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Sergeu [11.5K]
3 years ago
10

Each ride at the fair costs $2.50. Alex will spend at least $15 for rides. Write an inequality to determine the least number of

rides, r, Alex will go on. Find the solution set for your inequality. Describe how you would graph your inequality.
Mathematics
1 answer:
goblinko [34]3 years ago
4 0
0<r<6
the least number of ride he can go on is 0 which is none and the most is 6 because 15/2.50=6
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Vikki [24]

I guess the series is

\displaystyle\sum_{n=1}^\infty\frac{2^nn!}{n^n}

We have

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{2^{n+1}(n+1)!}{(n+1)^{n+1}}}{\frac{2^nn!}{n^n}}\right|=2\lim_{n\to\infty}\left(\frac n{n+1}\right)^n

Recall that

e=\displaystyle\lim_{n\to\infty}\left(1+\frac1n\right)^n

In our limit, we have

\dfrac n{n+1}=\dfrac{n+1-1}{n+1}=1-\dfrac1{n+1}

\left(\dfrac n{n+1}\right)^n=\dfrac{\left(1-\frac1{n+1}\right)^{n+1}}{1-\frac1{n+1}}

\implies\displaystyle2\lim_{n\to\infty}\left(\frac n{n+1}\right)^n=2\frac{\lim\limits_{n\to\infty}\left(1-\frac1{n+1}\right)^{n+1}}{\lim\limits_{n\to\infty}\left(1-\frac1{n+1}\right)}=\frac{2e}1=2e

which is greater than 1, which means the series is divergent by the ratio test.

On the chance that you meant to write

\displaystyle\sum_{n=1}^\infty\frac{2^n}{n!n^n}

we have

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{2^{n+1}}{(n+1)!(n+1)^{n+1}}}{\frac{2^n}{n!n^n}}\right|=2\lim_{n\to\infty}\frac1{(n+1)^2}\left(\frac n{n+1}\right)^2

=\displaystyle2\left(\lim_{n\to\infty}\frac1{(n+1)^2}\right)\left(\lim_{n\to\infty}\left(\frac n{n+1}\right)^n\right)=2\cdot0\cdot e=0

which is less than 1, so this series is absolutely convergent.

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3 years ago
Pls can probability be expressed as percentage ​
tia_tia [17]
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7 0
3 years ago
Instructions:Select the correct answer from the drop-down menu. Dave is helping his grandmother make trail mix. His grandmother
Mazyrski [523]
Set up a proportional relationship:

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4 years ago
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NikAS [45]

10x-61/12 is the difference of  (7x-6\frac{2}{3}) - (-3x + 4\frac{3}{4}).

<h3>What is Expression?</h3>

An expression is combination of variables, numbers and operators.

The given expression is (7x-6\frac{2}{3}) - (-3x + 4\frac{3}{4})

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The LCM of 3 and 4 is 12/

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Hence, 10x-61/12 is the difference of  (7x-6\frac{2}{3}) - (-3x + 4\frac{3}{4}).

To learn more on Expressions click:

brainly.com/question/14083225

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Clara's suitcase weighs 58 1/4 pounds, but the airline's weight limit for suitcases is 50 pounds. How much weight does she need
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8 pounds and 4 oz. 58.04 - 8.04=50
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