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4 years ago

Which set of line segments with the given lengths can be formed into a right triangle?

Mathematics

2 answers:

WINSTONCH [101]4 years ago

5 0

169 and 13 squared equals 168

Bond [772]4 years ago

4 0

5,12,13 because a squared + b squared = c squared. 25 + 144 = 169 and 13 squared equals 168

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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

A problem states: "There are 7 more girls than boys in a club. There are 23 members in the club in all. How many girls are there

dlinn [17]

Answer:

Step-by-step explanation:

Number of boys = g - 7.

g - 7 + g = 23

2g = 30

g = 15.

The are 15 girls in the class.

3 0

3 years ago

Read 2 more answers

Write the two missing values to make these equivalent fractions correct : ?/3 = 8/12= 4/?

Elodia [21]

X/3 = 8/12
12 * x = 8 * 3
12x = 24
x = 2

8/12 = 4/y
8y = 48
y = 6

8 0

3 years ago

|-25.6|+|-11.4| What is the answer to this

12345 [234]

37. The absolute value symbol turns any negative number positive if it's within those brackets, so that's why the answer is positive. Hope this helped!

3 0

3 years ago

Solve for x Log2 x=-5

Triss [41]

I went through the process and got 6

7 0

3 years ago