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2 years ago

6) Carpeting costs $9.99 a yard. If Jan buys 17.4 yards, how much will it cost here (Round your answer

Mathematics

2 answers:

Sergeeva-Olga [200]2 years ago

8 0

Answer:

$173.83

Step-by-step explanation:

Multiply the cost of 1 yard by 17.4 , that is

cost = $9.99 × 17.4 ≈ $173.83 ( to the nearest hundredth )

kogti [31]2 years ago

4 0

This is the answer

Hope it helped

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The dimensions of the right triangle shown below are given in feet. What is the length of the hypotenuse of the triangle, in fee

frutty [35]

Answer:

C) square root of 65

Step-by-step explanation:

4^2+7^2=hypotenuse^2

16+49=hypotenuse^2

65=hypotenuse^2

hypotenuse=square root of 65

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2 years ago

Simplify a-c when a=5,c=-1

PolarNik [594]

5-(-1) or you could simplify it further to 6

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2 years ago

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

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