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MicroCorp will hold its annual company picnic next week and will assign 3 planning duties to its employees. One person selected will reserve a venue, another will arrange catering, and a third will plan activities. There are 10 employees eligible to fulfill these duties, and no employee can be assigned more than one duty. How many different ways are there for duties to be assigned to employees?

(F) 7³

(G) 9³

(H) 10³

(J) 9 · 8 · 7

(K) 10 · 9 · 8

Triangle ACE, shown in the figure below, is isosceles with base . B lies on and D lies on . Segments and bisect AEC and CAE respectively. Which one of the following angle congruences is necessarily true?

(A) ∠CAE ≅ ∠BEC

(B) ∠CAD ≅ ∠AEC

(C) ∠CAE ≅ ∠ACE

(D) ∠AEC ≅ ∠ACE

(E) ∠BEC ≅ ∠DAE

Correct Answer: E

Greg is making a triangular sail for a boat, shaped like a right triangle and shown below.

The angle opposite the 120-foot side measures about 65.2°. Greg would like to make a second sail. This one will still be a right triangle with a 50-foot side as one leg, but the 120-foot side will be shortened until the angle opposite that side is about 10°. By about how many feet will Greg need to shorten the 120-foot side?

(Note: sin 10° ≈ .17, cos 10° ≈ .98, tan 10° ≈ .18)

(F) 9 (G) 49 (H) 71 (J) 111 (K) 122

Correct Answer: J

During their daily training race, Carl has to stop to tie his shoes. Melissa, whose shoes are velcro, continues to run and gets 20 feet ahead of Carl. Melissa is running at a constant rate of 8 feet per second, and Carl starts running at a constant rate of 9.2 feet per second to catch up to Melissa. Which of the following equations, when solved for s, gives the number of seconds Carl will take to catch up to Melissa?

(F) 8s + 20 = 9.2s (G) 8s - 20 = 9.2s (H) (J) 8s = 20 (K) 9.2s = 20

Correct Answer: F