Answer:
![r=\frac{2(23146)-(139)(333)}{\sqrt{[2(9661) -(139)^2][2(55457) -(333)^2]}}=1](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B2%2823146%29-%28139%29%28333%29%7D%7B%5Csqrt%7B%5B2%289661%29%20-%28139%29%5E2%5D%5B2%2855457%29%20-%28333%29%5E2%5D%7D%7D%3D1)
So then the we have perfect linear association. Because the heights and weights of the men are similar.
Step-by-step explanation:
Let X represent the Height and Y the weigth
We have the follwoing dataset:
X: 70, 69
Y: 169, 164
n=2
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use 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]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2%20-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2%20-%28%5Csum%20y%29%5E2%5D%7D%7D)
For our case we have this:
n=2 
And if we replace in the formula we got:
So then the we have perfect linear association. Because the heights and weights of the men are similar.
Well to find the value of x you need to get x alone. so you -1 from 3 and do 2/27 and your answer is 0.074
The pyhtagorean states that to find c, use the eqaution,
.
Substitute 1 for a and 20 for b;
c^2=1+400
c^2=401
c=
which is about 20.02
Hope this helps.
Let's to the first example:
f(x) = x^2 + 9x + 20
Ussing the formula of basckara
a = 1
b = 9
c = 20
Delta = b^2 - 4ac
Delta = 9^2 - 4.(1).(20)
Delta = 81 - 80
Delta = 1
x = [ -b +/- √(Delta) ]/2a
Replacing the data:
x = [ -9 +/- √1 ]/2
x' = (-9 -1)/2 <=> - 5
Or
x" = (-9+1)/2 <=> - 4
_______________
Already the second example:
f(x) = x^2 -4x -60
Ussing the formula of basckara again
a = 1
b = -4
c = -60
Delta = b^2 -4ac
Delta = (-4)^2 -4.(1).(-60)
Delta = 16 + 240
Delta = 256
Then, following:
x = [ -b +/- √(Delta)]/2a
Replacing the information
x = [ -(-4) +/- √256 ]/2
x = [ 4 +/- 16]/2
x' = (4-16)/2 <=> -6
Or
x" = (4+16)/2 <=> 10
______________
Now we are going to the 3 example
x^2 + 24 = 14x
Isolating 14x , but changing the sinal positive to negative
x^2 - 14x + 24 = 0
Now we can to apply the formula of basckara
a = 1
b = -14
c = 24
Delta = b^2 -4ac
Delta = (-14)^2 -4.(1).(24)
Delta = 196 - 96
Delta = 100
Then we stayed with:
x = [ -b +/- √Delta ]/2a
x = [ -(-14) +/- √100 ]/2
We wiil have two possibilities
x' = ( 14 -10)/2 <=> 2
Or
x" = (14 +10)/2 <=> 12
________________
To the last example will be the same thing.
f(x) = x^2 - x -72
a = 1
b = -1
c = -72
Delta = b^2 -4ac
Delta = (-1)^2 -4(1).(-72)
Delta = 1 + 288
Delta = 289
Then we are going to stay:
x = [ -b +/- √Delta]/2a
x = [ -(-1) +/- √289]/2
x = ( 1 +/- 17)/2
We will have two roots
That's :
x = (1 - 17)/2 <=> -8
Or
x = (1+17)/2 <=> 9
Well, this would be your answers.
Answer:
x=15
Step-by-step explanation:
(3x-10)+(2x+25)=90
5x+15=90
5x=75
x=15
(2x+25) = 55°
(3x-10)=35°
