Question
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Each of the lists below is in order from least to greate \( \mathrm{gr}^{\mathrm{st}} \) and has one number missing. List an example of a value that could correctly complete the blank in each list. 1. \( -\sqrt{49},-\frac{33}{5} \) \( \qquad \) ,\( -6 . \overline{4} \) 2. \( \qquad \) \( , 8.75,8 \frac{4}{5}, \sqrt{81} \) 3. \( -2 \frac{9}{10} \) \( \qquad \) \( ,-2 \frac{3}{5},-2.45 \)

Ask by Guzman Byrd. in the United States
Jan 24,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

Here are the example values to complete the lists: 1. **-6.5** 2. **8.5** 3. **-2.7**

Solution

Let's analyze each list to determine a suitable value that correctly completes the blank. ### 1. \( -\sqrt{49}, -\frac{33}{5} \),  **,** \(-6.\overline{4}\) **Step-by-Step:** - \( -\sqrt{49} = -7 \) - \( -\frac{33}{5} = -6.6 \) - \( -6.\overline{4} = -6.444\ldots \) The list is ordered from least to greatest: \[ -7 < -6.6 < \text{blank} < -6.444\ldots \] The blank must be a number between \(-6.6\) and \(-6.444\). **Example Value:** \[ -6.5 \] ### 2. **\(\text{blank}\), 8.75, \(8 \frac{4}{5}\), \(\sqrt{81}\)** **Step-by-Step:** - \( 8 \frac{4}{5} = 8.8 \) - \( \sqrt{81} = 9 \) The list is ordered from least to greatest: \[ \text{blank} < 8.75 < 8.8 < 9 \] The blank must be a number less than \(8.75\). **Example Value:** \[ 8.5 \] ### 3. \(-2 \frac{9}{10}\),  **,** \(-2 \frac{3}{5}\), \(-2.45\) **Step-by-Step:** - \(-2 \frac{9}{10} = -2.9\) - \(-2 \frac{3}{5} = -2.6\) The list is ordered from least to greatest: \[ -2.9 < \text{blank} < -2.6 < -2.45 \] The blank must be a number between \(-2.9\) and \(-2.6\). **Example Value:** \[ -2.7 \] ### **Summary of Example Values:** 1. **\(-6.5\)** 2. **\(8.5\)** 3. **\(-2.7\)**

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Extra Insights

For the first list, the missing number should be between \( -\sqrt{49} \) (which equals -7) and \( -6.\overline{4} \) (which is approximately -6.4). A suitable value is \( -7,5 \). In the second list, the missing number must fall between the empty spot and \( 8 \frac{4}{5} \) (which is equal to 8.8) and \( 8.75 \). A good candidate for this spot could be \( 8.5 \). For the third list, the missing number should be situated between \( -2 \frac{9}{10} \) (which is approximately -2.9) and \( -2 \frac{3}{5} \) (which is equal to -2.6). An example that fits is \( -2.8 \).

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