Explanations:To determine the day of the week for January 1, 2010, given that January 1, 2006, was a Sunday, we need to account for the number of days in each year, including leap years. Each non-leap year has 365 days, which is 52 weeks plus 1 day. Therefore, the day of the week advances by one day each year. Leap years, which occur every four years, have 366 days, advancing the day of the week by two days.
Let's break down the years from 2006 to 2010:
1. **2006**: This is a non-leap year, so the day of the week advances by 1 day. January 1, 2007, is a Monday.
2. **2007**: This is a non-leap year, so the day of the week advances by 1 day. January 1, 2008, is a Tuesday.
3. **2008**: This is a leap year, so the day of the week advances by 2 days. January 1, 2009, is a Thursday.
4. **2009**: This is a non-leap year, so the day of the week advances by 1 day. January 1, 2010, is a Friday.
Thus, the day of the week on January 1, 2010, is Friday. This calculation takes into account the leap year in 2008, which adds an extra day to the week cycle, making the correct day Friday.