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2 years ago

1) A spinner is spun 500 times.

Mathematics

2 answers:

mart [117]2 years ago

7 0

Answer:

20.8

Step-by-step explanation:

There are 104 times that red is spun.

104/500

butalik [34]2 years ago

5 0

Answer:

20.8%(If the problem asks you to round it would be 21%)

Step-by-step explanation:

To solve this question, we need to know 2 things:

The denominator, and the numerator.

The denominator is 500, as that is the amount of times we spin a spinner.

The numerator is 104, as that is the amount of times the spinner lands on red.

Now to find the percentage, we divide the numerator by the denominator to get:

$\frac{104}{500}$

20.8%

Hope this helps! :3

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2 years ago

Evaluate the infinite sum:

satela [25.4K]

Consider the k-th partial sum,

$S_k = 1 + \dfrac2\pi + \dfrac3{\pi^2} + \cdots + \dfrac k{\pi^{k-1}}$

More compactly,

$\displaystyle S_k = \sum_{i=1}^k \frac i{\pi^{i-1}} = \frac{(1-\pi)k+\pi^{k+1}-\pi}{(1-\pi)^2\pi^{k-1}}$

(this is just another case of a similar sum you asked about a while ago [24494877])

The infinite sum is the limit of the partial sum as k goes to infinity. We have

$\displaystyle \lim_{k\to\infty} \frac{(1-\pi)k+\pi^{k+1}-\pi}{(1-\pi)^2\pi^{k-1}} = \frac\pi{(1-\pi)^2} \lim_{k\to\infty} \left(\frac{(1-\pi)k}{\pi^k} + \pi - \frac1{\pi^{k-1}} \right) = \boxed{\frac{\pi^2}{(1-\pi)^2}}$