To determine which expression is equivalent to \( 4a + 2b + \frac{1}{4}c \), we need to analyze the given options one by one.
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Option: \( 4a + 2b + 1/4 c \)
- This matches exactly with the original expression.
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Option: \( 4a + 8b + c \)
- This does not match since the coefficients of \( b \) and \( c \) are different.
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Option: \( 4a + 2b + c \)
- This does not match since the coefficient of \( c \) is different.
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Option: \( 4a + 2b + 4c \)
- This does not match since the coefficient of \( c \) is also different.
After analyzing all the options, the expression that is equivalent to \( 4a + 2b + \frac{1}{4}c \) is:
\( 4a + 2b + 1/4 c \).