To understand what [tex]\( h(40) = 1400 \)[/tex] means in the context of the given problem, let’s break it down step-by-step:
1. Understanding [tex]\( h(40) = 1400 \)[/tex]:
- The notation [tex]\( h(x) \)[/tex] represents a function where [tex]\( x \)[/tex] is the number of hours of training.
- [tex]\( h(40) = 1400 \)[/tex] indicates that when the number of hours of training is 40, the monthly pay is [tex]$1400.
2. Interpreting the given table:
The table shows the relationship between hours of training and corresponding monthly pay:
\[
\begin{array}{|c|c|}
\hline
\text{Hours of Training} & \text{Monthly Pay} \\
\hline
10 & 1100 \\
\hline
20 & 1200 \\
\hline
30 & 1300 \\
\hline
40 & 1400 \\
\hline
50 & 1500 \\
\hline
60 & 1600 \\
\hline
70 & 1700 \\
\hline
\end{array}
\]
3. Analyzing each option:
- Option A: A worker with 1400 hours of training is paid $[/tex]40 per month.
- This option is incorrect. The units are mismatched; we are not talking about 1400 hours of training but about the relationship between 40 hours of training and pay of [tex]$1400.
- Option B: A worker who works 40 hours is paid $[/tex]1400.
- This option is also incorrect. This is not about working hours but training hours. The statement conflates working hours with training hours.
- Option C: There are 40 workers who are paid [tex]$1400 per month.
- This option is incorrect because the given data speaks about individual training hours and corresponding pay, not about the number of workers.
- Option D: A worker with 40 hours of training is paid $[/tex]1400 per month.
- This option is correct. It directly correlates the 40 hours of training with the monthly payment of [tex]$1400, which matches the interpretation of \( h(40) = 1400 \).
Therefore, the correct interpretation is given by Option D: A worker with 40 hours of training is paid $[/tex]1400 per month.
