To determine how the range changes if the number 6 replaces one of the 1's in the set of numbers \(6513212\), we need to first establish the current range and then calculate the range after the change.
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Current Validation of the Data The given number \(6513212\) appears to be a single number rather than a set of separate numbers, assuming we treat each digit individually, we have the set \( {6, 5, 1, 3, 2, 1, 2} \).
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Finding the Current Range
- The minimum number in the set \( {6, 5, 1, 3, 2, 1, 2} \) is \(1\).
- The maximum number is \(6\).
- The range is calculated as: \[ \text{Range} = \text{Maximum} - \text{Minimum} = 6 - 1 = 5 \]
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Replacing One of the 1's with a 6 If we replace one of the 1's with a 6, the new set would look like this: \( {6, 5, 6, 3, 2, 2} \).
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Finding the New Range
- The new minimum number is still \(2\) (since the 1 has been replaced).
- The maximum number remains \(6\).
- The new range would be: \[ \text{Range} = 6 - 2 = 4 \]
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Result of the Change The change changes the range from \(5\) to \(4\).
In conclusion, the range changes from 5 to 4 when one of the 1's is replaced with a 6.
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