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2 years ago

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Given the line of best fit for a data set of data points with the equation y=5x-2.5,what is the residual for the point (4,13)

1 answer:

BlackZzzverrR [31]2 years ago

7 0

Answer:

-4.5

Step-by-step explanation:

The predicted value from the model is calculated by substituting x with 4 in the regression equation;

y = 5(4) - 2.5

y = 17.5

The actual value when x is 4 is given as 13. The residual is simply the difference between the actual and the predicted value;

residual = actual value - predicted value

residual = 13 - 17.5

residual = -4.5

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In a geometric sequence, a4 = 54 and a7 = 1,458. what is the 12th term? <br><br> answer: B) 354,294

slamgirl [31]

Option B:

The 12th term is 354294.

Solution:

Given data:

$a_4=54$ and $a_7=1458$

To find $a_{12}:$

The given sequence is a geometric sequence.

The general term of the geometric sequence is $a_n=a_1\ r^{n-1}$ .

If we have 2 terms of a geometric sequence $a_n$ and $a_k$ (n > K),

then we can write the general term as $a_n=a_k\ r^{n-k}$ .

Here we have $a_4=54$ and $a_7=1458$ .

So, n = 7 and k = 4 ( 7 > 4)

$a_7=a_4\ .\ r^{7-4}$

$1458=54\ . \ r^3$

This can be written as

$$r^3=\frac{1458}{54}$

$$r^3=27$

$$r^3=3^3$

Taking cube root on both sides of the equation, we get

r = 3

$a_{12}=a_7\ .\ r^{12-7}$

$=1458\ .\ r^5$

$=1458\ .\ 3^5$

$a_{12}=354294$

Hence the 12th term of the geometric sequence is 354294.

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2 years ago

) dy 2x<br> ------ = ---------------<br> dx yx2 + y

larisa86 [58]

Step-by-step explanation:

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Rearranging the terms, we get

$ydy = \dfrac{2xdx}{x^2 + 1}$

We then integrate the expression above to get

$\displaystyle \int ydy = \int \dfrac{2xdx}{x^2 + 1}$

$\displaystyle \frac{1}{2}y^2 = \ln |x^2 +1| + k$

or

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Gemiola [76]

For this case, we observe that the triangles are similar.
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$
Clearing x we have:
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Answer:
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x = 6.25

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fenix001 [56]

Answer:

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Step-by-step explanation:

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