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3 years ago

Convert to a percent: 3.33 3/5

Mathematics

1 answer:

Free_Kalibri [48]3 years ago

7 0

3.33=333%
and
3/5=.6=60%
to find a percent find a decimal and move the decimal point two spaces right

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Find the general term of {a_n}

Assoli18 [71]

From the given recurrence, it follows that

$a_{n+1} = 2a_n + 1 \\\\ a_{n+1} = 2(2a_{n-1} + 1) = 2^2a_{n-1} + 1 + 2 \\\\ a_{n+1} = 2^2(2a_{n-2}+1) + 1 + 2 = 2^3a_{n-2} + 1 + 2 + 2^2 \\\\ a_{n+1} = 2^3(2a_{n-3} + 1) + 1 + 2 + 2^2 = 2^4a_{n-3} + 1 + 2 + 2^2 + 2^3$

and so on down to the first term,

$a_{n+1} = 2^na_1 + \displaystyle \sum_{k=0}^{n-1}2^k$

(Notice how the exponent on the 2 and the subscript of <em>a</em> in the first term add up to <em>n</em> + 1.)

Denote the remaining sum by <em>S</em> ; then

$S = 1 + 2 + 2^2 + \cdots + 2^{n-1}$

Multiply both sides by 2 :

$2S = 2 + 2^2 + 2^3 + \cdots + 2^n$

Subtract 2<em>S</em> from <em>S</em> to get

$S - 2S = 1 - 2^n \implies S = 2^n - 1$

So, we end up with

$a_{n+1} = 4\cdot2^n + S \\\\ a_{n+1} = 2^2\cdot2^n + 2^n-1 \\\\ a_{n+1} = 2^{n+2} + 2^n - 1 \\\\\implies \boxed{a_n = 2^{n+1} + 2^{n-1} - 1}$

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2 years ago

Describe how to approximate the value of an irrational number

Vesna [10]

I would either round it to the 10th or 100th place.

4 0

3 years ago

With her new trainer, Judy now bikes at an average speed of 24.1 MPH. That is 20.5% faster than she averaged with her old traine

marishachu [46]

Answer: an average of 13.5 mph is very respectable

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Help asap help please.

Xelga [282]

Answer:

30(x+1)/(x+7)

Step-by-step explanation:

This is not a rational expression because denominator has a domain of which it can be undefined.

To rationalize multiply by the reciprocal of the denominator (1/6+1/x+1)

___<u>5___ </u>*(6)(x+1) --> _____<u>30(x+1)_____</u> --><u> 30x+1</u>_ --> <u>30x+1</u>

1/6+1/x+1 *(6)(x+1)--> 6(x+1)/6 + 6(x+1)/(x+1) --> (x+1)+6 --> x+7

Final Answer: 30(x+1)/(x+7)

7 0

3 years ago

IXL geometry help please!

7nadin3 [17]

<h3>Answer: 104 degrees</h3>

================================

Work Shown:

Inscribed angle theorem

arc measure = 2*(inscribed angle)

arc BCD = 2*(angle A)

arc BCD = 2*(97)

arc BCD = 194 degrees

-------------

Break arc BCD into its smaller pieces

arc BCD = (minor arc BC) + (minor arc CD)

194 = (90) + (minor arc CD)

194-90 = minor arc CD

104 = minor arc CD

<h3>minor arc CD = 104 degrees</h3>

3 0

3 years ago