Explanation: To determine the day of the week for January 1, 2010, given that January 1, 2006, was a Sunday, we need to calculate the total number of days between these two dates and then find the remainder when this number is divided by 7. This remainder will tell us how many days have passed beyond complete weeks, which helps in determining the day of the week.
First, let's break down the years between 2006 and 2010:
- 2006: 365 days (non-leap year)
- 2007: 365 days (non-leap year)
- 2008: 366 days (leap year)
- 2009: 365 days (non-leap year)
Adding these together, we get:
\[ 365 + 365 + 366 + 365 = 1461 \text{ days} \]
Next, we need to find the remainder when 1461 is divided by 7:
\[ 1461 \div 7 = 208 \text{ remainder } 5 \]
This means that 1461 days is equivalent to 208 weeks and 5 extra days. Since January 1, 2006, was a Sunday, adding 5 days to Sunday gives us:
\[ \text{Sunday} + 5 \text{ days} = \text{Friday} \]
Therefore, January 1, 2010, was a Friday.
This method of calculating the day of the week is based on the principle that each week has 7 days, and the day of the week repeats every 7 days. By finding the remainder when the total number of days is divided by 7, we can determine the exact day of the week. It is important to account for leap years, as they add an extra day to the year, which affects the total number of days and, consequently, the day of the week.
In summary, the correct answer is Friday, as the calculation shows that 1461 days from a Sunday results in a Friday.