What does [tex]h(40)=1400[/tex] mean in terms of the problem?
| Hours of Training | Monthly Pay |
|---|---|
| 10 | 1100 |
| 20 | 1200 |
| 30 | 1300 |
| 40 | 1400 |
| 50 | 1500 |
| 60 | 1600 |
| 70 | 1700 |
A. A worker with 40 hours of training is paid $1400 per month.
B. A worker with 1400 hours of training is paid $40 per month.
C. There are 40 workers who are paid $1400 per month.
D. A worker who works 40 hours is paid $1400.
Answer (2)
h ( 40 ) = 1400 means that when the hours of training is 40, the monthly pay is $1400 .
Option A correctly interprets this as 'A worker with 40 hours of training is paid $1400 per month.'
Other options misinterpret the meaning of the function or introduce irrelevant information.
Therefore, the correct answer is A.
Explanation
Understanding the Notation The problem provides a table showing the relationship between hours of training and monthly pay. The notation h ( 40 ) = 1400 means that when the input (hours of training) is 40, the output (monthly pay) is $1400.
Analyzing the Options Now, let's interpret what h ( 40 ) = 1400 means in the context of the given options:
Option A: A worker with 40 hours of training is paid $1400 per month. This aligns perfectly with the meaning of h ( 40 ) = 1400 .
Option B: A worker with 1400 hours of training is paid $40 per month. This is the reverse of what h ( 40 ) = 1400 represents. Option C: There are 40 workers who are paid $1400 per month. This option doesn't relate to the function h or the hours of training. Option D: A worker who works 40 hours is paid $1400 . This is similar to option A, but it doesn't explicitly mention 'hours of training', which is what the function h is based on.
Conclusion Therefore, the correct interpretation is that a worker with 40 hours of training is paid $1400 per month.
Examples
Understanding functions like h ( x ) is crucial in many real-world scenarios. For instance, if you're analyzing the cost of producing a product, you might have a function c ( n ) that tells you the cost of producing n items. If c ( 100 ) = 500 , it means that producing 100 items costs $500 . Similarly, in physics, if d ( t ) represents the distance traveled by an object after t seconds, then d ( 5 ) = 25 would mean the object traveled 25 meters after 5 seconds. These functions help us model and understand relationships between different quantities.
The notation h ( 40 ) = 1400 indicates that when a worker has 40 hours of training, they are paid $1400 monthly. The correct choice is Option A, which accurately reflects this relationship. Other options misrepresent the details given in the problem.
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