Questions featuring probability & other concepts

1. How many rectangles are there in a line of fifteen squares where sides are lined up with the adjacent sides touching the entire length of the side?

2. If all the diagonals of a regular pentagon are drawn, how many triangles are formed?

3. If a 75-degree sector of a circle rotates around the center of a circle in 75-degree movements, how many sector movements will be needed for the sector to land directly in its original position?

4. A steel band is fitted around the equator. The band is removed and cut, and an additional 10 feet is added. The band now fits more loosely than it did before. How high off the ground is the band?

5. Using straight lines, connect these nine dots with the fewest number of lines without raising your pencil.

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