Some More Problems

[yuanshi]

Sixty students, including # and Jane, are to be split into three classes of equal size. What is the probability taht # and Jane will be in the same calss, provided that the split is done randomly?

a 33.0% b 32.2% c 27.7% d 21.5% e 10.9%

Let x, y, and z be positive integers such that one of the interges is twice one of the other intergers. If the aritmetic mean of x,y, and z is 11 and the geometric mean of x,y, and z is 6, then the harmonic mean of x,y, and z is _____.

a 4.5 b 3.3 c 7.8 d 4.4 e 3.8

A Ferris wheel has a radius of 7 meters and turns at 6 revolutions per minute. The bottom of the Ferris wheel is 1 meter above the ground. The height h of a passenger above the ground varies sinusoidally with time t. which of the following equations best describes the relationship between h and t?

a h=6+7cos(π/6*t) b h=8+7sin(π/5*t) c h=7-6cos(π/5*t) d h=7-8sin(π/3*t) e h=8-7cos(π/5*t)

I'm trying to learn how to do these before regionals, so if you could help before then, that'd be great! :D I might add more later if I have more troubles (which probably will happen.)

[88bobcat]

[Kenon]

[88bobcat]

[atater]

isn't the answer for the harmonic mean problem 3.3? i have always learned that Harmonic Mean * Arithmetic Mean= Geometric Mean^2

[88bobcat]

[yuanshi]

Ahh thank you guys so much for the help!
The harmonic mean one helped greatly, because I had tried to use geometric mean squared over arithmetic mean as well and I couldn't find another way to do it!
On the one about probability, my answer key said B, which is not 33.3% -__- My dad had actually said to do it that way as well, but I keep thinking that there might be a more in depth solution than that? I'm not sure, but thank you for the help anyways :D
And thank you so much for the help on the cosine/sine one! :D

Here's another one:
Two aircraft carriers leave Port O' Math at 6:00 a.m. Carrier FlatPlane travels at 14 mph on a bearing of 328 degrees. Carrier StraitRay travels 18 mph on a bearing of 240 degrees. How far apart will they be at 10:00 a.m. that same day?

A 92.7 mi B 89.7 mi C 88.0 mi D 63.6 mi E 44.8 mi

I haven't done vectors in a while, and I couldn't remember how to start this one!

[Kenon]

I suppose you could use vectors on that problem you posted, but I personally would use triangles and the good ol' law of cosines.

[unparseable or potentially dangerous latex formula] or [unparseable or potentially dangerous latex formula]

Total time is about 20-40 seconds due to me being slow on the calculator.

[atater]

I have one question.
#24 Invitiational B
A recent visit to the planet Strangebase discovered that the equation 3S^2 - 25S +66=0 has two solutions, 4 and 9. What base was being used for the number system on planet Strangebase.

Is there a fast way to do this problem?

[88bobcat]

[atater]

Thanks so much!

[atater]

One more question on UIL Test C or TMSCA #6
Problem 12
Find the shortest distance from the point (5,12) and the line 5x+12y=13

The answer is 12.
I have done this question using calculus and just graphing the lines and i keep getting 12.77

[88bobcat]

[AuSmith]

[AuSmith]

[RussiaPSJA]