To solve this problem, we need to find the number of items a company ships each minute given that they ship an average of 30,000 items each week.
We'll go through the conversion process step-by-step:
1. We start with the number of items shipped per week: [tex]\( \frac{30,000 \text{ items}}{1 \text{ week}} \)[/tex].
2. We need to convert weeks to days. There are 7 days in a week, so:
[tex]\[ \frac{30,000 \text{ items}}{1 \text{ week}} \cdot \frac{1 \text{ week}}{7 \text{ days}} = \frac{30,000 \text{ items}}{7 \text{ days}} \][/tex]
3. Next, we convert days to hours. There are 24 hours in a day, so:
[tex]\[ \frac{30,000 \text{ items}}{7 \text{ days}} \cdot \frac{1 \text{ day}}{24 \text{ hours}} = \frac{30,000 \text{ items}}{7 \times 24 \text{ hours}} \][/tex]
4. Then, we convert hours to minutes. There are 60 minutes in an hour, so:
[tex]\[ \frac{30,000 \text{ items}}{7 \times 24 \text{ hours}} \cdot \frac{1 \text{ hour}}{60 \text{ minutes}} = \frac{30,000 \text{ items}}{7 \times 24 \times 60 \text{ minutes}} \][/tex]
So, consolidating the steps, we have:
[tex]\[
\frac{30,000 \text{ items}}{1 \text{ week}} \cdot \frac{1 \text{ week}}{7 \text{ days}} \cdot \frac{1 \text{ day}}{24 \text{ hours}} \cdot \frac{1 \text{ hour}}{60 \text{ minutes}} = \frac{30,000 \text{ items}}{7 \times 24 \times 60 \text{ minutes}}
\][/tex]
Given the numerical result from the calculation of the above expression is approximately 2.976190476190476.
Thus, the correct choice is:
(2) [tex]\[
\frac{30,000 \text{ items}}{1 \text{ week}} \cdot \frac{1 \text{ week}}{7 \text{ days}} \cdot \frac{1 \text{ day}}{24 \text{ hours}} \cdot \frac{1 \text{ hour}}{60 \text{ minutes}}
\][/tex]
This conversion correctly calculates the number of items shipped per minute.
