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3 years ago

Solve n^4-11n^2+30÷n^4-7n^2+10

1 answer:

8 0

Factor the numerator and denominator...

(n^4-5n^2-6n^2+30)/(n^4-2n^2-5n^2+10)

[n^2(n^2-5)-6(n^2-5)]/[n^2(n^2-2)-5(n^2-2)]

[(n^2-5)(n^2-6)]/[(n^2-5)(n^2-2)] notice the (n^2-5)s cancel out

(n^2-6)/(n^2-2)

We could further factor this because each is a difference of squares to:

[(n+√6)(n-√6)]/[(n+√2)(n-√2)

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An automobile dealer wants to see if there is a relationship between monthly sales and the interest rate. A random sample of 4 m

SVETLANKA909090 [29]

Answer:

a) $y=-6.254 x +75.064$

b) r =-0.932

The % of variation is given by the determination coefficient given by $r^2$ and on this case $-0.932^2 =0.8687$ , so then the % of variation explained by the linear model is 86.87%.

Step-by-step explanation:

Assuming the following dataset:

Monthly Sales (Y) Interest Rate (X)

22 9.2

20 7.6

10 10.4

45 5.3

Part a

And we want a linear model on this way y=mx+b, where m represent the slope and b the intercept. In order to find the slope we have this formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=278.65-\frac{32.5^2}{4}=14.5875$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=696.9-\frac{32.5*97}{4}=-91.225$

And the slope would be:

$m=\frac{-91.225}{14.5875}=-6.254$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{32.5}{4}=8.125$

$\bar y= \frac{\sum y_i}{n}=\frac{97}{4}=24.25$

And we can find the intercept using this:

$b=\bar y -m \bar x=24.25-(-6.254*8.125)=75.064$

So the line would be given by:

$y=-6.254 x +75.064$

Part b

For this case we need to calculate the correlation coefficient given by:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

$r=\frac{4(696.9)-(32.5)(97)}{\sqrt{[4(278.65) -(32.5)^2][4(3009) -(97)^2]}}=-0.937$

So then the correlation coefficient would be r =-0.932

The % of variation is given by the determination coefficient given by $r^2$ and on this case $-0.932^2 =0.8687$ , so then the % of variation explained by the linear model is 86.87%.

6 0

4 years ago

Write an expression that represents the statement " the product of 6 and the sum of 3 times a number n and 5"

kramer

6(3x + 5 )

hope that helps

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3 years ago

Don’t know this one

tatiyna

Answer:

Step-by-step explanation:

The answer is B because in order for the square root of a number to be equal to another number, the answer squared should be the number under the square root.

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4 years ago

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Manuel's company makes solid balls out of scrap metal for various industrial uses. His current task is to make a batch of alumin

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Step-by-step explanation:

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What is 7 divided by 9102

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