Which of x- values are solutions to the following inequality?

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

3 years ago

If a² + b² = z and ab = y, which of the following is equivalent to 4z + 8y? Show all the steps.

Ivenika [448]

Answer:

The answer to your question is: (2a + 2b)²

Step-by-step explanation:

a² + b² = z

ab = y

Which is equivalent to 4z + 8y ?

Substitution

4(a² + b²) + 8(ab)

Simplify 4a² + 4b² + 8ab

Order 4a² + 8ab + 4b² It's a perfect square trynomial

Factorize (2a + 2b)²

7 0

3 years ago

Read 2 more answers

jenna brought a spool of ribbon that was 5 3/4 meters long. she used 3 1/4 meters of ribbon for a craft project. how many meters

sp2606 [1]

Answer:

So the answer will be 2 2/4

Step-by-step explanation:

If you need me to explain more please tell me.Hope it helps.

8 0

3 years ago

There are 14 boys and 9 girls in miss Keller’s music class what is the ratio of boys to girls ? And what is the ratio of girls t

11111nata11111 [884]

Answer:

Step-by-step explanation:

if there are 14 boys to 9 girls in a class the ratio would be

14:9

6 0

3 years ago

Read 2 more answers

If the square root of 61 is the longest side length in the triangle and the shorter sides are x and x+1, find the value of x tha

Tju [1.3M]

Answer:

x = 5

Step-by-step explanation:

You want to find x such that ...

x^2 +(x +1)^2 = 61

2x^2 +2x -60 = 0 . . . . . simplify, subtract 61

x^2 +x -30 = 0 . . . . . . . divide by 2

(x +6)(x -5) = 0 . . . . . . . . factor; solutions will make the factors be zero.

The relevant solution is x = 5.

5 0

3 years ago

Which of x- values are solutions to the following inequality?​

Which of x- values are solutions to the following inequality?