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3 years ago

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A university has 28,980 students. In a random sample of 180 students, 12 speak three or more languages. Predict the number of st

udents at the university who speak three or more languages. The expected number of students at the university who speak three or more languages is .

1 answer:

anygoal [31]3 years ago

5 0

Word | know | Unknown
Language| 12 | x
Total | 180 | 28980
Use cross multiply:
12(28980) = 180(x)
347760 = 180x
347760/180=1932

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Answer:

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Step-by-step explanation:

Apparently, you want to simplify ...

$\displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}$

so the denominator is rational. It looks like the form you want is ...

$\dfrac{A\sqrt{2} + B\sqrt{3} + C\sqrt{7} + D\sqrt{E}}{F}$

And you want to know the sum A+B+C+D+E+F.

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We can start by multiplying numerator and denominator by a conjugate of the denominator. Then we can multiply numerator and denominator by a conjugate of the resulting denominator.

$\displaystyle =\frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}\cdot\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{\sqrt{2} + \sqrt{3} - \sqrt{7}}=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\\\\=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\cdot\frac{\sqrt{6}+1}{\sqrt{6}+1}=\frac{(1+\sqrt{6})(\sqrt{2}+\sqrt{3}-\sqrt{7})}{10}\\\\=\frac{\sqrt{2}+\sqrt{3}-\sqrt{7}+2\sqrt{3}+3\sqrt{2}-\sqrt{42}}{10}=\frac{4\sqrt{2}+3\sqrt{3}-\sqrt{7}-\sqrt{42}}{10}$

Comparing this to the desired form we have ...

A = 4, B = 3, C = -1, D = -1, E = 42, F = 10

Then the sum is ...

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The sum of interest is 57.

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Step-by-step explanation:

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Yo sup??

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