3(2R-7)=6<br> I need help on finding this

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

3 years ago

If one bag of grass seed will cover 225 square feet, what is the minimum number of bags the haney family will need to cover thei

Veronika [31]

Answer:

9 bags

Step-by-step explanation:

First we will need to calculate the area of their entire backyard, which has a shape of trapezium.

So the formula for the area of a trapezium is $A=\frac{(a+b)*h}{2}$

a and b are the lenghts of the parallel sides and h is the height.

From the picture $a=10*5=50\\b=9*5=45\\h=8*5=40$

Then we plug into our formula

$A=\frac{(a+b)*h}{2} =\frac{(50+45)*40}{2} = 1200$ square feet

To get the number of bags required we just simply divide the aree of their entire yard by the space that 1 bag covers. We get:

$\frac{1900}{225} =8.444...$ bags

This is more than 8 bags so they will need 9 bags to cover their entire yard.

8 0

3 years ago

Determine if each set of ordered pairs represents a function. <br> (2,3), (6,-5), (-1,3)

docker41 [41]

Answer:

yes

Step-by-step explanation:

You can perform the "line test." If it is a function, there will not be two x's of the same value. In this case, x is 2,6,-1. No number repeats, thus making a function.

5 0

4 years ago

Please help meeeeeeeeee

sveticcg [70]

The measure of the largest angle is 74°

8 0

3 years ago

Please help........................

VashaNatasha [74]

Answer:

Step-by-step explanation:

If m∠ABC = 40° and BD is the bisector of ∠ABC, then

(1) m∠ABD = m∠DBC

(2) m∠ABC = m∠ABD + m∠DBC

From (1) and (2) we have:

m∠ABC = 2m∠ABD

Therefore

2m∠ABD = 40° <em>divide both sides by 2</em>

m∠ABD = 20°

3 0

3 years ago

3(2R-7)=6 I need help on finding this