Final answer:
The artist paints at a constant rate of 2 paintings every 3 hours. By continuing this pattern, we deduce that the artist will paint 8 paintings in 12 hours, which corresponds to option B.
Step-by-step explanation:
The student's question pertains to finding a relationship between the number of hours worked and the number of paintings completed by an artist, which is a typical problem in linear relationships in mathematics. By observing the provided table, we can see that the artist paints 2 paintings in 3 hours, and 4 paintings in 6 hours, indicating that the artist paints at a constant rate of 2 paintings every 3 hours. To complete the table and find out how many paintings the artist will paint in 12 hours, we simply extend this pattern
Here's the completed part of the table.
- 9 hours - 6 paintings
- 12 hours - 8 paintings (answer: B)
To confirm, we use the ratio of paintings to hours which is 2 paintings per 3 hours. This is a linear relationship with a constant rate of 2/3 paintings per hour.
Hours(Painting Rate) = Number of Paintings
3(2/3) = 2
6(2/3) = 4
9(2/3) = 6
12(2/3) = 8
It can be seen that in 12 hours, the artist will complete 8 paintings (B).