Translate the following phrase to a mathematical expression and then evaluate the expression for n = 5.

How many windows would Carpenter A install in 10 hours?

DerKrebs [107]

Answer:

vdv

Step-by-step explanation:

vfvfvdv

3 0

3 years ago

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

Solve the following system of equations for all three variables.

xz_007 [3.2K]

Answer:

Step-by-step explanation:

-2x + 3y – 4z = 8 ----------------(I)

5x – 3y + 5z = -8 -----------------(II)

7x – 3y + 3z = 8 ------------------(III)

Add equation (I) & (II) and thus y will be eliminated

(I) -2x + 3y – 4z = 8

(II) 5x – 3y + 5z = -8 {Add}

3x + z = 0 ------------------------(A)

Multiply equation (II) by (-1) and then add with equation (III). Thus y will be eliminated.

(II) * (-1) -5x + 3y - 5z = +8

7x – 3y + 3z = 8 {Add}

2x -2z = 16 ---------------(B)

Multiply equation (A) by 2 and then add. Thus z will be eliminated and we will get the value of x

(A) * 2 6x + 2z = 0

(B) 2x - 2z = 16 {Add}

8x = 16

Divide both sides by 8

x = 16/8

x = 2

Plugin x = 2 in equation (A)

3x + z = 0

3*2 + z = 0

6 + z = 0

z = -6

Plug in x = 2 and z = - 6 in equation (I)

-2x +3y - 4z = 8

-2*2 + 3y - 4*(-6) = 8

-4 + 3y + 24 = 8

3y + 20 = 8

3y = 8 - 20

3y = -12

y = -12/3

y = -4

7 0

3 years ago

Read 2 more answers

What is the measure of ZC?

Studentka2010 [4]

Answer:

55°

Step-by-step explanation:

$m\angle C = \frac{1}{2} (184 \degree - 74 \degree) \\ \\ \implies \: m\angle C = \frac{1}{2} (110 \degree) \\ \\ \implies \: m\angle C = 55 \degree$

8 0

3 years ago

Which sequence of transformations will map figure K onto figure K′? Two congruent kites, figure K and figure K prime, are drawn

elixir [45]

Answer:

The sequence of transformations will map figure K onto figure K′

is the first sequence option (1)

======================================================

Step-by-step explanation:

See the attached figure

as shown in the figure the K' is the image of K by reflection over x-axis

But  We need to know which sequence of transformations will give the same result.

So, we will test the options by any point from K and its image from K'

i.e: we will test the options using the points (6,5) , (6,-5)

(6,5) ⇒ (6,-5)

option (1):

Reflection across x = 4, 180° rotation about the origin, and a translation of (x + 8, y)

(6,5) ⇒ (2,5) ⇒(-2,-5) ⇒ (6,-5)

option (2):

Reflection across x = 4, 180° rotation about the origin, and a translation of (x − 8, y)

(6,5) ⇒ (2,5) ⇒(-2,-5) ⇒ (-10,-5)

option (3):

Reflection across y = 4, 180° rotation about the origin, and a translation of (x + 8, y)

(6,5) ⇒ (6,3) ⇒ (-6,-3) ⇒ (2,-3)

option (4):

Reflection across y = 4, 180° rotation about the origin, and a translation of (x − 8, y)

(6,5) ⇒ (6,3) ⇒ (-6,-3) ⇒ (-14,-3)

As shown: The sequence of transformations will map figure K onto figure K′

is the first sequence option (1)

7 0

4 years ago

Read 2 more answers