CPhill

In how many ways can a committee consisting of faculty members and students be formed if there are faculty members and students eligible to serve on the committee?

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Well.......that's a tough one to answer !!  We'd have to know three things:

1.  What is the composition of the committee??

2.  How many faculty members are there to be chosen from??

3.  How many students are there to be chosen from??

I can give you an abstract aswer. Let's suppose that we have a committe composed of "f" faculty members and "s" students. And we have "F" faculty members to choose from and "S" students to choose from. Then the total ways the committee can be formed is just C(F, f) * C(S,s), where C (n,r) means the total unordered sets that can formed by selecting r things from n things and r ≤ n.

I wondered about this....when I was answering the question - or, at least, what I thought was the question - there wasn't any website address below it !!

Weird !!!

Re: Find a possible solution to the equation sin(3x+13)=cos(4x).

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Using the fact that sine and cosine are co-functions,

Note that ....[3x + 13] + [4x] = 90

7x + 13 = 90

7x = 77

x = 11

check

sin[3(11) + 13]° = cos [4(11]]°    ???

sin[46]° = cos [44]°    ???

0.719339800339 = 0.719339800339  √

Re: what is 85million times one cent equal

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85,000, 000 x $(1 / 100) = $850, 000

2(x-1)-6>-6+(x+3)-4x

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Let's simplify this first......we have

2x - 2 - 6 > -6 + x + 3 - 4x

2x - 8 > -3 - 3x        Let's get the "x's" on the left and the "integers" on the right.... so we have

5x > 5    and

x > 1

In "interval" notation, we have (1, ∞)

To check that this is correct, pick two points on either "side" of 1......any values less than 1 should make the original inequality false, and any points greater than 1 should make it true.

Re: If x and y are positive integers, what are all the solutions (x,y) of the equation (3*x) + (2*y) = 11

-------------------------------------------------------------------------------------------------------------------------- What we have here is a line with the following equation.

y = (-3/2)x + 11/2  

It has  a y-intercept of (0, 11/2) and an x intercept of (11/3,0) ≈ (3.66, 0) Since you specified that x  and y must be positive integers, we're looking for any x values that lie between 1 and 3, inclusively.

So we have:

x = 1,   y = 4  

x = 2,   y = 5/2

x = 3,   y = 1

So, the only things that "work" are (1,4) and (3,1)  

Elimination. How do i solve this?

x+2y=13

-x+y=5

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Let's just add the equations together.......that will eliminate "x"

So we have

3y = 18      Divide both sides by 3 and we find that y = 6. Using either one of the equations - I'll pick the second one - substitute 6 for y to find x.  Thus, -x +6 = 5. Subtract 6 from both sides, and we get that -x = -1. Therefore, x = 1.

Make sure you check to see that both answers "work" in the first equation....I think they will...

WHAT IS THE DECIMAL OF 510%

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Drop the % sign, move the decinal two places to the left. Thus, 100% becomes 1.00.....60% is .60, etc.

I think you can do it now.......

When Θ = 5 pi over 3, what are the reference angle and the sign values for sine, cosine, and tangent?

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OK.......converting from rads to degrees, we have

(5pi)/3 = 180 degrees/pi = 300 degrees....this is just a 60 degree reference angle in the 4th quadrant. The normal sine value of a 60 degree angle is SQRT(3)/2  and the tangent value is SQRT(3). Since this angle is in the 4th quad, both of these will be negative. The cosine will have the same value as it does in the first quad....1/2.

out of 13 possible books, you plane to take 4 with you on vacation .How many different collection of 4 books can you take?

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This is given by the combinatorial  C(13,4)  .......we're counting the number of different sets we can make by choosing any 4 books of 13.

And C(13,4) = 715

One more note  ...   order within any set doesn't matter...the set of books {A,B,C,D} is the same thing as {A,D,B,C}