the sample table above represented 25 cm at site i and 20 cm at site ii
site i | site ii
5 | 2 | 0 5 5
5 0 | 3 | 0 0 0 0 5 5
5 5 5 5 | 4 | 0 0 0 5
5 0 | 5 | 0 0 5 5
5 5 5 5 5 0 | 6 | 0 0 0 5 5 5
5 5 5 5 5 5 0 0 | 7 |
5 5 0 0 0 | 8 |
5 5 0 0 | 9 |
5 5 | 10 |
0 | 11 | 0 0 5 5 5 5
| 12 | 0 0 0 0 5
(a) what are the least and greatest depths (in cm) of artifact finds at site i?
least
× cm
greatest
× cm
what are the least and greatest depths (in cm) of artifact finds at site ii?
least
× cm
greatest
× cm

Question

the sample table above represented 25 cm at site i and 20 cm at site ii
 site i | site ii
 5 | 2 | 0 5 5
 5 0 | 3 | 0 0 0 0 5 5
 5 5 5 5 | 4 | 0 0 0 5
 5 0 | 5 | 0 0 5 5
 5 5 5 5 5 0 | 6 | 0 0 0 5 5 5
 5 5 5 5 5 5 0 0 | 7 |
 5 5 0 0 0 | 8 |
 5 5 0 0 | 9 |
 5 5 | 10 |
 0 | 11 | 0 0 5 5 5 5
 | 12 | 0 0 0 0 5
 (a) what are the least and greatest depths (in cm) of artifact finds at site i?
 least
 × cm
 greatest
 × cm
 what are the least and greatest depths (in cm) of artifact finds at site ii?
 least
 × cm
 greatest
 × cm

Accepted Answer

### Part (a) - Site I
# Explanation:
## Step1: Find least depth (Site I)
The stem - leaf plot for Site I: The first row (stem 2) has leaf 5, but we check the smallest stem with leaves. Wait, actually, the stem is the tens place? Wait, looking at the plot, the stem is the number in the middle. For Site I, the first non - empty stem (lowest stem) with leaves: Let's list the stems and leaves. The stems are 2,3,4,5,6,7,8,9,10,11,12? Wait no, the middle column is the stem. So for Site I:
- Stem 2: leaf 5 (so depth 25? Wait, no, maybe the stem is the tens digit and leaf is the units digit? Wait the problem says "25 cm at Site I and 20 cm at Site II" in the sample. Wait, maybe the stem is the tens place, leaf is units. So for Site I:
  - Stem 2: leaf 5 → 25 cm? No, wait the first entry for Site I: stem 2, leaf 5. Then stem 3: leaves 5,0? Wait no, maybe the stem is the integer part, leaf is the decimal? No, the problem is about depth in cm, probably whole numbers. Wait, let's look at the stems and leaves structure. The middle column is the stem (tens place), left (Site I) and right (Site II) are leaves (units place). So for Site I:
  - The smallest stem with a leaf: stem 2 (tens place 2), leaf 5 → 25? No, wait the first row: Site I has leaf 5, stem 2, Site II has leaves 0,5,5. Wait maybe the stem is the ones place? No, that doesn't make sense. Wait, maybe the stem is the main number, and leaves are the digits. Wait, let's check the least depth. The first (top - most) non - zero? Wait, the stem 2: Site I has leaf 5. Then stem 3: leaves 5,0? Wait, no, the left side (Site I) leaves: for stem 2, leaf 5; stem 3, leaves 5,0; stem 4, leaves 5,5,5,5; stem 5, leaves 5,0; stem 6, leaves 5,5,5,5,5,0; stem 7, leaves 5,5,5,5,5,5,0,0; stem 8, leaves 5,5,0,0,0; stem 9, leaves 5,5,0,0; stem 10, leaves 5,5; stem 11, leaf 0; stem 12, no leaves. Wait, no, maybe the stem is the tens digit, leaf is units. So stem 2: 20 + 5 = 25? But the problem says "25 cm at Site I and 20 cm at Site II" in the sample. Wait, maybe the stem is the tens digit, leaf is units, so for Site I:
  - The smallest depth: the smallest stem with a leaf. The top - most stem is 2, leaf 5 → 25? No, that can't be. Wait, maybe I got the stem and leaf reversed. Wait, the left is Site I, middle is stem, right is Site II. So for example, stem 2: Site I has leaf 5, Site II has leaves 0,5,5. So depth for Site I at stem 2 is 2 (stem) and leaf 5 → 25? Wait, no, maybe the stem is the units digit? No, that would make stem 2 as 2 cm, leaf 5 as 0.5 cm? No, the problem is about depth in cm, probably whole numbers. Wait, let's think differently. The least depth is the smallest value in Site I's leaves. The stems start at 2, then 3,4,5,6,7,8,9,10,11,12. Wait, the first (top) leaf in Site I is at stem 2 (leaf 5), then stem 3 (leaves 5,0), stem 4 (leaves 5,5,5,5), stem 5 (leaves 5,0), stem 6 (leaves 5,5,5,5,5,0), stem 7 (leaves 5,5,5,5,5,5,0,0), stem 8 (leaves 5,5,0,0,0), stem 9 (leaves 5,5,0,0), stem 10 (leaves 5,5), stem 11 (leaf 0), stem 12 (no leaves). Wait, maybe the stem is the tens digit, and leaf is the units digit, so the depth is $10\times stem + leaf$. So for Site I:
  - Stem 2, leaf 5: $10\times2 + 5=25$
  - Stem 3, leaves 5,0: $10\times3 + 5 = 35$, $10\times3+0 = 30$
  - Stem 4, leaves 5,5,5,5: $10\times4 + 5=45$ (four times)
  - Stem 5, leaves 5,0: $10\times5 + 5 = 55$, $10\times5+0 = 50$
  - Stem 6, leaves 5,5,5,5,5,0: $10\times6 + 5 = 65$ (five times), $10\times6+0 = 60$
  - Stem 7, leaves 5,5,5,5,5,5,0,0: $10\times7 + 5 = 75$ (six times), $10\times7+0 = 70$ (two times)
  - Stem 8, leaves 5,5,0,0,0: $10\times8 + 5 = 85$ (two times), $10\times8+0 = 80$ (three times)
  - Stem 9, leaves 5,5,0,0: $10\times9 + 5 = 95$ (two times), $10\times9+0 = 90$ (two times)
  - Stem 10, leaves 5,5: $10\times10 + 5 = 105$ (two times)
  - Stem 11, leaf 0: $10\times11+0 = 110$
  - Stem 12, no leaves.

Wait, but the least depth would be the smallest value, which is when stem is smallest and leaf is smallest. The smallest stem is 2, leaf is 5 → 25? But that seems high. Wait, maybe the stem is the ones digit, and leaf is the tenths? No, the problem says "depth (in cm)", probably whole numbers. Wait, maybe I misread the stem - leaf plot. Let's look at the original plot again:

Site I | Stem | Site II
  --- | --- | ---
  5 | 2 | 0 5 5
  5 0 | 3 | 0 0 0 0 5 5
  5 5 5 5 | 4 | 0 0 0 5
  5 0 | 5 | 0 0 5 5
  5 5 5 5 5 0 | 6 | 0 0 0 5 5 5
  5 5 5 5 5 5 0 0 | 7 |
  5 5 0 0 0 | 8 |
  5 5 0 0 | 9 |
  5 5 | 10 |
  0 | 11 | 0 0 5 5 5 5
    | 12 | 0 0 0 0 5

Ah! Maybe the stem is the tens digit, and the leaf is the units digit, but the numbers are written as (leaf)(stem)? No, that would be leaf is tens, stem is units. Wait, for example, in the first row: Site I has leaf 5, stem 2 → 52? No, that doesn't make sense. Wait, maybe the stem is the units digit, and the leaf is the tens digit? No. Wait, maybe the depth is (stem + leaf/10)? No, the problem is about whole cm.

Wait, let's think of the stem as the main number, and the leaves as the digits. For Site I, the first entry (top - most) is 5 (leaf) at stem 2. So maybe the depth is $2\times10 + 5=25$, next row: 5 and 0 at stem 3 → 35 and 30, next row: four 5s at stem 4 → 45 (four times), next row: 5 and 0 at stem 5 → 55 and 50, next row: five 5s and a 0 at stem 6 → 65 (five times) and 60, next row: six 5s and two 0s at stem 7 → 75 (six times) and 70 (two times), next row: two 5s and three 0s at stem 8 → 85 (two times) and 80 (three times), next row: two 5s and two 0s at stem 9 → 95 (two times) and 90 (two times), next row: two 5s at stem 10 → 105 (two times), next row: 0 at stem 11 → 110, stem 12: no leaves.

So the least depth at Site I is the smallest number, which is 25? Wait, but the stem 2, leaf 5. Then the greatest depth is the largest number, which is 110 (stem 11, leaf 0). Wait, but let's check Site II.

### Part (a) - Site II
For Site II, using the same logic (stem is tens, leaf is units):
- Stem 2, leaves 0,5,5 → 20,25,25
- Stem 3, leaves 0,0,0,0,5,5 → 30,30,30,30,35,35
- Stem 4, leaves 0,0,0,5 → 40,40,40,45
- Stem 5, leaves 0,0,5,5 → 50,50,55,55
- Stem 6, leaves 0,0,0,5,5,5 → 60,60,60,65,65,65
- Stem 7, no leaves
- Stem 8, no leaves
- Stem 9, no leaves
- Stem 10, no leaves
- Stem 11, leaves 0,0,5,5,5,5 → 110,110,115,115,115,115
- Stem 12, leaves 0,0,0,0,5 → 120,120,120,120,125

So the least depth at Site II is 20 (stem 2, leaf 0), and the greatest depth is 125 (stem 12, leaf 5).

Wait, but going back to Site I: the first leaf at stem 2 is 5, so 25. The last leaf at stem 11 is 0, so 110. So:

# Answer (Site I):
least: 25 cm
greatest: 110 cm

# Answer (Site II):
least: 20 cm
greatest: 125 cm

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Part (a) - Site I

Step1: Find least depth (Site I)

Answer: