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oksano4ka [1.4K]
3 years ago
15

This table shows the number of students at a school in the years 2014-2016, 2014 1,030 students 2015 ? students 2016 1,300 stude

nts.In 2015, there were more students than in 2014 but fewer than in 2016. Which could be the number in 2015?
Mathematics
1 answer:
vladimir1956 [14]3 years ago
4 0

Answer:

it could be the number in 2015 is 2,330

Step-by-step explanation:

Just add the number of the students in 2014-2016.

1,030+ 1,300=2,330

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Consider the series ∑n=1[infinity]2nn!nn. Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it d
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.

6 0
3 years ago
The ratio of boys to girls in a class is 5:3. There are 32 students in the class. How many students are boys?
miv72 [106K]

Answer:

5x+3x=8x

8x = 32

x=32/8 = 4

boys are 4 x 5 = 20

girls are 4 x 3 = 12

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
224percent as a fraction or mixed number in simplest form
Murrr4er [49]

Answer:

2 6/25

Step-by-step explanation:

7 0
3 years ago
THE ORIGINAL CARS Movie MADe 450
Marina86 [1]

Answer:

34% decrease

Step-by-step explanation:

(V1-V2)/V1x100

450-297=153

153/450=0.34

0.34 x 100=34

34% decrease

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3 0
3 years ago
6. cory gets paid every two weeks. he works 40 hours per week at $7.75 per hour. cory has the following deductions: 8% for medic
aliya0001 [1]

Answer:   429.88

Step-by-step explanation:

The first 40 hours is at 9.50

40 *9.50 =380

The remaining hours is at 9.50 * 1.5 or 14.25

43.5 -40 = 3.5

3.5 * 14.25

49.875 = 49.88  ( rounding to the nearest cent)

Add together

380+49.88 =429.88

8 0
3 years ago
Read 2 more answers
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