Answer:
![15.~f(g(2))=\Large\boxed{11}\\](https://tex.z-dn.net/?f=15.~f%28g%282%29%29%3D%5CLarge%5Cboxed%7B11%7D%5C%5C)
![16.~g(f(2.5))=\Large\boxed{16}](https://tex.z-dn.net/?f=16.~g%28f%282.5%29%29%3D%5CLarge%5Cboxed%7B16%7D)
![17.~g(f(-5))=\Large\boxed{1}](https://tex.z-dn.net/?f=17.~g%28f%28-5%29%29%3D%5CLarge%5Cboxed%7B1%7D)
![18.~f(g(-5))=\Large\boxed{-3}](https://tex.z-dn.net/?f=18.~f%28g%28-5%29%29%3D%5CLarge%5Cboxed%7B-3%7D)
Step-by-step explanation:
<h3>Given information</h3>
![f(x)=x+4](https://tex.z-dn.net/?f=f%28x%29%3Dx%2B4)
![g(x)=2x+3](https://tex.z-dn.net/?f=g%28x%29%3D2x%2B3)
<h3>Question 15. f(g(2))</h3>
<u>Substitute values into the first function</u>
![g(2)=2(2)+3](https://tex.z-dn.net/?f=g%282%29%3D2%282%29%2B3)
![g(2)=4+3](https://tex.z-dn.net/?f=g%282%29%3D4%2B3)
![g(2)=7](https://tex.z-dn.net/?f=g%282%29%3D7)
<u>Substitute the values of the first function into the second</u>
![f(g(2))=f(7)](https://tex.z-dn.net/?f=f%28g%282%29%29%3Df%287%29)
![f(7)=(7)+4](https://tex.z-dn.net/?f=f%287%29%3D%287%29%2B4)
![f(7)=\Large\boxed{11}](https://tex.z-dn.net/?f=f%287%29%3D%5CLarge%5Cboxed%7B11%7D)
<h3>Question 16. g(f(2.5))</h3>
<u>Substitute values into the first function</u>
![f(2.5)=(2.5)+4](https://tex.z-dn.net/?f=f%282.5%29%3D%282.5%29%2B4)
![f(2.5)=6.5](https://tex.z-dn.net/?f=f%282.5%29%3D6.5)
<u />
<u>Substitute the values of the first function into the second</u>
![g(f(2.5))=g(6.5)](https://tex.z-dn.net/?f=g%28f%282.5%29%29%3Dg%286.5%29)
![g(6.5)=2(6.5)+3](https://tex.z-dn.net/?f=g%286.5%29%3D2%286.5%29%2B3)
![g(6.5)=13+3](https://tex.z-dn.net/?f=g%286.5%29%3D13%2B3)
![g(6.5)=\Large\boxed{16}](https://tex.z-dn.net/?f=g%286.5%29%3D%5CLarge%5Cboxed%7B16%7D)
<h3>Question 17. g(f(-5))</h3>
<u>Substitute values into the first function</u>
![f(-5)=(-5)+4](https://tex.z-dn.net/?f=f%28-5%29%3D%28-5%29%2B4)
![f(-5)=-1](https://tex.z-dn.net/?f=f%28-5%29%3D-1)
<u>Substitute the values of the first function into the second</u>
![g(f(-5))=g(-1)](https://tex.z-dn.net/?f=g%28f%28-5%29%29%3Dg%28-1%29)
![g(-1)=2(-1)+3](https://tex.z-dn.net/?f=g%28-1%29%3D2%28-1%29%2B3)
![g(-1)=-2+3](https://tex.z-dn.net/?f=g%28-1%29%3D-2%2B3)
![g(-1)=\Large\boxed{1}](https://tex.z-dn.net/?f=g%28-1%29%3D%5CLarge%5Cboxed%7B1%7D)
<h3>Question 18. f(g(-5))</h3>
<u>Substitute values into the first function</u>
![g(-5)=2(-5)+3](https://tex.z-dn.net/?f=g%28-5%29%3D2%28-5%29%2B3)
![g(-5)=-10+3](https://tex.z-dn.net/?f=g%28-5%29%3D-10%2B3)
![g(-5)=-7](https://tex.z-dn.net/?f=g%28-5%29%3D-7)
<u>Substitute the values of the first function into the second</u>
![f(g(-5))=f(-7)](https://tex.z-dn.net/?f=f%28g%28-5%29%29%3Df%28-7%29)
![f(-7)=(-7)+4](https://tex.z-dn.net/?f=f%28-7%29%3D%28-7%29%2B4)
![f(-7)=\Large\boxed{-3}](https://tex.z-dn.net/?f=f%28-7%29%3D%5CLarge%5Cboxed%7B-3%7D)
Hope this helps!! :)
Please let me know if you have any questions
Answer:
Option B: |x - 27.6| = 5.3
Step-by-step explanation:
We are told that the average time for athletes on the Central High School track team to run 200 meters is 27.6 seconds.
We are also told that the slowest and fastest recorded times varied from the average by 5.3 seconds.
This means that the slowest time varied by 5.3 seconds more than the average while the fastest time varied by 5.3 seconds less than the average.
If x is to represent the slowest or fastest time, the absolute value equation can be written as;
|x - 27.6| = 5.3
You can work out that K≈2.9262 and then plugging this in gives us θ≈2.34∘
Answer:
5%
Step-by-step explanation:
<u>price after discount :</u>
9 600 - 9 600×40%
= 5760
<u>Original price (price without profit) :</u>
let x be the original price of the device.
x + x × 20% = 5760
Then
x = (5 760×100)÷120
= 4 800
<u>Original price increased by 30% :</u>
4 800 + 4 800×30%
= 6 240
<u>the discount needed to increase the profit by 10% :</u>
[(9 600-6 240)÷9 600]×100
= 35%
Then
to increase the profit by 10% ,we have to reduce
the percent of discount to :
40% - 35%
= 5%