Answer:
0.05547
Step-by-step explanation:
Given :
_____Peter __ Alan __ Sui__total
Before 1838 __ 418 ___1475 _3731
After _ 1420 __ 329 ___1140_2889
Total _3258 __ 747 __ 2615 _6620
The expected frequency = (Row total * column total) / N
N = grand total = 6620
Using calculator :
Expected values are :
1836.19 __ 421.006 __ 1473.8
1421.81 ___325.994__ 1141.2
χ² = Σ(Observed - Expected)² / Expected
χ² = (0.00177817 + 0.0214571 + 0.000974852 + 0.00229642 + 0.0277108 + 0.00125897)
χ² = 0.05547
Answer:
its how much money he will get
Step-by-step explanation:
-20=-4x-6x
4x+6x=20
10x=20
x=20:10
x=2
proof:
-20=-4×2-6×2
-20=-8-12
(-8)+(-12)=-20
Note that f(x) as given is <em>not</em> invertible. By definition of inverse function,
![f\left(f^{-1}(x)\right) = x](https://tex.z-dn.net/?f=f%5Cleft%28f%5E%7B-1%7D%28x%29%5Cright%29%20%3D%20x)
![\implies f^{-1}(x)^3 - f^{-1}(x) + 2 = x](https://tex.z-dn.net/?f=%5Cimplies%20f%5E%7B-1%7D%28x%29%5E3%20-%20f%5E%7B-1%7D%28x%29%20%2B%202%20%3D%20x)
which is a cubic polynomial in
with three distinct roots, so we could have three possible inverses, each valid over a subset of the domain of f(x).
Choose one of these inverses by restricting the domain of f(x) accordingly. Since a polynomial is monotonic between its extrema, we can determine where f(x) has its critical/turning points, then split the real line at these points.
f'(x) = 3x² - 1 = 0 ⇒ x = ±1/√3
So, we have three subsets over which f(x) can be considered invertible.
• (-∞, -1/√3)
• (-1/√3, 1/√3)
• (1/√3, ∞)
By the inverse function theorem,
![\left(f^{-1}\right)'(b) = \dfrac1{f'(a)}](https://tex.z-dn.net/?f=%5Cleft%28f%5E%7B-1%7D%5Cright%29%27%28b%29%20%3D%20%5Cdfrac1%7Bf%27%28a%29%7D)
where f(a) = b.
Solve f(x) = 2 for x :
x³ - x + 2 = 2
x³ - x = 0
x (x² - 1) = 0
x (x - 1) (x + 1) = 0
x = 0 or x = 1 or x = -1
Then
can be one of
• 1/f'(-1) = 1/2, if we restrict to (-∞, -1/√3);
• 1/f'(0) = -1, if we restrict to (-1/√3, 1/√3); or
• 1/f'(1) = 1/2, if we restrict to (1/√3, ∞)
Just subtract 2.003 and 0.520 which gives you 1.483 so there is 1.483 kilogram of soil remaining hope this helps!