To solve the expression \( 6:3(3+3) \), we need to follow the order of operations.
First, let's simplify the expression step by step:
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Calculate the expression inside the parentheses: \[ 3 + 3 = 6 \]
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Now, substitute this back into the original expression: \[ 6:3(6) \]
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The expression can be interpreted as division and multiplication. \( 6:3 \) is equivalent to \( 6 \div 3 \): \[ 6 \div 3 = 2 \]
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Now, multiply this result by \( 6 \): \[ 2 \times 6 = 12 \]
Thus, the value of the expression \( 6:3(3+3) \) is 12.
The answer from the options provided (11, 12, 9, 10) is \( \boxed{12} \).