Let's generalize problem 6 to a regional ultimate frisbee tournament where there are n teams attending. teams are assigned numbers (1 through n) when they register. as before, each team will play each other team exactly once. (a) how many games does team 1 play? (b) how many games does team 2 play? wait that counts the team 1 versus team 2 game twice. how many not-yet-counted games does team 2 play? (c) keep going. how many "new" (uncounted) games does team i play? (d) how many games are played in total?

add the numbers under frequency to find the total number:

5 + 8 +7 + 4 + 0 +1 = 25

the answer is 25.

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west