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3 years ago

Use the data from the table to create a scatter plot.

Mathematics

1 answer:

steposvetlana [31]3 years ago

8 0

By definition, a scatter plot is a diagram generally used to compare two setz of data. As you can see, in this exercise asked for the relationship between "Age (years)" at the x axis and "Lenght (in)" at the y axis. Therefore, to plot the data given in the problem, you should order the numbers in a table, as you can see in the figure attached. Then, you can plot the following points:

(3,13); (3,15); (2,10); (5,17); (4,17); (5,19); (7,23); (6,18); (8,21); (6,19)

You can see the completed scatter plot in the figure attached.

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Lim (n/3n-1)^(n-1) n → ∞

n200080 [17]

Looks like the given limit is

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1}$

With some simple algebra, we can rewrite

$\dfrac n{3n-1} = \dfrac13 \cdot \dfrac n{n-9} = \dfrac13 \cdot \dfrac{(n-9)+9}{n-9} = \dfrac13 \cdot \left(1 + \dfrac9{n-9}\right)$

then distribute the limit over the product,

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \lim_{n\to\infty}\left(\dfrac13\right)^{n-1} \cdot \lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}$

The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.

For the second limit, recall the definition of the constant, e :

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

To make our limit resemble this one more closely, make a substitution; replace 9/(n - 9) with 1/m, so that

$\dfrac{9}{n-9} = \dfrac1m \implies 9m = n-9 \implies 9m+8 = n-1$

From the relation 9m = n - 9, we see that m also approaches infinity as n approaches infinity. So, the second limit is rewritten as

$\displaystyle\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8}$

Now we apply some more properties of multiplication and limits:

$\displaystyle \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m} \cdot \lim_{m\to\infty}\left(1+\dfrac1m\right)^8 \\\\ = \lim_{m\to\infty}\left(\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = e^9 \cdot 1^8 = e^9$

So, the overall limit is indeed 0:

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \underbrace{\lim_{n\to\infty}\left(\dfrac13\right)^{n-1}}_0 \cdot \underbrace{\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}}_{e^9} = \boxed{0}$

7 0

3 years ago

What would be the amount of his last monthly bill in order. The bill amount to be 110 for all 12 months

meriva

Add up all the numbers the divide by the amount of numbers in the set.
1199/11 = 109
B. 109 answer

8 0

3 years ago

Are the graphs of each pair of equations parallel, perpendicular, or neither? x=4 y=4

Vlad1618 [11]

Both graphs x =4 and y =4 will be perpendicular to each other.

The graph of x = 4 is a vertical line down the Graph scope
The graph of y =4 is a horizontal line side the Graph scope.

Both the Lines will meet exactly at ( 4, 4 ) perpendicularly at each other both of them intersecting at 90 degrees.

Vertical and Horizontal lines are perpendicular to each other (90 Degrees).

Know more about Perpendicular Lines: brainly.com/question/1202004

5 0

1 year ago

Read 2 more answers

Cressida decided to save a part of her income in a savings account that compounds interest every four months. Her account balanc

hichkok12 [17]

The answer is "the number of times the account compounds interest".
The general formula is the following:
$3,545(1+r)^n$
wherein r is the interest rate compound each four months.
Since there is 3*4 months in a year, then each year we compute the interest Three time, there where the factor 3 comes.

6 0

3 years ago

Read 2 more answers

What is 18 2/3-3 5/8

xxTIMURxx [149]

Answer:

=15 1/24

Step-by-step explanation:

18 2/3−3 5/8

=15 1/24

5 0

3 years ago