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Slav-nsk [51]
3 years ago
14

If the number of equally likely sample outcomes of a single stage of an experiment is 4, what is the total number of elements in

the sample
space if the experiment has 3 stages?
Ο Α.
16
OB. 12
OC. 64
OD.
81
Mathematics
2 answers:
kogti [31]3 years ago
8 0
Yes it would be 64
frutty [35]3 years ago
6 0
OC. 64

because it’s 64
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<h2>Question :</h2>

  • \tt \dfrac{x+2}{x-2} + \dfrac{x-2}{x+2} = \dfrac{5}{6}

<h2>Answer :</h2>

  • \large \underline{\boxed{\bf{x = \dfrac{\pm 2\sqrt{119}}{7}}}}

<h2>Explanation :</h2>

\tt : \implies \dfrac{x+2}{x-2} + \dfrac{x-2}{x+2} = \dfrac{5}{6}

\tt : \implies \dfrac{(x+2)(x+2) + (x-2)(x-2)}{(x-2)(x+2)} = \dfrac{5}{6}

\tt : \implies \dfrac{(x+2)^{2} + (x-2)^{2}}{(x-2)(x+2)} = \dfrac{5}{6}

<u>Now, we know that</u> :

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\tt : \implies \dfrac{x^{2}+2^{2}+ 2 \times x \times 2 + x^{2}+2^{2} - 2 \times x \times 2 }{x^{2}-2^{2}} = \dfrac{5}{6}

\tt : \implies \dfrac{x^{2}+ 4 + \cancel{4x} + x^{2}+ 4 - \cancel{4x}}{x^{2}-4} = \dfrac{5}{6}

\tt : \implies \dfrac{x^{2} + x^{2} + 4 + 4}{x^{2}-4} = \dfrac{5}{6}

\tt : \implies \dfrac{2x^{2} + 8}{x^{2}-4} = \dfrac{5}{6}

<u>By cross multiply</u> :

\tt : \implies (2x^{2} + 8)6= 5(x^{2}-4)

\tt : \implies 12x^{2} + 48 = 5x^{2}-20

\tt : \implies 12x^{2} + 48 - 5x^{2} + 20 = 0

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\tt : \implies 7x^{2} + 0x + 68 = 0

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\tt : \implies x = \dfrac{\pm \cancel{2} \times 2\sqrt{7\times 17}}{\cancel{14}}

\tt : \implies x = \dfrac{\pm2\sqrt{119}}{7}

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