Answered

Naterloo Park posted the following schedule listing the number of hours an employee works on a given day. Let [tex]\( B(x) \)[/tex], [tex]\( T(x) \)[/tex], [tex]\( R(x) \)[/tex], and [tex]\( S(x) \)[/tex] represent the number of hours worked by Bill, Ted, Rufus, and Socrates, respectively, on a given day [tex]\( x \)[/tex].

[tex]\[
\begin{tabular}{|l|r|r|r|r|r|}
\hline
& Mon & Tues & Wed & Thurs & Fri \\
\hline
Bill & 6 & 5 & 4 & 7 & 8 \\
\hline
Ted & 4 & 0 & 6 & 10 & 3 \\
\hline
Rufus & 8 & 3 & 6 & 5 & 0 \\
\hline
Socrates & 1 & 2 & 3 & 4 & 0 \\
\hline
\end{tabular}
\][/tex]

What is the value of [tex]\( S^{-1}(0) \)[/tex]?

[tex]\( S^{-1}(0) = \square \)[/tex]



Answer :

GinnyAnswer
To find the value of [tex]\( S^{-1}(0) \)[/tex], we need to determine the day on which Socrates worked 0 hours. Let’s look at the hours worked by Socrates for each day:

[tex]\[ \begin{array}{|l|r|r|r|r|r|} \hline & \text{Mon} & \text{Tues} & \text{Wed} & \text{Thurs} & \text{Fri} \\ \hline \text{Socrates} & 1 & 2 & 3 & 4 & 0 \\ \hline \end{array} \][/tex]

We observe the following:

- On Monday, Socrates worked 1 hour.
- On Tuesday, Socrates worked 2 hours.
- On Wednesday, Socrates worked 3 hours.
- On Thursday, Socrates worked 4 hours.
- On Friday, Socrates worked 0 hours.

From these observations, we see that Socrates worked 0 hours on Friday.

Given the days of the week are indexed as follows:

- Monday is [tex]\( x = 0 \)[/tex]
- Tuesday is [tex]\( x = 1 \)[/tex]
- Wednesday is [tex]\( x = 2 \)[/tex]
- Thursday is [tex]\( x = 3 \)[/tex]
- Friday is [tex]\( x = 4 \)[/tex]

Since Socrates worked 0 hours on Friday, and Friday corresponds to [tex]\( x = 4 \)[/tex], we have:

[tex]\[ S^{-1}(0) = 4 \][/tex]

So, the answer is:
[tex]\[ \boxed{4} \][/tex]