Answer:
Step-by-step explanation:
Hello!
Given the independent variable X and the dependent variable Y (see data in attachment)
The regression equation is
^Y= b₀ + bX
Where
b₀= estimation of the y-intercept
b= estimation of the slope
The formulas to manually calculate both estimations are:


n=7
∑X= 42
∑X²= 292
∑Y= 49
∑Y²= 403
∑XY= 249




^Y= 13.75 - 1.13X
Using the raw data you can calculate the coefficient of determination as:
![R^2= \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]}](https://tex.z-dn.net/?f=R%5E2%3D%20%5Cfrac%7Bb%5E2%5BsumX%5E2-%5Cfrac%7B%28sumX%29%5E2%7D%7Bn%7D%20%5D%7D%7B%5BsumY%5E2-%5Cfrac%7B%28sumY%29%5E2%7D%7Bn%7D%20%5D%7D)
![R^2= \frac{(-1.13)^2[292-\frac{(42)^2}{7} ]}{[403-\frac{(49)^2}{7} ]}= 0.84](https://tex.z-dn.net/?f=R%5E2%3D%20%5Cfrac%7B%28-1.13%29%5E2%5B292-%5Cfrac%7B%2842%29%5E2%7D%7B7%7D%20%5D%7D%7B%5B403-%5Cfrac%7B%2849%29%5E2%7D%7B7%7D%20%5D%7D%3D%200.84)
This means that 84% of the variability of the dependent variable Y is explained by the response variable X under the model ^Y= 13.75 - 1.13X
I hope this helps!
Answer:
A cuz x+6 is double x-3 so divide them and equate it to 2 you'd get x+6 = 2x-6
12=2x-x
Please send a picture of the figure
For this case we must simplify the following expression:![7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {16x}) - 3 (\sqrt [3] {8x})](https://tex.z-dn.net/?f=7%20%28%5Csqrt%20%5B3%5D%20%7B2x%7D%29%20-%203%20%28%5Csqrt%20%5B3%5D%20%7B16x%7D%29%20-%203%20%28%5Csqrt%20%5B3%5D%20%7B8x%7D%29)
We rewrite:

We rewrite the expression:
![7 (\sqrt [3] {2x}) - 3 (\sqrt [3] {2 ^ 3 * 2x}) - 3 (\sqrt [3] {2 ^ 3 * x}) =](https://tex.z-dn.net/?f=7%20%28%5Csqrt%20%5B3%5D%20%7B2x%7D%29%20-%203%20%28%5Csqrt%20%5B3%5D%20%7B2%20%5E%203%20%2A%202x%7D%29%20-%203%20%28%5Csqrt%20%5B3%5D%20%7B2%20%5E%203%20%2A%20x%7D%29%20%3D)
By definition of properties of powers and roots we have:
![\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}](https://tex.z-dn.net/?f=%5Csqrt%20%5Bn%5D%20%7Ba%20%5E%20m%7D%20%3D%20a%20%5E%20%7B%5Cfrac%20%7Bm%7D%20%7Bn%7D%7D)
Then, taking the terms of the radical:
![7 (\sqrt [3] {2x}) - 3 (2 \sqrt [3] {2x}) - 3 (2 \sqrt [3] {x}) =\\7 \sqrt [3] {2x} -6 \sqrt [3] {2x} -6 \sqrt [3] {x} =](https://tex.z-dn.net/?f=7%20%28%5Csqrt%20%5B3%5D%20%7B2x%7D%29%20-%203%20%282%20%5Csqrt%20%5B3%5D%20%7B2x%7D%29%20-%203%20%282%20%5Csqrt%20%5B3%5D%20%7Bx%7D%29%20%3D%5C%5C7%20%5Csqrt%20%5B3%5D%20%7B2x%7D%20-6%20%5Csqrt%20%5B3%5D%20%7B2x%7D%20-6%20%5Csqrt%20%5B3%5D%20%7Bx%7D%20%3D)
We add similar terms:
![\sqrt [3] {2x} -6 \sqrt [3] {x}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B2x%7D%20-6%20%5Csqrt%20%5B3%5D%20%7Bx%7D)
Answer:
Option C
Answer:
49
Step-by-step explanation: