Let's examine each list to determine if they are ordered correctly in increasing order.
(A) [tex]\(-3.50, -2.75, -2.25, -1.05, 0.05\)[/tex]:
- [tex]\( -3.50 \)[/tex]
- [tex]\( -2.75 \)[/tex]
- [tex]\( -2.25 \)[/tex]
- [tex]\( -1.05 \)[/tex]
- [tex]\( 0.05 \)[/tex]
This list is increasing from left to right. Therefore, list A is ordered correctly.
(B) [tex]\(-\frac{1}{5}, -\frac{1}{7}, \frac{1}{7}, \frac{1}{5}, 40\%\)[/tex]:
- [tex]\( -\frac{1}{5} \approx -0.20 \)[/tex]
- [tex]\( -\frac{1}{7} \approx -0.14 \)[/tex]
- [tex]\( \frac{1}{7} \approx 0.14 \)[/tex]
- [tex]\( \frac{1}{5} = 0.20 \)[/tex]
- [tex]\( 40\% = 0.40 \)[/tex]
This list is increasing from left to right. Therefore, list B is ordered correctly.
(C) [tex]\(-\sqrt{11}, -\sqrt{9}, \sqrt{5}, 3, \sqrt{10}\)[/tex]:
- [tex]\( -\sqrt{11} \approx -3.32 \)[/tex]
- [tex]\( -\sqrt{9} = -3 \)[/tex]
- [tex]\( \sqrt{5} \approx 2.24 \)[/tex]
- [tex]\( 3 \)[/tex]
- [tex]\( \sqrt{10} \approx 3.16 \)[/tex]
This list is increasing from left to right. Therefore, list C is ordered correctly.
(D) [tex]\(-\frac{4}{3}, -\sqrt{4}, -\sqrt{1}, -0.08, -0.07\)[/tex]:
- [tex]\( -\frac{4}{3} \approx -1.33 \)[/tex]
- [tex]\( -\sqrt{4} = -2 \)[/tex]
- [tex]\( -\sqrt{1} = -1 \)[/tex]
- [tex]\( -0.08 \)[/tex]
- [tex]\( -0.07 \)[/tex]
To be ordered correctly, the sequence after [tex]\( -2 \)[/tex] should be increasing. However, the sequence [tex]\( -1.33 \)[/tex] comes before [tex]\( -2 \)[/tex], which is incorrect. Hence, list D is not ordered correctly.
Thus, the list that is NOT ordered correctly is:
(D) [tex]\( -\frac{4}{3}, -\sqrt{4}, -\sqrt{1}, -0.08, -0.07 \)[/tex]
