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3 years ago

Solve for w. 1/3w + 5/6w - 2 = -w

Mathematics

2 answers:

Scorpion4ik [409]3 years ago

6 0

Answer: $w=\frac{12}{13}$

Step-by-step explanation:

To solve for w, we want to isolate the variable.

$\frac{1}{3}w +\frac{5}{6}w-2=-w$ [add both sides by 2 and w]

$\frac{1}{3}w +\frac{5}{6}w+w=2$ [convert to same denominator]

$\frac{2}{6}w +\frac{5}{6}w+\frac{6}{6} w=2$ [add]

$\frac{13}{6} w=2$ [multiply both sides by 6/13]

$w=\frac{12}{13}$

Now we know that $w=\frac{12}{13}$ .

Brrunno [24]3 years ago

4 0

Answer:

Step-by-step explanation:

1/3w + 5/6w - 2 = -w Collect like terms on the left.

Before I do, I'm going to assume the question is (1/3)w + (5/6)w - 2 = - w

(1/3)w + (5/6)w - 2 = - w

1/3 + 5/6 = 2/6 + 5/6 = 7/6

(7/6)w - 2 = -w Add w to both sides

(7/6)w + w - 2 = 0 Combine the left

(7/6)w + 6/6 w - 2 = 0

(13 / 6) w - 2 = 0 Add 2 to both sides

(13/ 6) w = 2 Divide by 13/6

w = (2/1 ) ÷ (13/6) Invert the denominator and multiply

w = 2/1 * 6/13

w = 12/13

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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:

$y=0.3225 x -0.27$

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