To determine which expression is equal to \( 1930 + 43(10 - 7 \cdot 40) \), we need to simplify the given expression and see if it matches any of the options.
Let's simplify \( 1930 + 43(10 - 7 \cdot 40) \):
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Calculate \( 7 \cdot 40 \): \[ 7 \cdot 40 = 280 \]
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Substitute it back into the expression: \[ 1930 + 43(10 - 280) \]
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Calculate \( 10 - 280 \): \[ 10 - 280 = -270 \]
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Substitute it back: \[ 1930 + 43 \cdot (-270) \]
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Calculate \( 43 \cdot (-270) \): \[ 43 \cdot (-270) = -11610 \]
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Now, combine the results: \[ 1930 - 11610 = -9670 \]
Now, we will analyze the options:
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403: Not equal to -9670.
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\(\frac{40}{3}\): Not equal to -9670.
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\(193 + 43(10 - 7 \cdot 4)\): Calculate:
- \(7 \cdot 4 = 28\)
- So \(10 - 28 = -18\).
- Then calculate \(43 \cdot (-18) = -774\).
- Now \(193 - 774 = -581\). Not equal to -9670.
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5: Not equal to -9670.
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\(193 + 43(10 - 7 \cdot 1)\): Calculate:
- \(7 \cdot 1 = 7\)
- So \(10 - 7 = 3\).
- Then calculate \(43 \cdot 3 = 129\).
- Now \(193 + 129 = 322\). Not equal to -9670.
After evaluating all options, none of the provided expressions are equal to \( 1930 + 43(10 - 7 \cdot 40) \).