Melody

P = −4 + 2.5n − 0.2n^2

Profit greatest when dP/dn=0

dP/dn = 2.5-0.4n

2.5-0.4n=0

2.5=0.4n

2.5/0.4=n

n=6.25 thousand widgets

n=6 thousand widgets to the nearest 1000.

Here is the graph to back up my answer.  

https://www.desmos.com/calculator/ula6msgsc8

f(x)=3x^2-2

Yes it is a function... What about it ?

There is a calc on the home page.   

I know your fingers aren't broken because you can type ://

A sample of copper with a mass of 63.5 g contains 6.02*10^23 atoms. Calculate the mass of a single copper atom.

(63.5)/(6.02*10^23)

=10.5481276*10^-23

=1.0548 * 10^-22 grams per atom

For a number to be divisable by 4 the last 2 digits must be divisable by 4.

HENCE one of these can never be divisable by 4

And if a number is not divisable by 4 it is impossible for it to be divisable by 8.

Why don't you try to work out the answer?

You can cheat a little and use a calculator if you need to :))

What is the square root of 2004 without a calculator?

I can see straight off without any working that it is just a little less then 45

Squaring numbers that end in 5 is really easy.

eg  75^2:     7*7+7=56 so the answer is 5625   works every time :))

So in your case 

4^2+4=20

so 45^2=2025

44^2=(40+4)^2=1600+2*40*4+16=1936

So it is between 44 and 45, closer to 45     

Since sqrt(2004) is an irrational number so it cannot be written exactly in digits no matter how many digits that you use. :)  

x2-3x+2=0

I think the intended question was 

\(x^2-3x+2=0\\ (x-2)(x-1)=0\\ x=2\;\;or\;\;x=1\)

(2x to the power of 1/3)(-4x to the power of 5/3) 

\(2x^{1/3}*-4x^{5/3}=-8x^{(5+1)/3} = -8x^2\)

Thanks Rom, you are probably right but

I thought that in chemistry it was taught that if a zeros were put after the point it implied that all the digits up to that one were significant.  Hence 5

If it had been written as 3100* 10^2   I would have said with confidence that there were only 2 significant figures.  ://

12g * 78mg

If m  ang are pronumerals then the answer is    12*78mg^2 = 936mg^2

If g stands for grams and mg stands for miligrams, the question makes no sense :/