The equation that relates the number of parts the machine can make and the time in hours is p = 14t. Using this equation, we can predict that the machine can make 133 parts in 9 hours and 30 minutes.
To write an equation that relates the number of parts the machine can make and the time in hours, we need to determine the rate at which the machine produces parts.
Let's use the given information to find the rate.
In 4 hours, the machine can make 56 parts, so the rate of production is 56 parts / 4 hours = 14 parts per hour.
In 5 hours, the machine can make 70 parts, so the rate of production is 70 parts / 5 hours = 14 parts per hour.
Since the rate is the same in both cases, we can conclude that the machine has a constant rate of production of 14 parts per hour.
Now, let's use this information to write the equation.
Let p represent the number of parts and t represent the time in hours. The equation that relates the number of parts and the time in hours is:
p = 14t
This equation states that the number of parts produced (p) is equal to the rate of production (14) multiplied by the time in hours (t).
To predict how many parts the machine can make in 9 hours and 30 minutes (which is equivalent to 9.5 hours), we can substitute t = 9.5 into the equation:
p = 14 * 9.5
p = 133
Therefore, the machine can make 133 parts in 9 hours and 30 minutes.