To determine the number of days per year you would be asleep if you sleep 6 hours a day every day for a year, given that this is equivalent to [tex]\(\frac{1}{4}\)[/tex] of the year, we start with the total number of days in a year, which is 365 days.
### Step-by-Step Solution:
1. Fraction of the Year Slept: We are given that sleeping 6 hours a day equates to [tex]\(\frac{1}{4}\)[/tex] of the year.
2. Calculate the Exact Days Slept:
- To find out how many days that corresponds to, we take [tex]\(\frac{1}{4}\)[/tex] of 365 days.
- [tex]\[\frac{1}{4} \times 365 = 91.25\][/tex]
3. Convert the Decimal to a Mixed Number:
- The result 91.25 days means we have 91 whole days plus a fraction of a day.
- The decimal part, 0.25, needs to be converted to a fraction.
- [tex]\[0.25 = \frac{1}{4}\][/tex]
4. Combined Result as Mixed Number:
- So, the total number of days slept can be expressed as:
- [tex]\[91 \frac{1}{4}\][/tex]
Therefore, the number of days per year that you would sleep, expressed as a mixed number, is [tex]\(91 \frac{1}{4}\)[/tex] days. Thus, the correct answer is:
[tex]\[ \boxed{91 \frac{1}{4} \text{ days}} \][/tex]
