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marusya05 [52]
2 years ago
12

If a given triangle

Mathematics
2 answers:
BartSMP [9]2 years ago
4 0

Answer:

solution,

x+85+24=180 (being sum of angle of triangle)

x+109=180

x=180-109

x=71

therefore, the third angle is 71

Furkat [3]2 years ago
4 0

Answer just below :-

Step-by-step explanation:

Let the third angle be x

Then;

24°+85°+x = 180 ( sum of interior angles of a triangle is 180°)

or; 109°+x = 180°

or; x = 180°-109°

:x=71°

Therefore the measure of third angle is 71°

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Samantha bought 26 total fish. Each goldfish cost $3 and each guppy costs $4. She spent $86 total. How many guppies did she buy?
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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.

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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.

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The standard deviation of the binomial distribution is:

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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)}.

Assume that there is a 0.905 probability that a passenger with a ticket will show up for the  flight.

This means that p = 0.905

Also assume that the airline sells 200 tickets

This means that n = 200

Question 1:

Exactly, so we can use the P(X = x) formula, to find P(X = 180).

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

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Z = \frac{180.5 - 181}{4.15}

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p + 0.4522 = 1

p = 1 - 0.4522 = 0.5478

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

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