# CE Board Problems May 2017

## Angle Between Two Zero-Based Vectors in XY-Plane

**Problem**

What is the angle between zero-based vectors ${\bf V_1} = (-\sqrt{3}, ~ 1)$ and ${\bf V_2} = (2\sqrt{3}, ~ 2)$ in an *x*-*y* coordinate system?

A. 0° | C. 150° |

B. 180° | D. 120° |

## Probability of Winning the Carnival Game of Tossing a Coin Into a Table

**Problem**

In a common carnival game, a player tosses a penny from a distance of about 5 feet onto the surface of a table ruled in 1-inch squares. If the penny (3/4 inch in diameter) falls entirely inside a square, the player receives 5 cents but does not get his penny back; otherwise he loses his penny. If the penny lands on the table, what is his chance to win?

A. 5/16 | C. 9/256 |

B. 1/16 | D. 3/128 |