a certain amount of time

yep, this is correct. Totally makes sense.

just cause

Any one? 

If N is the number, then -N is its opposite.     So we have  ......

-3 + 4(-N)  = N + 27   simplify

-3 - 4N  = N + 27    add 4N to both sides and subtract 27 from both sides

-30  = 5N    divide both sides by 5

-6 = N

There are six things possible for the first die, five for the second, four for the third and three for the fourth.

And there are 6^4  = 1296 total possible outcomes for rolling four dice.

So

 [6 x 5 x 4 x 3 ] / 1296  =  360 / 1296 =  5/18 = about 28%

I'll give this one a shot......we have the following combos as possibilites

(2,10)  (3,9) (4,8) (5,7) (6,6)

In the first four cases we have 16 ways to form each .....choose any one of four cards from the first given rank and choose the same from the second one. So C(4,1) * C(4,1) = 16

In the last case we just want to choose any two of the four "6s" and there are C(4.2) ways to do that = 6 ways

So, the total possibilities  = 16*4 + 6 = 70

And the total possibilities from choosing any 2 cards from 52 = C(52, 2)   = 1326

So.....  70 / 1326 =  about .053 = about 5.3% 

Someone else needs to check this, since I'm never sure about these "counting" problems  !!!

28a^2c^2

If you multiplied the variables, it would be a^4c^4

-y<-9-8 simplify (-9-8)

-y<-17 divide both sides by -1 (to get rid of the negative signs)

y>17 (Rule: When dividing by a negative number, the sign must be swapped.

The answer is 1e+62

Pretty neat, radio....I've never heard of that......!!!!

 24 ≥1/2(6x-8y)   multiply both sides by 2

48  ≥ 6x - 8y        rearrange as

8y  ≥   6x  - 48    divide through by  8

y    ≥  (3/4)x  - 6

Nice one, radio.......!!!!!

2x -3 y =  8   rearrange as

3y = 2x - 8    divide both sides by 3

y = (2/3)x - 8/3

The gradient (slope) is  2/3   and the y-intercept is  -8/3     ..... or (0,  -8/3)   expressed as a coordinate

See Bertie's answer below.

.

Melody, try it with boxes of size 6, 9 and 20.

.

Maths always makes me peckish, so if you don't mind could you please spell it "Pie"?

🍕   🍕   🍕   🍕

True, but usually in problems like this they mean solve for y=0.

I expect poster will indicate whether that's the case here. 

  🐙   🐙   🐙

I don't know 

To find the midpoint between 2 points, we can do $${\frac{\left({{\mathtt{x}}}^{{\mathtt{1}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{x}}}^{{\mathtt{2}}}\right)}{{\mathtt{2}}}}$$,$${\frac{\left({{\mathtt{y}}}^{{\mathtt{1}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{y}}}^{{\mathtt{2}}}\right)}{{\mathtt{2}}}}$$. 

So by inputting the coordinates you gave, $${\frac{\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)}{{\mathtt{2}}}} = {\mathtt{1}}$$,$${\frac{\left({\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}\right)}{{\mathtt{2}}}} = {\mathtt{6}}$$.

Then we can simply solve for x and y.

$$\underset{\,\,\,\,{\textcolor[rgb]{0.66,0.66,0.66}{\rightarrow {\mathtt{x}}}}}{{solve}}{\left(\begin{array}{l}{\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}={\mathtt{2}}\\
{\mathtt{x}}=-{\mathtt{1}}\end{array}\right)} \Rightarrow {\mathtt{x}} = -{\mathtt{1}}$$

$$\underset{\,\,\,\,{\textcolor[rgb]{0.66,0.66,0.66}{\rightarrow {\mathtt{y}}}}}{{solve}}{\left(\begin{array}{l}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}={\mathtt{12}}\\
{\mathtt{y}}={\mathtt{14}}\end{array}\right)} \Rightarrow {\mathtt{y}} = {\mathtt{14}}$$

So C= (-1,14)

(x-2)(x+3)-(x-2)(x+4)

You can see there are two terms and they each have a common factor (x-2), so

if we take out the common factor it becomes

(x-2) [x+3 - (x+4)]

Now it's just a matter of removing the brackets around x+4 when there is

a negative sign in front of it.

(x-2) [x+3-x-4)]

And this can be simplified finally to .....

this is left as an exercise for you to finish. 

Silicon! 

One mole of a substance weighs the same as it's RAM (Relative Atomic Mass) in grams.

The RAM of silicon is ≈ 28.  Therfore one mole of silicon weighs ≈ 28g.

Hope this helps,

---

- Loosifer

What is the use of doing that Radio ?

Thanks MG  :))

@@ End of Day Wrap   Sat 11/4/15    Sydney, Australia    Time 12:20 am  (Really Sun)  ♪ ♫

Hi  all,

Our eminent answerers today were Alan, Bertie, Zacixmyname, Badinage, jjonesekb, Geno3141, Harrypotter, saseflower, BrittanyJ, Radio and Nauseated.  Thank you, you are all wonderful.  Even you are wonderful occasionally Nauseated.  :)

Interest posts:

FTJ means "For the Juniors"