Triangle Rotating in Square

Equilateral triangle EKP with side EK of length 2 inches is placed inside square EAMI with side of length 4 inches so that K is on side EA. The triangle is rotated clockwise about K, then P, and so on along the sides of the square until E, K, and P return to their original positions. The length of the path in inches traversed by vertex P is equal to:

  1. 20/3
  2. 32/3
  3. 12
  4. 40/3
  5. 15

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Wind Farm

Denmark is a major manufacturer of energy-producing wind turbines. Suppose both the following statements are true:

1. Some wind turbines in Ohio are not from Denmark, but are American-built.
2. All of the wind turbines in Lorain County are indeed from Denmark.

From these two statements, which of the following can be concluded?

  1. Some American-built wind turbines are in Lorain County.
  2. All Lorain county wind turbines are not American-built.
  3. Some American-built wind turbines are not in Lorain County.
  4. No Lorain County wind turbine is American-built.
  5. Some wind turbines in Ohio, but not in Lorain County, were built in Denmark.

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