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Here is my answer:

I don't understand electricity.  This is based solely on the info given.

\(I=\frac{V}{R}\\ R\propto L\\ I=\frac{V}{kL}\\ find\;\;k\\ When \;\;V=50\;\;I=200,\;\;L=2\\ 200=\frac{50}{2k}\\ k=0.125\\so\\ I=\frac{V}{0.125L}\\~\\ Find\; I\;\;when\;V=300\;and\;L=1\\ I=\frac{300}{0.125*1}\\ I=2400\;milliamps \)

LaTex:

I=\frac{V}{R}\\
R\propto L\\
I=\frac{V}{kL}\\
find\;\;k\\
When \;\;V=50\;\;I=200,\;\;L=2\\
200=\frac{50}{2k}\\
k=0.125\\so\\
I=\frac{V}{0.125L}\\~\\
Find\; I\;\;when\;V=300\;and\;L=1\\
I=\frac{300}{0.125*1}\\
I=2400\;milliamps

G + 16 = 3/5 (40 - G)

G + 16 = 24 - 3/5 G

8/5 G = 8

G = 8 * 5/8 = 5                                I do not know why the equation with J in it was included.....

(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 54, 56, 60, 63, 64, 70, 72, 80, 81, 84, 90, 96, 105, 108, 112, 120, 126, 128, 135, 140, 144, 160, 162, 168, 180, 189, 192, 210, 216, 224, 240, 252, 270, 280, 288, 315, 320, 324, 336, 360, 378, 384, 405, 420, 432, 448, 480, 504, 540, 560, 567, 576, 630, 640, 648, 672, 720, 756, 810, 840, 864, 896, 945, 960, 1008, 1080, 1120, 1134, 1152, 1260, 1296, 1344, 1440, 1512, 1620, 1680, 1728, 1890, 1920, 2016, 2160, 2240, 2268, 2520, 2592, 2688, 2835, 2880, 3024, 3240, 3360, 3456, 3780, 4032, 4320, 4480, 4536, 5040, 5184, 5670, 5760, 6048, 6480, 6720, 7560, 8064, 8640, 9072, 10080, 10368, 11340, 12096, 12960, 13440, 15120, 17280, 18144, 20160, 22680, 24192, 25920, 30240, 36288, 40320, 45360, 51840, 60480, 72576, 90720, 120960, 181440, 362880)>>Total Number ==160 divisors>>Their Product==6.040079156 x 10^444

For starters, you were supposed to respond with a direct thank you to Catmg and to CPhill. (not to me) 

And give both of them a point, which you have done, thanks  

Then I was hoping you would think about the wording of future posts with regard to what I have said to you.

You do not need to respond again unless you want to.  

You can paint it the following number of ways:

(3 and 1),  (1 and 3),  (2 and 1),  (1 and 2) ==4 different ways.

That's incorrect 

G+16=24-3/4*G

G=8-3/4*G

7/4*G=8

G=(32)/7

since the final polynomial is a fourth-degree polynomial, Q(x) must be quadratic, and since it is monic, Q(x) is also monic. Therefore, Q(x) can be expressed as x^2+cx+d, where c and d are real numbers. If you were to square it, you would get x^4 + 2 c x^3 + c^2 x^2 + 2 d x^2 + 2 c d x + d^2. Therefore, we can solve it using equations by matching the coefficients:

\(2c=1\\c=1\\2d+c^2=2d+1=-4\\d=-2.5\)

Now just match the coefficients once again to solve for a and b, and then add them up. Can you finish it?

I can't think of a fast method, but you could find the number of factors, divide that by 2 and multiply 9! by it?

=^._.^=

thanks!!!

For the second one, try drawing two of the same length lines out that intersect. Then connect the 4 points, do they always form right angles?

=^._.^=

You are getting a negative number because you have an unmatched parenthesis. Probably whatever you use to do the computation computes the argument of the natural log (ln) as a number smaller than 1 (<1) and thereby gives you a negative number.

Botch had 67 dollars after he  gave 1/4 to his friend. How many dollars did he have to start?

If Botch gave away 1/4 of his cash, he has 3/4 left and that is 67 dollars.

x = the amount he had at the start

3/4 * x = 67   multiply both sides by  4/3 to get:

     x = 67 * 4/3 =~~~  89.33

Perhaps you meant to say $a^2+b^2+c^2+ab+ac+bc=81$ instead.  If that's the case, then there are three solutions:
    (3, 4, 4)
    (4, 3, 4)
    (4, 4, 3)
 

Thanks! That helped, but I'm still having trouble with the other problems. Can anyone spell them out for me? :) in a good way, of course

Property 1 & 2 can be combined into
\[
    xf(x) + yf(y) = 1+(x+y)f(x+y)
\]
for all $x\in S$ and $y\in S$ such that $x+y\in S$.  Taking $x=y=1$, the combined property asserts that $2f(1) = 1+2f(2)$.  Taking $x=-1$, Property 1 asserts that $f(-1) = -f(-1)$; thus $f(-1) = 0$.  Taking $x=2$ and $y=-1$, the combined property asserts that $2f(2)=1+f(1)$.  Solving the system of two equations
\begin{eqnarray*}
    2f(1) &=& 1+2f(2) \\
    2f(2) &=& 1+f(1)
\end{eqnarray*}
gives $f(1) = 2$ (with $f(2)=3/2$ but we don't need to know that).  Thus $n\times s = 1\times 2 = 2$.

Say A and B are two of the points on the sphere, and that O is the center of the sphere and OH is the perpendicular bisector of AB. Then the image you see above shows the intersection of the sphere and a plane through the three points O, A, and B. The ant can minimize the distance between A and B by walking on the arc AB. So if we had the length of this arc, we could multiply it by 3 to find the total minimum distance a smart ant would choose to traverse. So help the ant and find the needed arc length (Hint: what is the measure of the angle AOB, given that \(AH=\frac{\sqrt{2}}{2}\), and that OA is 1 unit long?

It took Mr I   5 hours to drive 240 miles        avg speed   =   240 / 5 = 48  m /hr for the trip

    If we look at ONLY the time he was actually  driving, he drove 240 miles in 4 hours = 60 m/hr

Average speed = total distance / total time

                         = (50 m/hr *4 hr     + 30 m/hr *1 hr) / ( 4+1 hrs)

                          = 230 miles / 5 hrs = _______________ m/hr

See if you can do the others...........

3x^2-8x-2 =

3 (x^2 - 8/3x)   -2     complete the square for 'x'

3 ( x -4/3)^2   - 48/3 - 2

3 (x - 4/3)^2 - 18         You can finish I hope!    

How to solve this exponential equation?

10 00000 * .9^t = 0

         .9^t   must equal 0

              which is not possible ........

If x = -2

f(-1/2) + -1/2 * f(2) = 2

If x = 1/2

f(2) + 2 * f(-1/2) = 2

f(-1/2) + -1/2 * f(2) = 2

2 * f(-1/2) - f(2) = 4

f(2) + 2 * f(-1/2) = 2

-f(2) - f(2) = 2

f(2) = -1

=^._.^=

Squares have each of their angles = 90 degrees

   an equilateral triangle has internal angles of 60 degrees.....can you deduce what the angle CDB is with this info?

Melody, 

Thanks, I guess i was just in a rush. (I really don't know how to respond to this)