A researcher has discovered six new species of insects overseas and needs to transport them home. Some species will harm each other and so cannot be transported in the same container.Species A cannot be housed with species C or F.Species B cannot be housed with species D or F.Species C cannot be housed with species A, D, or E.Species D cannot be housed with species B, C, or F.Species E cannot be housed with species C or F.Species F cannot be housed with species A, B, D, or E. Use graph coloring to determine the minimum number of containers the researcher will need to transport the insects. The image contains four geometric diagrams, each labeled with points A, B, C, D, E, and F. These represent different configurations of hexagons with various intersecting lines.1. **Top Left Diagram**: - A hexagon with vertices labeled in sequence: A, B, C, D, E, F. - Lines connect A to B, B to C, C to D, D to E, E to F, and F back to A, forming the perimeter. - Diagonal lines AC and BE intersect within the hexagon.2. **Top Right Diagram**: - Another hexagonal shape with points A, B, C, D, E, and F. - The periphery of the hexagon is formed by lines AF, FB, AC, CD, DE, and EF. - Diagonal lines AD, BD, and CE intersect inside the hexagon, creating multiple triangles.3. **Bottom Left Diagram**: - This diagram displays a convex hexagon with points A through F. - The boundary lines are similar to the prior diagrams. - Inside the shape are intersecting lines AC, AD, and BE, creating a complex internal structure with additional smaller triangles.4. **Bottom Right Diagram**: - A six-sided figure consists of points A, B, C, D, E, and F arranged with diverse intersections. - The outer edges are connected as in previous figures looped from F to E, and A to B through to D. - Internal lines AB, BD, EC, and EF are drawn, generating an intricate pattern of intersecting triangles.Each diagram provides a unique arrangement of intersecting lines within the hexagonal shape, illustrating concepts relevant to geometry, such as diagonals and internal angles. These diagrams can aid in understanding geometric properties and relationships in hexagons and other polygons.

Name: A researcher has discovered six new species of insects overseas and ne
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: A researcher has discovered six new species of insects overseas and needs to transport them home. Some species will harm each other and so cannot be transported in the same container.Species A cannot be housed with species C or F.Species B cannot be

A researcher has discovered six new species of insects overseas and needs to transport them home. Some species will harm each other and so cannot be transported in the same container. Let (x, y) means x species and y species must be in different containers that are denoted by joining a line between them. Species A cannot be housed with species C or F.So, (A, C) and (A, F) should be present. Species B cannot be housed with species D or F.So, (B, D) and (B, F) should be present. Species C cannot be housed with species A, D, or E.So, (C, A), (C, D), and (C, E) should be present. Species D cannot be housed with species B, C, or F.So, (D, B), (D, C), and (D, F) should be present. Species E cannot be housed with species C or F.So, (E, C) and (E, F) should be present. Species F cannot be housed with species A, B, D, or E.So, (F, A), (F, B), (F, D), and (F, E) should be present. Now, we will check all the options and the above conditions that are supposed to satisfy.Notice that the third option is satisfying all the above criteria. Answer: Thus, the red circled graph is the correct answer.Now, we will use graph coloring to determine the minimum number of containers the researcher will need to transport the insects. Let us start coloring from node A. Hence, the researcher will need 3 containers to transport insects.