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3 years ago

2 of the dozen eggs in a cartoon are cracked about what percent of the carton is not cracked

Mathematics

2 answers:

jek_recluse [69]3 years ago

8 0

since there are a total of 30 eggs in a carton and 2 dozen are broken (24) it'd be 20% that isn't broken

pychu [463]3 years ago

4 0

well, a carton has a dozen, namely 12 or the 100%, two were cracked.

if we know 12 is the 100%, what is 2 off of it in percentage?

$\bf \begin{array}{ccll}
amount&\%\\
\cline{1-2}
12&100\\
2&x
\end{array}\implies \cfrac{12}{2}=\cfrac{100}{x}\implies x=\cfrac{2\cdot 100}{12}\implies x=16.\overline{66}$

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I'm guessing the series is supposed to be

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By the ratio test, the series converges if the following limit is less than 1.

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7\cdot14\cdot21\cdot\cdots\cdot(7n)\cdot(7(n+1))}}{\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}}\right|$

The first $n$ terms in the numerator's denominator cancel with the denominator's denominator:

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7(n+1)}}{n^2x^n}\right|$

$|x^n|$ also cancels out and the remaining factor of $|x|$ can be pulled out of the limit (as it doesn't depend on $n$ ).

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