Answer:
To determine the number of each type of fish in the pond based on the data collected by Jake, let's first analyze the sample data he obtained:
Sample Bluegill Largemouth Bass
1 15 5
2 10 4
3 8 3
4 12 4
5 15 6
Now, let's calculate the average proportion of each type of fish across the samples:
For Bluegill:
Sample 1:
15
20
=
0.75
20
15
=0.75
Sample 2:
10
14
≈
0.714
14
10
≈0.714
Sample 3:
8
11
≈
0.727
11
8
≈0.727
Sample 4:
12
16
=
0.75
16
12
=0.75
Sample 5:
15
21
≈
0.714
21
15
≈0.714
Average proportion of Bluegill:
0.75
+
0.714
+
0.727
+
0.75
+
0.714
5
≈
0.731
5
0.75+0.714+0.727+0.75+0.714
≈0.731
For Largemouth Bass:
Sample 1:
5
20
=
0.25
20
5
=0.25
Sample 2:
4
14
≈
0.286
14
4
≈0.286
Sample 3:
3
11
≈
0.273
11
3
≈0.273
Sample 4:
4
16
=
0.25
16
4
=0.25
Sample 5:
6
21
≈
0.286
21
6
≈0.286
Average proportion of Largemouth Bass:
0.25
+
0.286
+
0.273
+
0.25
+
0.286
5
≈
0.269
5
0.25+0.286+0.273+0.25+0.286
≈0.269
Now, let's use these average proportions to estimate the total number of each type of fish in the pond. Since Jake put a total of 120 fish in the pond, we can multiply the average proportions by 120 to estimate the number of Bluegill and Largemouth Bass:
Estimated number of Bluegill:
0.731
×
120
≈
87.72
0.731×120≈87.72 (approximately 88)
Estimated number of Largemouth Bass:
0.269
×
120
≈
32.28
0.269×120≈32.28 (approximately 32)
Based on these calculations, I would predict that there are approximately 88 Bluegill and 32 Largemouth Bass in the pond. This estimation is based on the average proportions observed in the samples collected by Jake.
Step-by-step explanation:
