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um... take a look at this...$${\sqrt[{{\mathtt{3}}}]{{\mathtt{8}}}} = {\mathtt{2}}$$

-Robert

or $${\frac{{\mathtt{4}}}{{\mathtt{3}}}}$$, which is 1.33333333333333333333333333333333333333...

-Robert

x(3x - 4)  ≤  (6x² - 3x + 5) / 10

Simplify:

3x² - 4x  ≤   (6x² - 3x + 5) / 10

30x² - 40x  ≤  6x² - 3x + 5

24x² - 37x - 5  ≤  0

Factoring:  (8x + 1)(3x - 5)  ≤  0

This divides the number line into three parts:  x < -1/8,  -1/8 < x < 5/3,  x > 5/3

Try a a number in the lower region:  I tried -1:  [8(-1) + 1][3(-1) - 5]  =  56. Since this is not less than or equal to zero, all numbers less than -1/8 will not work.

Try a number in the middle region:  I tried 0:  [8(0) + 1][3(0) - 5]  =  -5. Since this is less than zero, all numbers in this region work.    Answer:  -1/8 < x < 5/3

Try a a number in the upper region:  I tried 2:  [8(2) + 1][3(2) - 5]  =  17. Since this is not less than or equal to zero, all numbers greater than 5/3 will not work.

Now, to answer the question, you will have to figure out (count) the number of integers in the region 

-1/8 < x < 5/3.

There will have to be one commity with 3 accountants, 1 marketing agent, and 3 board members.

hope it helped

-Robert

list of large numbers

 hope it helps

-Robert

From the first bag, you are choosing 2 out of a possible 4; that is a combination of 4 taken 2 at a time,

or  4nCr2 = 6.

Similarly, for the second bag; 

thus the answer will be  4nCr2 x 4nCr2  =  6 x 6  =  36

Although you want (n - 2)(n + 4) < 0, look at  (n - 2)(n + 4)  =  0

This is a great place to start, because it give you the two values  -4  and  2.

This divides the number line into three sections: those numbers below -4, those numbers between -4 and 2, and those numbers greater than 2.

Now, let's go back to the original inequality:  (n - 2)(n + 4) < 0.

If you try any number smaller than -4, both of the sections  n - 2  and  n + 4  will be negative, so their answer won't be < 0.

If you try any number larger than -4 and smaller than 2, one of the sections will be negative and the other will be positive, so their product will be negative, so all these numbers work.

If you try any number larger than 2, both of the sections will be positive, so their answer won't be < 0.

Answer:  -4 < n < 2.

To get the final answer, find the integers between (and not including) -4 and 2.

for hard people:$${\frac{{\mathtt{76}}}{{\mathtt{87}}}}{\mathtt{\,-\,}}{\frac{{\mathtt{367}}}{{\mathtt{387}}}}$$like that. Or as Medoly said, use the divide by sign. Hope i helped!

-Robert

We can also cut a circle with radius R in half by removing a circular area with a radius = R/√2 from within the circle...

To prove this, we have

pi*R^2 - pi*r^2 = (1/2)*pi*R^2   ......where r is the radius we're looking for........so.......

(1/2)pi*R^2 = pi*r^2   divide both sides by pi

(1/2)R^2 = r^2   take the positive root of both sides

r = (1/√2)R = R/√2

Note that......as long as the circular area removed lies totally witin the circle, it doesn't have to be concentric with the larger circle!!!

Rewrite as:              8t² + 10t - 3  ≤  0

Factor:                (4t - 1)(2t + 3)  ≤  0

Solving for t:         t = 1/4   or  t  =  -3/2

These two point divide the number line into three sections:  t ≤ -3/2    -3/2 ≤  t ≤  1/4    t ≥ 1/4

Try a number that is less than -3/2, say -2:  8(-2)² + 10(-2) - 3  =  9  -->  this section doesn't work!

Try a number between -3/2 and 1/2, say 0:  8(0)² + 10(0) - 3  =  -3  -->  this section works!

Try a number greater than 1/4, say 2:   8(2)² + 10(2) - 3  =  49  -->  this section doesn't work!

The only region that works is:   -3/2 ≤  t ≤  1/4   --->  [-3/2, 1/4] 

or the real answer is $${\frac{{\mathtt{1}}}{{\mathtt{3}}}} = {\mathtt{0.333\: \!333\: \!333\: \!333\: \!333\: \!3}}$$.

-Robert

are you trying to say there are $${\mathtt{\infty}} = \infty$$ possibilities to make a circle into $${\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$? oh, i knew that. :)

-Robert

thanks! if i add 1 to the highest number i know, the answer is 4582343254837654823548.

So, first distribut the 4. 4(6-2x) is 24-8x. Add 8x to both sides. 24 is not equal to 13x-2. Then, add two to both sides. 26 is not equal to 13x. Divide both sides by 13. x is not equal to 2.

here is a longer version. 3.1415926535897932 check on the calculatour.

-robert

P.S. i'm a year 5.

Oops, did not see that there. Sorry, geno3141!

So, first 2/3 times 18. You have to find the reciprocal of 18 which is 1/18. Then, multiply 2/3 by 1/18. 2 will get canceled out, and 18 will become 9. So, 1/3*1/9 is 1/27. I think this is correct. Hope this helped you!

To divide, multiply by the reciprocal (the reciprocal of  18  is  1/18):

(2/3) ÷ 18  =  (2/3) x (1/18)  =  2/54  =  1/27

(-2)^8  =  -2 x -2 x -2 x -2 x -2 x -2 x -2 x -2  =  256

If you don't use a straight line, there will be an infinite number of ways to divide a circle into two parts, where each part has the same area as the other.

The yin-yang picture is one.

(x+3)²  will always be positive.

The only integers less than or equal to 1 are 0 and 1.

How can (x+3)² = 0 ?  --->  x = -3

How can (x+3)² = 1 ?  --->  (x + 3) = 1  or (x + 3) = -1  --->  x = -4  or  x = -2

Answer:  3 integers: -2, -3, and -4 

I don't understand what you are trying to say.

Please somebody help me on this.

400!  =  400 x 399 x 398!

So, 400! / 398!  =  400 x 399  = 159 600