To find a number that represents the depth at which the emerald is located, we need to identify a number that falls within the range between \(-\frac{1}{2}\) and \(-\frac{5}{3}\) meters.
First, let's convert the fractions to have a common denominator for easier comparison:
- \(-\frac{1}{2} = -\frac{3}{6}\)
- \(-\frac{5}{3} = -\frac{10}{6}\)
So the range is between: \[ -\frac{5}{3} \text{ meters} \quad \text{to} \quad -\frac{1}{2} \text{ meters} \] or: \[ -\frac{10}{6} \text{ meters} \quad \text{to} \quad -\frac{3}{6} \text{ meters} \]
Now, let's check each option to see if it lies within this range:
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Negative \(2 \frac{1}{3}\) meters (which is \(-\frac{7}{3}\)): \(-\frac{7}{3}\) is less than \(-\frac{10}{6}\) (it is more negative), so it does not fit in the range.
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Negative \(\frac{3}{4}\) meters: This is equivalent to \(-0.75\) or \(-\frac{9}{12}\), which is larger (less negative than) both \(-\frac{10}{6}\) and \(-\frac{3}{6}\), so it does not fit in the range.
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Negative \(\frac{1}{4}\) meters: This is equivalent to \(-0.25\) or \(-\frac{3}{12}\), which is larger than \(-\frac{3}{6}\), so it does not fit in the range.
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Negative \(1 \frac{5}{6}\) meters (which is \(-\frac{11}{6}\)): \(-\frac{11}{6}\) is also less than \(-\frac{10}{6}\), so it does not fit in the range.
Since we have checked all options and found none fall within \(-\frac{10}{6}\) and \(-\frac{3}{6}\), none of the provided numbers represents the depth at which the emerald is located.
Upon double-checking:
- The valid numbers must be in the range \(-\frac{10}{6} \leq \text{number} < -\frac{3}{6}\), equivalent to \(-1.6667\) to \(-0.5\).
None of the given numbers fit that criteria: So:
None of the provided options accurately represent the depth.