Let's analyze each of the statements one by one to determine if they are true.
Statement #1: \(3 \cdot 20 = 4(6 + 9)\)
Calculating each side:
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Left side: \[ 3 \cdot 20 = 60 \]
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Right side: \[ 4(6 + 9) = 4 \cdot 15 = 60 \]
Both sides are equal, so Statement #1 is true.
Statement #2: \(4 \cdot 12 = 6 \cdot (8 \cdot 2) \quad 12 + 6 \cdot \sqrt{64} = 2 \cdot 4 \cdot 8\)
We'll break this down into two parts.
Part A: \[ 4 \cdot 12 \quad \text{and} \quad 6 \cdot (8 \cdot 2) \]
Calculating each side:
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Left side: \[ 4 \cdot 12 = 48 \]
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Right side: \[ 6 \cdot (8 \cdot 2) = 6 \cdot 16 = 96 \]
So part A is false.
Now for Part B: \[ 12 + 6 \cdot \sqrt{64} \quad \text{and} \quad 2 \cdot 4 \cdot 8 \]
Calculating:
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Left side: \[ 6 \cdot \sqrt{64} = 6 \cdot 8 = 48 \]
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Thus, \[ 12 + 48 = 60 \]
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Right side: \[ 2 \cdot 4 \cdot 8 = 8 \cdot 8 = 64 \]
So part B is also false.
Therefore, Statement #2 is false.
Statement #3: \(4 \cdot 18 - 4 \cdot 6 = 42 + 4 \cdot 8\)
Calculating each side:
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Left side: \[ 4 \cdot 18 - 4 \cdot 6 = 72 - 24 = 48 \]
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Right side: \[ 42 + 4 \cdot 8 = 42 + 32 = 74 \]
Since \(48 \neq 74\), Statement #3 is false.
Summary of Statements:
- Statement #1: True
- Statement #2: False
- Statement #3: False
Therefore, the only true statement is Statement #1.