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Tasya [4]
3 years ago
10

Factorise 24p2 + pq - 23q²​

Mathematics
1 answer:
Novosadov [1.4K]3 years ago
3 0

<em>24p² + pq - 23q² = </em>

<em>= 24p² + 24pq - 23pq - 23q²</em>

<em>= 24p(p + q) - 23q(p + q)</em>

<em>= (p + q)(24p - 23q)</em>

<em />

<em />

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Using the binomial distribution, the probabilities are given as follows:

a) 0.4159 = 41.59%.

b) 0.5610 = 56.10%.

c) 0.8549 = 85.49%.

<h3>What is the binomial distribution formula?</h3>

The formula is:

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

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

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
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For this problem, the values of the parameters are:

n = 3, p = 0.76.

Item a:

The probability is P(X = 2), hence:

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

P(X = 2) = C_{3,2}.(0.76)^{2}.(0.24)^{1} = 0.4159

Item b:

The probability is P(X < 3), hence:

P(X < 3) = 1 - P(X = 3)

In which:

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

P(X = 3) = C_{3,3}.(0.76)^{3}.(0.24)^{0} = 0.4390

Then:

P(X < 3) = 1 - P(X = 3) = 1 - 0.4390 = 0.5610 = 56.10%.

Item c:

The probability is:

P(X \geq 2) = P(X = 2) + P(X = 3) = 0.4159 + 0.4390 = 0.8549

More can be learned about the binomial distribution at brainly.com/question/24863377

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Answer:

Step-by-step explanation:

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Answer:

The answer to your question is:  letter D

Step-by-step explanation:

First we need to find the distances between the points,

distance AB = 8       get it just by counting the points in the graph

distance AC = 9       get it just by counting the points in the graph

To know the distance BC, use the pythagorean theorem

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         c2 = 8² + 9²

         c² = 64 + 81

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Finally, perimeter = AB + AC + BC

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