Question

1. four people have found the distance in kilometers across a canyon using different methods. their results are given in the table.

distance across quarry canyon (km)
juana lee ann ryne jackson
\\(\sqrt{28}\\) \\(\frac{23}{4}\\) \\(5.\overline{5}\\) \\(5\frac{1}{2}\\)

which two statements are true about the situation?

a. juana, lee ann, ryne, and jackson are in order from least to greatest.

b. ryne’s distance is closer to jackson’s distance than lee ann’s distance.

c. the values \\(\sqrt{28}\\), \\(5\frac{1}{2}\\), \\(5.\overline{5}\\), \\(\frac{23}{4}\\) are listed in order from least to greatest.

d. the difference between lee ann’s distance and ryne’s distance is 2 km.

Explanation:

Step1: Convert all values to decimals

• $\sqrt{28} \approx 5.2915$
• $\frac{23}{4} = 5.75$
• $5.\overline{5} = 5.555...$
• $5\frac{1}{2} = 5.5$

Step2: Evaluate Option A

Order the values: $\sqrt{28} \approx 5.2915$, $5\frac{1}{2}=5.5$, $5.\overline{5}=5.555...$, $\frac{23}{4}=5.75$. The given order (Juana, Lee Ann, Ryne, Jackson) is incorrect.

Step3: Evaluate Option B

Calculate distances:

• Ryne to Jackson: $|5.555... - 5.5| = 0.055...$
• Lee Ann to Jackson: $|5.75 - 5.5| = 0.25$

Since $0.055... < 0.25$, this statement is true.

Step4: Evaluate Option C

Order the given values: $\sqrt{28} \approx 5.2915$, $5\frac{1}{2}=5.5$, $5.\overline{5}=5.555...$, $\frac{23}{4}=5.75$. This matches the listed order, so the statement is true.

Step5: Evaluate Option D

Calculate difference: $|5.75 - 5.555...| = 0.194...
eq 2$, so the statement is false.

Answer:

B. Ryne's distance is closer to Jackson's distance than Lee Ann's distance.
C. The values $\sqrt{28}$, $5\frac{1}{2}$, $5.\overline{5}$, $\frac{23}{4}$ are listed in order from least to greatest.