Solution:
Diameter=11ft
Therefore radius=5.5 ft(Since radius=Diameter/2)
Volume of sphere=4/3py r^3
= 4/3.22/7.5.5^3
=697.19 Cubic feet.
Therefore the volume of sphere is 697.19 cubic feet.This is your required solution.
Answer:
![x= \frac{5^{14}+3}{2}](https://tex.z-dn.net/?f=x%3D%20%5Cfrac%7B5%5E%7B14%7D%2B3%7D%7B2%7D)
Step-by-step explanation:
The correct steps to solve the equation are:
![14=log_5(2x-5)](https://tex.z-dn.net/?f=14%3Dlog_5%282x-5%29)
![5^{14}=5^{log_5(2x-3)}](https://tex.z-dn.net/?f=5%5E%7B14%7D%3D5%5E%7Blog_5%282x-3%29%7D)
Because ![a^{log_am}=m](https://tex.z-dn.net/?f=a%5E%7Blog_am%7D%3Dm)
So, solving we get:
![5^{14}=2x-3](https://tex.z-dn.net/?f=5%5E%7B14%7D%3D2x-3)
Sum 3 on every side:
![5^{14}+3=2x-3+3\\5^{14}+3=2x](https://tex.z-dn.net/?f=5%5E%7B14%7D%2B3%3D2x-3%2B3%5C%5C5%5E%7B14%7D%2B3%3D2x)
Dividing by 2 into both sides:
![\frac{5^{14}+3}{2}=\frac{2x}{2}\\\frac{5^{14}+3}{2}=x](https://tex.z-dn.net/?f=%5Cfrac%7B5%5E%7B14%7D%2B3%7D%7B2%7D%3D%5Cfrac%7B2x%7D%7B2%7D%5C%5C%5Cfrac%7B5%5E%7B14%7D%2B3%7D%7B2%7D%3Dx)
So, the answer is ![x= \frac{5^{14}+3}{2}](https://tex.z-dn.net/?f=x%3D%20%5Cfrac%7B5%5E%7B14%7D%2B3%7D%7B2%7D)
The carrot cakes are the fraction of the cake given by
multiplied by ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
- The fraction of the cakes that are carrot cakes is
![\underline {\dfrac{1}{21}}](https://tex.z-dn.net/?f=%5Cunderline%20%7B%5Cdfrac%7B1%7D%7B21%7D%7D)
<h3>How are the cakes evaluated as fractions?</h3>
The fraction of the cake that are chocolate cake = ![\dfrac{2}{3}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B3%7D)
The fraction of the remaining cake that cheesecakes = ![\dfrac{6}{7}](https://tex.z-dn.net/?f=%5Cdfrac%7B6%7D%7B7%7D)
The rest of the cakes = carrot cakes
Required:
The fraction of the cake that are carrot cakes
Solution:
The fraction of the cakes that are not chocolate cake = ![1 - \dfrac{2}{3} = \mathbf{ \dfrac{1}{3}}](https://tex.z-dn.net/?f=1%20-%20%5Cdfrac%7B2%7D%7B3%7D%20%3D%20%5Cmathbf%7B%20%5Cdfrac%7B1%7D%7B3%7D%7D)
The fraction of the remaining cakes that are cheesecake = ![\dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{ \dfrac{6}{21}}](https://tex.z-dn.net/?f=%5Cdfrac%7B6%7D%7B7%7D%20%5Ctimes%20%5Cdfrac%7B1%7D%7B3%7D%20%3D%20%5Cmathbf%7B%20%5Cdfrac%7B6%7D%7B21%7D%7D)
The fraction of the cake that are carrot cake = ![\dfrac{1}{3} - \dfrac{6}{7} \times \dfrac{1}{3} = \mathbf{\dfrac{1}{21}}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B3%7D%20-%20%5Cdfrac%7B6%7D%7B7%7D%20%5Ctimes%20%5Cdfrac%7B1%7D%7B3%7D%20%3D%20%5Cmathbf%7B%5Cdfrac%7B1%7D%7B21%7D%7D)
- The fraction of the cakes that are carrot cake is
![\underline{\dfrac{1}{21}}](https://tex.z-dn.net/?f=%5Cunderline%7B%5Cdfrac%7B1%7D%7B21%7D%7D)
Learn more about fractions here:
brainly.com/question/3840488
I think it’s c............