If a pie chart is drawn to represent the total butter cookies produced by four companies, what is the central angle corresponding to the butter cookies produced by Company C?

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**Solution:**

1. Calculate the total number of butter cookies produced by all four companies:
   - Total cookies produced (butter + chocolate) = $100 	imes 10 = 1000$
   - Total chocolate cookies produced = $100 	imes 6 = 600$
   - Therefore, total butter cookies produced = $1000 - 600 = 400$

2. Calculate the butter cookies produced by Company C:
   - Total cookies by Company C = $35 	imes 10 = 350$
   - Chocolate cookies by Company C = $40 	imes 6 = 240$
   - Butter cookies by Company C = $350 - 240 = 110$

3. Find the central angle for Company C's butter cookies in the pie chart:
   $$	ext{Central angle} = \frac{	ext{Company C butter cookies}}{	ext{Total butter cookies}} 	imes 360 = \frac{110}{400} 	imes 360 = 99^\circ$$

**Answer:** $99^\circ$

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