Answer:
g and f are inverse functions because g(f(x)) = f(g(x)) = x
Step-by-step explanation:
Let's start by finding f(g(x)) and g(f(x)). As we discussed in another question, to find a composite function, apply the outer function to whatever the inner function evaluates to. We can start with f(g(x)):
Now, let's find g(f(x)):
There is a property that says that if f(g(x)) = g(f(x)) = x, the two functions are inverse. This suggests that g and f are inverse functions. We can verify this by taking one function, switching y and x, and then solving for y. If we complete this process and find that we get the OTHER function, it means the two functions are inverse. Let's try that:
Swap x and y:
Solve for y:
Notice that we got g, which means f and g are inverse.
You can choose to expand the equation to find the coefficient of x7 but that would take a lot of time. Here is a useful tactic that can help;
11C(something)(1)(x)⁷ ----> This gives the coefficient of x⁷
11C7(1)⁴(x)⁷ ----> You know that pascal's triangle is equal on both sides
11C7×1⁴ = coefficient of x⁷ (just ignore x⁷)
330x1⁴=330
This means that the coefficient of x⁷ is 330. You can double check by expanding the equation. If you do not understand what I did there, you can ask me how I got to the solution.
Hope I helped :)
Answer:
The prediction error is calculated as the difference between the actual value and the predicted value of the hurricane tracks.
the actual and the predicted value can then be converted into stationary miles
Step-by-step explanation:
The prediction error is calculated as the difference between the actual value and the predicted value of the hurricane tracks.
Now,
both the values i.e the actual and the predicted value can then be converted into stationary miles using the conversion factor without changing the association with the year,
Hence,
it will do the same for the Prediction error.
Answer:
FV= $34,222.33
Step-by-step explanation:
<u>First, we need to calculate the weekly interest rate:</u>
Weekly interest rate= 0.0289/52= 0.00056
<u>To calculate the future value (FV), we need to use the following formula:</u>
FV= {A*[(1+i)^n-1]}/i
A= weekly deposit
n= 15*52= 780
A= $35
FV= {35*[(1.00056^780) - 1]} / 0.00056
FV= $34,222.33
Answer:
5%
Step-by-step explanation:
15/300 = 0.05
5%
