To compare the expressions \( 8 \) and \( B \left( \frac{5}{6} \times 250 \right) + B \left( \frac{1}{3} \times 250 \right) + B \left( \frac{1}{2} \times 250 \right) \), we can analyze the component parts without doing any actual calculations.
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First Term: \( B \left( \frac{5}{6} \times 250 \right) \)
- This term is dependent on the value of \( B \). Its value will be a little less than \( 250 \) because \( \frac{5}{6} \) represents a little less than \( 1 \).
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Second Term: \( B \left( \frac{1}{3} \times 250 \right) \)
- This term will be approximately \( \frac{250}{3} \), which is around \( 83.33B \).
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Third Term: \( B \left( \frac{1}{2} \times 250 \right) \)
- This term simplifies to \( 125B \).
Combining these terms, we have:
\[ B \left( \frac{5}{6} \times 250 \right) + B \left( \frac{1}{3} \times 250 \right) + B \left( \frac{1}{2} \times 250 \right) \]
Adding these gives:
\[ B \left( \frac{5 \times 250}{6} + \frac{250}{3} + \frac{250}{2} \right) \]
Now, we can look at the right-hand side without calculating the exact values. The sum of these fractions will yield a total that scales with \( B \).
Notably, for comparison:
- \( B(125 + \frac{250}{2} + \frac{250}{3}) \) will vary greatly depending on \( B \).
- Since \( 125 + \frac{250}{2} + \frac{250}{3} \) simplifies to something clearly larger than the \( 8 \) (since the individual components imply values of \( B \) which are at least nonzero and likely greater than \( 8 \), provided \( B \) is positive).
Thus, without calculating exact numerical values, we can infer:
- If \( B \) takes a non-negative value, the expression on the right will almost certainly exceed \( 8 \).
- Therefore, \( 8 \) would be less than or equal to the combined expression if \( B \) is positive.
Conclusion:
Assuming \( B \) is a positive constant, the expression \( B \left( \frac{5}{6} \times 250 \right) + B \left( \frac{1}{3} \times 250 \right) + B \left( \frac{1}{2} \times 250 \right) \) is likely greater than \( 8 \).