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marusya05 [52]
3 years ago
6

the table shows the types of popcorn buckets sold at a concession station for one day. what percent of the buttered popcorn buck

ets were large

Mathematics
1 answer:
vlada-n [284]3 years ago
7 0
Hi there! The answer is about 23%

First we need to find the total amount of buttered popcorn sold. This is 182 + 140 + 97 = 419 buckets.

To find the percentage of the buttered popcorn buckets that were large, we use the following formula:
\frac{part}{total} \times 100\%

Filling in this formula brings us to our answer:
\frac{97}{419} \times 100\% = 23.15
Hence, the answer is about 23%
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<img src="https://tex.z-dn.net/?f=%20%20%5Crm%20%20%5Clim_%7Bk%20%5Cto%20%5Cinfty%20%7D%20%5Csqrt%5B%20%20k%5D%7B%20%5CGamma%20%
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and as k goes to ∞, the exponent converges to a definite integral. So the limit is

\displaystyle \lim_{k\to\infty} \sqrt[k]{\Gamma\left(\dfrac1k\right) \Gamma\left(\dfrac2k\right) \cdots \Gamma\left(\dfrac kk\right)} \\\\ = \exp\left(\lim_{k\to\infty} \frac1k \sum_{i=1}^k \ln\left(\Gamma\left(\frac ik\right)\right)\right) \\\\ = \exp\left(\int_0^1 \ln\left(\Gamma(x)\right)\, dx\right) \\\\ = \exp\left(\dfrac{\ln(2\pi)}2}\right) = \boxed{\sqrt{2\pi}}

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