Answer:
the correlation coefficient of the line of best fit is, 0.98247.
Step-by-step explanation:
Correlation Coefficient are used to find how strong relationship between the data. It expressed its values between +1 and -1. It is represented by r.
* if 0<r<1 indicates a strong positive relationship.
* -1<r <0 indicates a strong negative relationship.
* r=0 indicates no relationship at all.
The formula for this :
![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%20%3D%20%5Cfrac%7Bn%28%5Csum%20xy%29-%28%5Csum%20x%29%28%5Csum%20y%29%7D%7B%5Csqrt%7B%5Bn%5Csum%20x%5E2-%28%5Csum%20x%29%5E2%5D%5Bn%5Csum%20y%5E2-%28%5Csum%20y%29%5E2%5D%7D%7D)
Given the data: (-3, -40) , (1, 12), (5, 72) and (7,137)
Here, n = 4
To calculate the correlation coefficient r;
Substitute the values of data in above formla of r , as shown in the Figure 1:
then;
![r=\frac{4\cdot 1451-(10)(181)}{[4\cdot84-(10)^2][4\cdot 256977 -(181)^2]}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%5Ccdot%201451-%2810%29%28181%29%7D%7B%5B4%5Ccdot84-%2810%29%5E2%5D%5B4%5Ccdot%20256977%20-%28181%29%5E2%5D%7D)
or
![r=\frac{5804-1810}{\sqrt{[336-100][102788 -32761]}}=\frac{3994}{\sqrt{[236][70027]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B5804-1810%7D%7B%5Csqrt%7B%5B336-100%5D%5B102788%20-32761%5D%7D%7D%3D%5Cfrac%7B3994%7D%7B%5Csqrt%7B%5B236%5D%5B70027%5D%7D%7D)
or
Therefore, the correlation coefficient r is, 0.98247 (Positive relationship)
It should have 1 solution, x = 2. :)
Answer:
x = 45
y = 7
Step-by-step explanation:
To obtain the value of x and y, do the following:
√7 – 3√5
Rearrange
– 3√5 + √7
Multiply through by –1
3√5 – √7 ... (1)
Express 3√5 as a single surd
3√5 = √(3 × 3 × 5)
3√5 = √45
Replace 3√5 with √45 in equation 1
3√5 – √7
√45 – √7
Comparing
√45 – √7 and √x – √y i.e
√45 – √7 = √x – √y
x = 45
y = 7
Answer: 350 adult tickets
Step-by-step explanation:
(omg I remember this question!)
- a stands for the number of adult tickets sold
student tickets : a + 65
<em>the equation for the prob: </em>
765 = a + (a + 65)
<em>solve:</em>
combine 'like terms'
1.) 765 = a + a + 65
2.) 765 = 2a + 65
<u>- 65 - 65 </u>
700= 2a
divide by 2
700/2 = 2a/2
<em>(700/2 = 350) </em>
<em>(the "2" in 2a is cancelled out by the other 2)</em>
<u>350 = a </u>
