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dexar [7]
4 years ago
15

2/3x+7=5/6 Rewrite the equation below so that it doesn’t have fractions please.

Mathematics
1 answer:
kipiarov [429]4 years ago
5 0

To eliminate all of the fractions in an equation, we can multiply the equation by the least common denominator of all of the fractions in the equation. To find the LCD, we need to find a number that has at least all of the factors of each of the denominators.


To find the LCD of the fractions in this equation, let's look at our denominators, 3 and 6. We can say 3 = 3 and 6 = 2 * 3. By examining this, we can see that our LCD <em>has to have </em>a 3 and 2, since those numbers are found in at least one of the fractions. Thus, our LCD is 3 * 2 = 6.


Now we know to multiply our entire equation by 6. This is solved as shown:

6(\dfrac{2}{3}x + 7) = 6(\dfrac{5}{6}) \Rightarrow \boxed{4x + 42 = 5}


Our answer is 4x + 42 = 5.

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Step-by-step explanation

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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  

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