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4 years ago

1/x + 1/4 = 7/12 solve for x

1 answer:

5 0

Given equation is
$\frac{1}{x} + \frac{1}{4} = \frac{7}{12}$

We can solve it by subtracting 1/4 both side
$\frac{1}{x} + \frac{1}{4} - \frac{1}{4} = \frac{7}{12} - \frac{1}{4}$

$\frac{1}{x} = \frac{7}{12} - \frac{1}{4}$
                          $= \frac{7 - 3}{12}$
                          $= \frac{4}{12}$
                          $= \frac{1}{3}$

So $\frac{1}{x} = \frac{1}{3}$
On comparing x = 3.

SO the solution of equation is x = 3

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Previous concepts

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We can model the number of correct questions answered with a binomial distribution $X \sim Binom(n = 6, p = 1/4=0.25)$

Solution to the problem

Assuming the following questions:

a) the first question she gets right is the 6th question?

For this case we want the first 5 questions incorrect and the last one correct, assuming independence we have:

$p = (3/4)^5 *(1/4) =0.0593$

(b) she gets all of the questions right?

For this case we want all the questions right so then we want this:

$P(X=6) = (6C6) (0.25)^6 (1-0.25)^{6-6}= 0.000244$

(c) she gets at least one question right?

For this case we want this probability:

$P(X \geq 1)$

And we can use the complement rule like this:

$P(X \geq 1) = 1-P(X$

$P(X=0) = (6C0) (0.25)^0 (1-0.25)^{6-0}= 0.17798$

And replacing we have:

$P(X \geq 1) = 1-P(X$

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