Alan

Not all negative numbers are whole numbers!  For example, -1.5 is not a whole number.

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Use the calculator here.

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As it's a fifth-order polynomial there are 5 roots. Call them a, b, c, d and e (not necessarily all different).

The polynomial can be written as: (x-a)(x-b)(x-c)(x-d)(x-e) and this must be the same as your polynomial.  Note that if you multiply out the terms in brackets you will end up with the constant term as a*b*c*d*e.

Compare this with the constant term in your polynomial and we see that we must have:

a*b*c*d*e = 30000

Now the factors of 30000 are 2⁴*3*5⁴  which we can rewrite as (2*5)⁴*3 or 10⁴*3.  This is the product of the five numbers 10, 10, 10, 10 and 3, so it's a distinct possibility that we could have a=b=c=d=10 and e=3.

You could then check by multiplying out (x-10)⁴(x-3) to see if the other terms matched (which they do in this case of course).  If they didn't match you could try making five other integers from   2⁴*3*5⁴ .

Simply divide 5 by 3.271*10^-22 and round to the nearest whole number.

$${\frac{{\mathtt{5}}}{\left({\mathtt{3.271}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left(-{\mathtt{22}}\right)}\right)}} = {\mathtt{15\,285\,845\,307\,245\,490\,675\,634.362\: \!580\: \!250\: \!687\: \!863}}$$

So: 15 285 845 307 245 490 675 634 

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It is pOH = -log₁₀(10^-10) = 10 

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100P3  = 100!/(100-3)!  = 100*99*98 .   This can be done on the calculator here using npr(100,3):

$${\left({\frac{{\mathtt{100}}{!}}{({\mathtt{100}}{\mathtt{\,-\,}}{\mathtt{3}}){!}}}\right)} = {\mathtt{970\,200}}$$

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You can enter this directly on the calculator here exactly as written (or without the parentheses, as multiplication is done before addition).

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What set of numbers has no mean?!!

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The median is the middle value when you've sorted the numbers in order, so here that is 6.

The mean is obtained by adding them all up and dividing the result by how many there are:

(1+3+4+6+6+8+9+10+12)/9

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If you extend the sloping sides of the trapezoid upwards, you would see two equilateral triangles, one inside the other.  Because both triangles are equilateral the sides of the smaller triangle are all of size 2, which means the sides of the larger one are all 4.  This means the perimeter of the trapezoid shown is 4 + 2*3 = 10.

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