The fraction a/b must be equal to which expression

The accompanying data on x = current density (mA/cm2) and y = rate of deposition (m/min)μ appeared in a recent study.

gtnhenbr [62]

Answer:

a) $r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857$

The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables

b) $m=\frac{64.5}{2000}=0.03225$

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

$\bar x= \frac{\sum x_i}{n}=\frac{200}{4}=50$

$\bar y= \frac{\sum y_i}{n}=\frac{5.37}{4}=1.3425$

$b=\bar y -m \bar x=1.3425-(0.03225*50)=-0.27$

So the line would be given by:

$y=0.3225 x -0.27$

Step-by-step explanation:

Part a

The correlation coeffcient is given by this formula:

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

For our case we have this:

n=4 $\sum x = 200, \sum y = 5.37, \sum xy = 333, \sum x^2 =12000, \sum y^2 =9.3501$

$r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857$

The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables

Part b

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

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:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=12000-\frac{200^2}{4}=2000$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=333-\frac{200*5.37}{4}=64.5$

And the slope would be:

$m=\frac{64.5}{2000}=0.03225$

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

$\bar x= \frac{\sum x_i}{n}=\frac{200}{4}=50$

$\bar y= \frac{\sum y_i}{n}=\frac{5.37}{4}=1.3425$

And we can find the intercept using this:

$b=\bar y -m \bar x=1.3425-(0.03225*50)=-0.27$

So the line would be given by:

$y=0.3225 x -0.27$

4 0

2 years ago

Sin(x)= 4/5 dilated by 2

Damm [24]

It would remain the same (4/5). <span>Sin of the angle is unchanged regardless of the size; it is a ratio related only to the angle, not the size of the triangles.</span>

6 0

2 years ago

WILL GIVE BRAINLIEST ANSWER TO THE CORRECT ONE!

AleksandrR [38]

I think it would best be displayed as a line plot.

5 0

2 years ago

An entrepreneur buys some microscopes. Each one cost $200 and resells online for $526. What is the mark-up percentage?

Dafna11 [192]

Answer:

326

Step-by-step explanation:

Given: Microscopes. Each one costs $200 and resells online for $526.

To find: What is the mark-up percentage?

Solution: Simply take the sales price minus the unit cost, and divide that number by the unit cost. Then, multiply by 100 to determine the markup percentage.

$526 - 200 = 326$

Net Profit Margin = 61.98%

Net Profit = $326.00

Profit Percentage = 163.00%

Find more here: brainly.com/question/23345732

6 0

2 years ago

Says the directions in the picture.<br> Please help me before my next geometry class tomorrow.

SashulF [63]

Distance formula= [(x2-x1)^2 + (y2-y1)^2]^1/2
Origin= white house = (0,0)
Capitol= (2300,800)
Put the value,
(2300² + 800² )^1/2
= 2435 meters
Thus distance is 2435 m

3 0

3 years ago