Answer:
[tex]\textsf{C.} \quad \dfrac{65+58}{2}[/tex]
Step-by-step explanation:
The given expression is:
[tex]100\left(\dfrac{0.65f+0.58f}{2f}\right)[/tex]
Rewrite 100 as ¹⁰⁰/₁ :
[tex]\implies \dfrac{100}{1}\cdot \left(\dfrac{0.65f+0.58f}{2f}\right)[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\cdot\dfrac{b}{d}=\dfrac{ab}{cd}:[/tex]
[tex]\implies \dfrac{100(0.65f+0.58f)}{2f}[/tex]
Distribute the parentheses:
[tex]\implies \dfrac{100\cdot 0.65f+100\cdot 0.58f}{2f}[/tex]
[tex]\implies \dfrac{65f+58f}{2f}[/tex]
Factor out f from the numerator:
[tex]\implies \dfrac{(65+58)f}{2f}[/tex]
Cancel the common term f:
[tex]\implies \dfrac{65+58}{2}[/tex]
