Answer:
<u>Option A:</u>
![R(x)=20x^2+300x+1080](https://tex.z-dn.net/?f=R%28x%29%3D20x%5E2%2B300x%2B1080)
Explanation:
The revenue, R(x) is the product of the number of teams who entered the tournament, T(x), times the entry fee paid by each team, F(x); then you can write:
Thus you must multiply the two functions (polynomials):
Use distributive property:
![R(x)=(4x+24)\times (5x+45)=(4x)(5x)+(4x)(45)+(24)(5x)+(24)(45)](https://tex.z-dn.net/?f=R%28x%29%3D%284x%2B24%29%5Ctimes%20%285x%2B45%29%3D%284x%29%285x%29%2B%284x%29%2845%29%2B%2824%29%285x%29%2B%2824%29%2845%29)
Simplify:
![R(x)=(4x)(5x)+(4x)(45)+(24)(5x)+(24)(45)=20x^2+180x+120x+1080](https://tex.z-dn.net/?f=R%28x%29%3D%284x%29%285x%29%2B%284x%29%2845%29%2B%2824%29%285x%29%2B%2824%29%2845%29%3D20x%5E2%2B180x%2B120x%2B1080)
Add like terms:
![R(x)=20x^2+180x+120x+1080=20x^2+300x+1080](https://tex.z-dn.net/?f=R%28x%29%3D20x%5E2%2B180x%2B120x%2B1080%3D20x%5E2%2B300x%2B1080)
To find f(3), plug x = 3 in f(x),
∴ f(3) = 3(3)+1 = 9+1 = 10
Therefore, the ordered pair is (3,10)
For second one,
plug x = 10 in f⁻¹(x),
f⁻¹(10) = 10-1/3 = 9/3 = 3
Therefore, the ordered pair is (10,3)
Answer:
Goodness of fit
Step-by-step explanation:
Given
The theoretical probabilities
<em>See comment for complete question</em>
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Required
The type of test to be use
From the question, we understand that you are to test if the die is loaded or not using the given theoretical probabilities.
This test can be carried out using goodness of fit test because the goodness of fit is basically used to check the possibility of getting the outcome variable from a distribution. In this case, the outcome of the variables are the given theoretical probabilities.
In a nutshell, the goodness fit of test determines if the given data (in this case, the theoretical probabilities) is a reflection of what to expect in the original population.
Answer:
Step-by-step explanation:
percent increase = (new number - original number) / (original number) * 100
= (1200 - 840) / (840) * 100
= (360) / 840 * 100
= 0.4285 * 100
= 42.85% rounded to nearest percent = 43% <==
C = 2 pi r given r = 4
so
C = 2 pi (4)
C = 8 pi
answer
C. C = 8pi