<img src="https://tex.z-dn.net/?f=5%20%2B%20%20%5Cfrac%7Bx%20-%202%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7Bx%20%2B%203%7D%7B8%7D%20" i

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2 years ago

d="TexFormula1" title="5 + \frac{x - 2}{3} = \frac{x + 3}{8} " alt="5 + \frac{x - 2}{3} = \frac{x + 3}{8} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

sammy [17]2 years ago

7 0

First multiply each term by 24(the common denominator found by 8×3) to remove the fractions and make things easier.
$24(5) + 24( \frac{x - 2}{3} ) = 24( \frac{x + 3}{8} )$
This will give you,
$120 + 8(x - 2) = 3(x + 3)$
Then just continue to simplify and isolate the variable.
$120 + 8x - 16 = 3x + 9$
$8x + 104 = 3x + 9$
$5x = - 95$
$x = - 19$

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a. 0.1681 = 16.81% probability that all five qualify for the favorable rate.

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Binomial probability distribution

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

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.

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

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This means that $p = 0.7$

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a. All five qualify for the favorable rate

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

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b. At least four qualify for the favorable rates

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$P(X \geq 4) = P(X = 4) + P(X = 5)$

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$P(X \geq 4) = P(X = 4) + P(X = 5) = 0.3602 + 0.1681 = 0.5283$

0.5283 = 52.83% probability that at least four qualify for the favorable rates

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