To find the factory's unit rate of bottles per minute, you need to determine how many bottles are produced each minute.
1. Identify the total number of bottles and the total time:
- The factory produces a total of 511 bottles of juice.
- The total time taken to produce these bottles is 7 minutes.
2. Set up the rate as a fraction:
- The rate can be written as [tex]\(\frac{511 \text { bottles}}{7 \text { minutes}}\)[/tex].
3. Simplify the fraction to find the unit rate:
- To find the unit rate of bottles per minute, divide the total number of bottles by the total number of minutes:
[tex]\[
\frac{511 \text { bottles}}{7 \text { minutes}} = 73 \text { bottles per minute}
\][/tex]
Therefore, the factory's unit rate is [tex]\(\frac{73 \text { bottles}}{1 \text { minute}}\)[/tex]. Hence, the correct option is [tex]\(\frac{73 \text { bottles}}{1 \text { minute}}\)[/tex].
