SOLUTION
From the question, we are told that y varies inversely as x
This is mathematically written as
![\begin{gathered} y\propto\frac{1}{x} \\ \propto\text{ is a sign of proportionality } \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%5Cpropto%5Cfrac%7B1%7D%7Bx%7D%20%5C%5C%20%5Cpropto%5Ctext%7B%20is%20a%20sign%20of%20proportionality%20%7D%20%5Cend%7Bgathered%7D)
Now, we will remove the proportionality sign and replace it with equal to sign =
If we do this, we will intoduce a constant k
![\begin{gathered} y\propto\frac{1}{x} \\ y=k\times\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%5Cpropto%5Cfrac%7B1%7D%7Bx%7D%20%5C%5C%20y%3Dk%5Ctimes%5Cfrac%7B1%7D%7Bx%7D%20%5C%5C%20y%3D%5Cfrac%7Bk%7D%7Bx%7D%20%5Cend%7Bgathered%7D)
So we have the formula
![y=\frac{k}{x}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bk%7D%7Bx%7D)
We will substitute the values of x for 10 and y for 8 into the formula to get k, we have
![\begin{gathered} y=\frac{k}{x} \\ 8=\frac{k}{10} \\ k=8\times10 \\ k=80 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D%5Cfrac%7Bk%7D%7Bx%7D%20%5C%5C%208%3D%5Cfrac%7Bk%7D%7B10%7D%20%5C%5C%20k%3D8%5Ctimes10%20%5C%5C%20k%3D80%20%5Cend%7Bgathered%7D)
Now, we will substitute k for 80 back into the formula to get the inverse function, we have
![\begin{gathered} y=\frac{k}{x} \\ y=\frac{80}{x} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D%5Cfrac%7Bk%7D%7Bx%7D%20%5C%5C%20y%3D%5Cfrac%7B80%7D%7Bx%7D%20%5Cend%7Bgathered%7D)
Hence the answer is option C
The number of different ways that they can stand in line is 6 ways.
Given that,
- There are three students namely Josiah, Hudson, and Gianna.
- They are line up behind the other.
Based on the above information, the number of different ways should be
Here we use the permutation formula to determine the no of different ways
![= ^3P_3\\\\= \frac{3!}{3 -3}!\\\\= 3!\\\\= 3\times 2\times 1](https://tex.z-dn.net/?f=%3D%20%5E3P_3%5C%5C%5C%5C%3D%20%5Cfrac%7B3%21%7D%7B3%20-3%7D%21%5C%5C%5C%5C%3D%203%21%5C%5C%5C%5C%3D%203%5Ctimes%202%5Ctimes%201)
= 6
Therefore we can say that the number of different ways that they can stand in line is 6 ways.
Learn more: brainly.com/question/19212668
Answer: 8.9%
Step-by-step explanation: 13 - 4.1
The largest number of caps Laura can purchase is 162.
x(number of caps)6 + 25 = c (cost)
(162)6 + 25 = 997
972 + 25 = 997
Hope this helps! <3