To evaluate the expression \( 3_2 + (9 \times 4) - 7 \) according to the order of operations, we will follow these steps:
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Parentheses: Evaluate the expression inside the parentheses. \[ 9 \times 4 = 36 \]
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Substituting back into the expression: Replace the parentheses with the result. \[ 3_2 + 36 - 7 \]
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**Now we need to determine what \( 3_2 \) means. In mathematical notation, the subscript usually signifies the base of the numeral system. In this case, \( 3_2 \) is the representation of the number 3 in base 2 (binary). The decimal equivalent of \( 3_2 \) is: \[ 3_2 = 1 \times 2^1 + 1 \times 2^0 = 2 + 1 = 3 \]
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Substituting \( 3_2 \): Replace \( 3_2 \) with its decimal equivalent. \[ 3 + 36 - 7 \]
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Proceed with the addition and subtraction:
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First, add \( 3 + 36 \): \[ 3 + 36 = 39 \]
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Now subtract \( 7 \): \[ 39 - 7 = 32 \]
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Thus, the final result is: \[ \boxed{32} \]