Alan

$$$$\frac{851}{315}=\frac{X}{2412}$$\\
Multiply both sides by 2412 $$\frac{2412*851}{315}=X$$\\$$

$${\mathtt{X}} = {\frac{{\mathtt{2\,412}}{\mathtt{\,\times\,}}{\mathtt{851}}}{{\mathtt{315}}}} \Rightarrow {\mathtt{X}} = {\mathtt{6\,516.228\: \!571\: \!428\: \!571\: \!428\: \!6}}$$

X ≈ 6516

I guess you want to find y if -2(3y - 7) = 56

Divide both sides by -2 to get

3y - 7 = -28

Add 7 to both sides

3y = -21

Divide both sides by 3

y = -7

60% of 150 = 0.6*150 = 90 Hence there were 90 females and 60 males to start with.

After some females died the remainder comprised 52% of the new total, so the males must have been 48% of the new total.  48% of new total = 60, so new total = 60/0.48 = 125.  Hence there were 125 - 60 = 65 females left.

That means that 90 - 65 = 25 females died.

The best-fit linear regression equation to your three points is y = 1 + 1.25x (see graph below).  hence the y-intercept is y=1.

I can't see your graph, but here is one:

You can see that there is not going to be any solution in terms of real numbers; that's why you get {} - this means the empty set (i.e. nothing in it).  

The only solutions exist in the complex number domain as the previous replies showed.

The mean is given by

To find the median, integrate p(x) with respect to x and then find the value of x that makes the result equal 0.5. That is, you find the "half-way" value of the cumulative distribution function.

You should find  $$\mu=4\frac{1}{6}$$  and median = 15 - 5√5 (≈ 3.82)

If you are trying to find a zero of xcos(x)-1/x you should note that there are an infinite number of them - see the graph below.

There is no solution at 5.166 radians!

$${\mathtt{5.166}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{5.166}}{\mathtt{\,\times\,}}{\mathtt{180}}}{{\mathtt{\pi}}}}\right)}{\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{5.166}}}} = {\mathtt{2.070\: \!241\: \!313\: \!464\: \!202\: \!4}}$$

Here's the result as calculated to 50 decimal places by Mathcad's symbolic maths system:

Looks like the local calculator is accurate up to about 11 decimal places.

NB Looks like the image above has cut off the "i" in the decimal answer! 

c is a constant which is just 1/2 in your case.  

However, let me do it with just your numbers:

f = (5x - 4)^1/2

Let z = 5x - 4     ...(1)     so 

f = z^1/2

Differentiate f with respect to z

df/dz = (1/2)*z^(1/2)-1 or df/dz = (1/2)*z^-1/2    ...(2)

We want df/dx not df/dz, so we use the chain rule df/dx = df/dz*dz/dx   ...(3)

We have df/dz, so we need dz/dx

From (1) above we find dz/dx = 5  ...(4)

Put (2) and (4) into (3) to get

df/dx = df/dz*dz/dx = (1/2)*z^-1/2*5 = 5/(2*z^1/2)

Replace z using (1) to get

df/dx = 5/(2*(5x-4)^1/2)

Is this any clearer?