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2 years ago

12

At Charles Walters Middle School, 25% of the students live more than 8 miles from school, What fraction of the students live mor

e than 8 miles from school? Write your answer as a fraction in simplest form. ?

2 answers:

Vanyuwa [196]2 years ago

8 0

Answer:

1/4

Step-by-step explanation:

0.25 = 1/4

galben [10]2 years ago

4 0

Answer:

1/4

Step-by-step explanation:

25% is 25/100. 25/100 simplified is 1/4.

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Identify whether the series sigma notation infinity i=1 15(4)^i-1 is a convergent or divergent geometric series and find the sum

const2013 [10]

Answer: The correct option is

(d) This is a divergent geometric series. The sum cannot be found.

Step-by-step explanation: The given infinite geometric series is

$S=\sum_{i=1}^{\infty}15(4)^{i-1}.$

We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.

We have the D' Alembert's ratio test, states as follows:

Let, $\sum_{i=1}^{\infty}a_i$ is an infinite series, with complex coefficients $a_i$ and we consider the following limit:

$L=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}.$

Then, the series will be convergent if L < 1 and divergent if L > 1.

For the given series, we have

$a_i=15(4)^{i-1},\\\\a_{i+1}=15(4)^i.$

So, the limit is given by

$L\\\\\\=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i-1}}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i}4^{-1}}\\\\\\=\dfrac{1}{4^{-1}}\\\\=4>1.$

Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.

Thuds, (d) is the correct option.

7 0

4 years ago

Read 2 more answers

antiseptic1488 [7]

Woohhh ok so this is how we will go ahead and do this cool thing today for the rest of the week

5 0

3 years ago

Please help with 5 I don’t get it

Alexxandr [17]

Answer:

It’s saying for every 1/4 inch, you have 3 feet. Let’s say I had an inch. That means I have 12 feet. Hope this helped!

Step-by-step explanation:

I only have an explanation. I don’t have the answer, but maybe I could help!

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Tatiana [17]

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Step-by-step explanation:

hope it helps

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