Final answer:
The number of different segments that can be formed by connecting the vertices of a cube is 16.
Step-by-step explanation:
The number of different segments that can be formed by connecting the vertices of a cube can be found by counting the number of pairs of vertices and subtracting the number of edges. Each pair of vertices is connected by a segment, so there are 8 Choose 2 or 28 pairs of vertices. However, each edge of the cube is counted twice as it connects two pairs of vertices, so we need to subtract the number of edges which is 12. Therefore, the number of different segments that can be formed is 28 - 12 = 16.