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For all in the U.S.A. 

Off topic  post above 

ANOTHER method to indicate multiplication:

3 * 3   =   3 x 3  = 3 . 3  =  3(3)  

Sorry! Forgot to put in the numbers!

Thanks for the tip guest yep I don't use a smart phone and I can't acess that site "parental controls" but thanks I will try that...

HiylinLink, regarding your "the dot is suppose to be in the middle I jsut can't find the function for that" 

Here's one way to do it.  You have to be using a real computer, though, not a smartphone. 

Turn on the numeric keypad.  You're going to use numbers, but the numbers across the top won't work.

Locate your cursor at the point where you want to insert the dot. 

Press and hold the Alt key.  On the keypad, type 0149 then release the Alt key. 

Some other characters you can make the same way are found at http://www.dtp-aus.com/ext_set.htm 

.

In the first situation, the population density is given by :

[ 7.6 x 10⁹ ]              7.6

__________  =      ____   x   10   ≈   14.9  people / km^2

[5.1 x 10⁸ ]              5.1

In the second situation, we have

[7.6 x 10⁹ ]                    7.6

______________   = ________  x 10   ≈   49.7  people /km^2

[ 5.1 x 10⁸ x .30]           5.1 x .3

Just divide:

[7.6 x 10^9] / [5.1 x 10^8] =~15 people per km^2 - human population density.

30% x [5.1 x 10^8] =1.53 x 10^8 Km^2 - the surface area of all the land.

[7.6 x 10^9] / [1.53 x  10^8] =~ 50 people per km^2 on all habitable land. 

Thanks 

Your Very Welcome, Wizard ;P

Thanks alot anderson! ; )

The dot means multiplication.

They have changed mathematics to have the dot instead of the x to signify multiplication because by the time you get to algebra your problems will have variables which are x, y, and z. So to no confuse the person solving they use a dot instead of an x so that no one thinks its a variable.

Hope this Helps ;P

The medication cost is $32

But since it differs up to 8 so the inequality will maximum goes up to 8. And the medication cost $32 is a range fron $24 and $40.

Also all the other answers do not make sense with the cost of the medication. Two of them (which are B and D) say less than $24 and greater than $40 which isn't the amount of $32. 

Then for A the inequality symbol is not facing the correct way. Since the medication costs $32 but differs as much as $8 then it should be greater than the absolute value.

So your answer would be C. |x − 32| ≤ 8; The medication costs range from $24 to $40.

Hope this Helps ;P

There are three way's you can show multiplication 

1. put a multiplication symbol down (30 X 30) 

2. Put a dot in between both number's(30 . 30) NOTE: you proably know the dot is suppose to be in the middle I jsut can't find the function for that. 

3.Put the number's next to one another 30(30) 

and all of these method's will equal the same product.

No, the GCF can't be 2, (even withstanding the zero on the bottom line), for whatever the value of n, if the top line is even the bottom line will be odd and if the bottom line is even then the top line will be odd.

Suppose that the GCF is k, and that

\(\displaystyle n^{2}-9=m_{1}k\dots \dots(1)\\ \text{and}\\ n^{2}-4=m_{2}k\dots \dots(2)\)

Subtracting (1) from (2),

\(\displaystyle 5=m_{2}k-m_{1}k=(m_{2}-m_{1})k,\)

so either 

\(\displaystyle m_{2}-m_{1}=5\text{ and }k=1, \text{ (which is of no interest)}\)

or

\(\displaystyle m_{2}-m_{1}=1\text{ and }k=5, \text{ (which is).}\)

If k = 5, then, from (1), \(\displaystyle 9+5m_{1} = n^{2}.\)

(Substitution into (2) leads to the same equation.)

Beginning with m1 = 1, the lhs side runs through the numbers, 14, 19, 24, 29, 34, 39, ...

so what we are looking for are squares with final digit 4 or 9.

The first one is 49, n = 7, and the next 64, n = 8.

After that, 144, n = 12, and then 169, n = 13.

Now that's interesting, in pairs 5 apart ......... .

Thanks! 

Let the center of the circle be  (h, 0)

distance between  (h, 0)  and  (3, -2)   =   distance between (h, 0)  and  (-2, 3)

\(\begin{array}{r} \sqrt{(-2-0)^2+(3-h)^2}&\ =&\ \sqrt{(-2-h)^2+(3-0)^2}\\~\\ (-2-0)^2+(3-h)^2&=&(-2-h)^2+(3-0)^2\\~\\ (-2-0)^2-(3-0)^2&=&(-2-h)^2-(3-h)^2 \end{array}\)

Notice here that if  h = 0  both sides of the equation are identical.

If you want to, you can expand both sides to also find that  h = 0.

So the center of the circle is  (0, 0)

And the radius  =  \(\sqrt{(-2-0)^2+(3-0)^2}\ =\ \sqrt{4+9}\ =\ \sqrt{13}\)

2)  sin(pi/4 + x)  - sin(pi/4 - x)  = 

[sin pi/4 cosx + sinx cos pi/4]  -  [ sin pi/4 cosx - sinx cos pi/4]  =

2 sin x cos pi/4  =

2 sin x  *  [√ 2 ] / 2  =

√2 * sin x

tan x  * tan (x/2)  =

tan x    *    tanx

             ________   =

              1 + sec x

tan^2 x

_______   =

1 + sec x

sec^2 x  - 1

_________  =

sec x + 1

(sec x + 1) (sec x - 1)

_________________  =

     sec x +  1

sec x  -  1

Thanks Phil!

We are looking for the first positive integer with exactly 20  divisors

I believe this is

2^4 * 3 * 5 =  240

The divisors  are

1,2,3,4,5,6,8,10,12,15,16,20,24,30,40,48,60,80,120,240

She can form rectangles

1 x 240              6 x 40

2 x 120              8  x 30

3 x  80              10 x 24          

4 x  60              12 x 20

5 x  48              15 x 16

See the following  image : 

Let  A  = (0,6)     B  = (0,0)     C = (8,0)

If AD is an angle bisector, we have by the angle bisector theorem that

AB / AC  =  BD / DC

6 / 10  =  BD /DC

3 / 5  = BD/DC

Then  BC  is  divided in 8 equal parts  and BD is 3 of them...so

(3/8) BC  =  (3/8)*8  =  3

So....BD  =  3     which implies that   D  = (3,0)

So  ...by the distance formula

AD^2  =  (3 - 0)^2  +  ( 6 - 0)^2

AD^2  =  3^2 + 6^2

AD^2   =  9 + 36

AD^2  =  45

I think you misunderstood the question

a) i = 1600 * 1/2^(t/8)

b) i = 1600 * 1/2^(1/2)

     i = 1600 * 0.7071067812......

     i =1,131.37 - grams remaining after 4 days(Exactly)

Since half-life is 8 days, it therefore means that in 4 days about 1/4 of 1600 would have decayed, or:

1600 - 400  = 1,200 grams (approx.) would remain after 4 days.