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aalyn [17]
3 years ago
9

Factor completely 4x^2-1

Mathematics
1 answer:
allochka39001 [22]3 years ago
4 0
<span>4x^2-1 = (2x +1)(2x - 1)

using a^2 - b^2 = (a+b)(a-b)

hope that helps</span>
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Determinar la longitud de la hipotenusa del siguiente triángulo si se conocen las medidas que se indican de los demás triángulos
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2 years ago
Carlos has scored 83, 81, and 73 on his previous three tests. What score does he need on his next test so that his average (mean
disa [49]

Answer:

95

Step-by-step explanation:

let x be his mark in the fourth test, then

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3 years ago
For each given p, let ???? have a binomial distribution with parameters p and ????. Suppose that ???? is itself binomially distr
pshichka [43]

Answer:

See the proof below.

Step-by-step explanation:

Assuming this complete question: "For each given p, let Z have a binomial distribution with parameters p and N. Suppose that N is itself binomially distributed with parameters q and M. Formulate Z as a random sum and show that Z has a binomial distribution with parameters pq and M."

Solution to the problem

For this case we can assume that we have N independent variables X_i with the following distribution:

X_i Bin (1,p) = Be(p) bernoulli on this case with probability of success p, and all the N variables are independent distributed. We can define the random variable Z like this:

Z = \sum_{i=1}^N X_i

From the info given we know that N \sim Bin (M,q)

We need to proof that Z \sim Bin (M, pq) by the definition of binomial random variable then we need to show that:

E(Z) = Mpq

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The deduction is based on the definition of independent random variables, we can do this:

E(Z) = E(N) E(X) = Mq (p)= Mpq

And for the variance of Z we can do this:

Var(Z)_ = E(N) Var(X) + Var (N) [E(X)]^2

Var(Z) =Mpq [p(1-p)] + Mq(1-q) p^2

And if we take common factor Mpq we got:

Var(Z) =Mpq [(1-p) + (1-q)p]= Mpq[1-p +p-pq]= Mpq[1-pq]

And as we can see then we can conclude that   Z \sim Bin (M, pq)

8 0
3 years ago
Find the greatest common factor of 4c3 and 6m2.
Brums [2.3K]

Answer:

The GCF is 2

Step-by-step explanation:

Here, we want to find the greatest common factors of the two terms

We have the terms written in terms of the products of their multiples as follows;

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3 0
3 years ago
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