .