C. 31 [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
1. Convert mixed numbers into improper fractions:
[tex]\frac{29}{4}[/tex] · 2² + ( [tex]\frac{17}{2}[/tex] - 2) ÷ 3
2. Calculate within the parenthesis:
[tex]\frac{29}{4}[/tex] · 2² + [tex]\frac{13}{2}[/tex] ÷ 3
3. Calculate the exponent:
[tex]\frac{29}{4}[/tex] · 4 + [tex]\frac{13}{2}[/tex] ÷ 3
4. Multiply and divide (left to right):
29 + [tex]\frac{13}{2}[/tex] ÷ 3
29 + [tex]\frac{13}{6}[/tex]
5. Add:
[tex]\frac{187}{6}[/tex]
6. Convert the improper fraction to a mixed number:
= 31 [tex]\frac{1}{6}[/tex]
hope this helps!