Answer: $57.6
Step-by-step explanation:
Given : A businesswoman sells a bag for $52.32.
Let cuurent selling price : SP = $52.32
As they are making 9% profit now.
That means SP= Cp +0.09 CP , where Cp is the cost price of bag.
i..e ![52.32=Cp(1+0.09) \ \text{[Substituted value of SP in LHS and taking Cp common outside in RHS]}](https://tex.z-dn.net/?f=52.32%3DCp%281%2B0.09%29%20%5C%20%5Ctext%7B%5BSubstituted%20value%20of%20SP%20in%20LHS%20and%20taking%20Cp%20common%20outside%20in%20RHS%5D%7D)
![\Rightarrow\ 52.32=Cp(1.09)\Rightarrow\ CP=\dfrac{52.32}{1.09}=48](https://tex.z-dn.net/?f=%5CRightarrow%5C%2052.32%3DCp%281.09%29%5CRightarrow%5C%20CP%3D%5Cdfrac%7B52.32%7D%7B1.09%7D%3D48)
i..e Cost price of bag = 48
Selling price to gain 20% profit = Cp+0.20CP
= CP(1+0.20)
=48 (1.20)
= 57.6
Hence, the selling price the businesswoman should ask in order to make 20% profit = $57.6
An equivalent measurement to 2 meters is 200 cm. Since 1 meter is equivalent to 100 cm, multiply both of them by two. So, your answer is - 2 meters is equivalent to 200 cm.
Hope it helps :)
ANSWER
![g(f( - 1)) = \frac{1}{5 }](https://tex.z-dn.net/?f=g%28f%28%20-%201%29%29%20%3D%20%5Cfrac%7B1%7D%7B5%20%7D)
EXPLANATION
The given function is:
![f(x) = {x}^{2}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%7Bx%7D%5E%7B2%7D%20)
and
![g(x) = \frac{1}{2x + 3}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%20%5Cfrac%7B1%7D%7B2x%20%2B%203%7D%20)
![g(f(x)) = g( {x}^{2} )](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%20g%28%20%7Bx%7D%5E%7B2%7D%20%29)
![g(f(x)) = \frac{1}{2{x}^{2} + 3 }](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%20%5Cfrac%7B1%7D%7B2%7Bx%7D%5E%7B2%7D%20%2B%203%20%7D%20)
To find g(f(-1)), we substitute x=-1, to obtain;
![g(f( - 1)) = \frac{1}{2{( - 1)}^{2} + 3 }](https://tex.z-dn.net/?f=g%28f%28%20-%201%29%29%20%3D%20%5Cfrac%7B1%7D%7B2%7B%28%20-%201%29%7D%5E%7B2%7D%20%2B%203%20%7D%20)
We simplify the square in the denominator to get,
![g(f( - 1)) = \frac{1}{2+ 3 }](https://tex.z-dn.net/?f=g%28f%28%20-%201%29%29%20%3D%20%5Cfrac%7B1%7D%7B2%2B%203%20%7D%20)
We now add the denominator to obtain;
![g(f( - 1)) = \frac{1}{5 }](https://tex.z-dn.net/?f=g%28f%28%20-%201%29%29%20%3D%20%5Cfrac%7B1%7D%7B5%20%7D%20)