Answer:
Model A
Step-by-step explanation:
Given the table :
___________M 1 ____ M 2 ____ M 3 ____M 4
Multiple R _ 0.993 ___ 0.991 ___0.936__ 0.746
R Square __0.987___ 0.982 ___0.877 __0.557
Adj R² ____ 0.982___ 0.978 __ 0.849 ___0.513
S E_______ 4,043 __ 4,463 ___11,615 __20,878 Observations_ 12 _____ 12 _____ 12 ____12
Based on the detains of the model given, we could use the R value, R² and standard error values to evaluate the performance of the different models.
The best model will be one with Correlation Coefficient (R value) closet to 1. The model with the highest R value will also have the highest Coefficient of determination, R² value. The a best model is one which has a low a standard error value.
From the table, Model A has the highest R and R² values. It also has the lowest standard error value. Hence, we can conclude that model A provides the best fit.
Answer: x = {-4, -1, 2}
<u>Step-by-step explanation:</u>
q p
F(x) = x³ + 3x² - 6x - 8
Possible rational roots are: +/- {1, 2, 4, 8}
F(1) = (1)³ + 3(1)² - 6(1) - 8
= 1 + 3 - 6 - 8
= -10 <em>Since the remainder is not 0, then x = 1 is not a root</em>
F(-1) = (-1)³ + 3(-1)² - 6(-1) - 8
= -1 + 3 + 6 - 8
= 0 <em>Since the remainder is 0, x = -1 is a root.</em>
Use synthetic division to find the remaining factor:
x = -1 → x + 1 = 0
-1 | 1 3 -6 -8
<u>| ↓ -1 -2 8 </u>
1 2 -8 0
(x + 1)(x² + 2x - 8) = 0
Next, factor the polynomial:
(x + 1)(x + 4)(x - 2) = 0
x + 1 = 0 x + 4 = 0 x - 2 = 0
x = -1 x = -4 x = 2
Answer:
Any equation of the form
y = kx + b,
with b different from zero
Step-by-step explanation:
For example
y = 5*x +3
cannot be written in the form
y = k*x, because there is a term that shifts the graph upwards.
6x+4/5=8
subtract 6x from both sides
4/5=8-6x
multiply both sides by 5 to get rid of the fraction
4=40-30x
divide both sides by 2
2=20-15x
add 15x to both sides
15x+2=20
subtract 2 from both sides
15x=18
divide both sides by 15
x=1.2
