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2 years ago

D.

Mathematics

1 answer:

Alex2 years ago

3 0

Answer:

Step-by-step explanation:

This is your correct answer if ur aim is simplification!

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Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

Phantasy [73]

Answer:

$y=-2.95836 x +234.56159$

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

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

Where:

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

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

So we can find the sums like this:

$\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479$

$\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694$

$\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897$

$\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226$

$\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22$

And the slope would be:

$m=-\frac{-4152.222}{1403.556}=-2.95836$

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

$\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222$

$\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111$

And we can find the intercept using this:

$b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159$

So the line would be given by:

$y=-2.95836 x +234.56159$

7 0

2 years ago

Segment addition postulate What’s the answer?

Free_Kalibri [48]

$\bf Step-by-step~explanation:$

Keep in mind: The entire line segment (VX) is equal to 14.

$\bf Step~1:$

Let's see how the line segment looks like first.

Line segment VX is 14 units long.

______________

V X

W is on the line segment somewhere, and VW is equal to 3.

3 ?

______________

V W X

$\bf Step~2:$

We have to solve for the ?. Let's put ? as x. So now we are solving for x.

We have to set up our equation like this:

x + 3 = 14

Since our unknown value plus 3 is equal to 14, we have to subtract 3 from 14 to get our answer.

14 - 3 = 11

3 11

______________

V W X

$\large\boxed {\bf Our~final~answer: ~WX=11}$

3 0

2 years ago

How many 1/4 cups in 3 1/2 cups

seropon [69]

If you have 3 1/2 cups of something and you want to find how many 1/4 cups there are the you just need to divide 3 1/2 by 1/4
$3 \frac{1}{2} ÷ \frac{1}{4}$
the answer is 14, there are 14 1/4 cups in 3 1/2 cups.
hope I helped :)

6 0

3 years ago

The volume of this cylinder is 1,909.92384 cubic millimeters. What is the radius? Use n=3.14 and round your answer to the neares

klemol [59]

Remember that the volume of a cylinder is