Type of Cap/Year 2008 2009 2010 2011 2012 M 576 896 287 896 884 N 560 753 473 560 637 Q 586 637 576 753 678 R 778 780 560 780 678
Cap Production Comparison: Find Equal Output Year
The question asks us to identify the specific year when the production volume (in thousands) of Cap Q was exactly the same as the production volume of Cap R. We can determine this by carefully examining the data provided in the table.
| Type of Cap/Year | 2008 | 2009 | 2010 | 2011 | 2012 |
| M | 768 | 962 | 878 | 968 | 884 |
| N | 560 | 753 | 473 | 560 | 637 |
| Q | 586 | 637 | 576 | 753 | 678 |
| R | 778 | 780 | 560 | 780 | 678 |
Detailed Data Analysis: Cap Q vs Cap R Production
To find the year where Cap Q production equals Cap R production, we will compare their values year by year:
- 2008: Cap Q production was 586 (thousand), while Cap R production was 778 (thousand). These are not equal.
- 2009: Cap Q production was 637 (thousand), while Cap R production was 780 (thousand). These are not equal.
- 2010: Cap Q production was 576 (thousand), while Cap R production was 560 (thousand). These are not equal.
- 2011: Cap Q production was 753 (thousand), while Cap R production was 780 (thousand). These are not equal.
- 2012: Cap Q production was 678 (thousand), and Cap R production was also 678 (thousand). These values are equal.
The condition is met when the production of Cap Q is the same as Cap R. Using mathematical notation, we are looking for a year 'Y' such that: $Production_Q(Y) = Production_R(Y)$
Based on our analysis, this equality holds true for the year 2012, where both Cap Q and Cap R had a production of 678 thousand units.
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