To solve \(2 \frac{3}{4} + (1 \frac{1}{2} + 3.8)\), we first convert everything to decimal form.
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Convert \(2 \frac{3}{4}\): \[ 2 \frac{3}{4} = 2 + \frac{3}{4} = 2 + 0.75 = 2.75 \]
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Convert \(1 \frac{1}{2}\): \[ 1 \frac{1}{2} = 1 + \frac{1}{2} = 1 + 0.5 = 1.5 \]
Now, we calculate the expression inside the parentheses: \[ 1.5 + 3.8 = 5.3 \]
Next, we add this result to \(2.75\): \[ 2.75 + 5.3 = 8.05 \]
Thus, the final answer is: \[ \boxed{8.05} \]