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If n is the number of years for the populations to match then you want to solve:

50000*1.07ⁿ = 70000*0.96ⁿ for n

Take logs of both sides and use the fact that log(a*b) = log(a) + log(b) and log(aⁿ) = n*log(a)

log(50000) + n*log(1.07) = log(70000) + n*log(0.96)

$${log}_{10}\left({\mathtt{50\,000}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{n}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{1.07}}\right) = {log}_{10}\left({\mathtt{70\,000}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{n}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{0.96}}\right) \Rightarrow {\mathtt{n}} = {\frac{\left({\mathtt{35\,885\,121}}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{70\,000}}\right)}{\mathtt{\,-\,}}{\mathtt{35\,885\,121}}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{50\,000}}\right)}\right)}{{\mathtt{3\,892\,841}}}} \Rightarrow {\mathtt{n}} = {\mathtt{3.101\: \!679\: \!961\: \!830\: \!667\: \!4}}$$

so n ≈ 3years.

Subtract the second equation from the first and you get:

x - 5y - 3z = 2

But the third equation says that

x - 5y - 3z = 5

They can't both be true at the same time, hence there is no solution!

Volume = mass/density

The density of gold is about 19.3 gm/cm³ or 1205 lb/ft³ or 0.6973 lb/in³.

Can you take it from there?

Let y=sinx

Then solve for y

Then put the sinx back in and solve for x

Give it a go from there. 

Im on a little phone I will look again after im home :)

I see Alan beat me.  Thanks Alan :)

49.3 milligrams is 49.3*10^-3 grams;

so number of atoms = 49.3*10^-3/(1.79*10^-22) = 49.3*10¹⁹/1.79 ≈ 2.75*10²⁰ atoms

First set y = sinx and solve:   2y² + y - 1 = 0 for y.

Since the LHS factors nicely, we have (y+1)*(2y-1) = 0

so y = -1 and y = 1/2

sin(x) = -1 implies x = 3pi/2 + 2npi  where n is an integer

I'll leave you to work out what values of x make sin(x) = 1/2 .

It might be better if you recognise that 12/4=3 

The probability of getting an answer right is 1/5, so the expected number of right answers is (1/5)*20 = 4.

The probability of getting exactly 14 right is (1/5)¹⁴*(4/5)⁶*nCr(20,14)  (nCr(20,14) is the numb er of ways of choosing 14 out of 20).

The probability of getting exactly 15 right is  (1/5)¹⁵*(4/5)⁵*nCr(20,15) 

The probability of getting exactly 16 right is  (1/5)¹⁶*(4/5)⁴*nCr(20,16) 

... etc. to

The probability of getting exactly 20 right is  (1/5)²⁰*(4/5)⁰*nCr(20,16) 

Calculating all these and adding them up we find the probability of getting a C is approximately 2*10^-6, so the probability of getting less than a C is 1 - 2*10^-6.

Successive powers of 443 end in 443; 249; 307; 001.  These then repeat (see below).

The first of these occurs when mod(power,4) = 1, the second when mod(power,4) = 2, the third when mod(power,4) = 3 and the fourth when mod(power,4) = 0.

Since mod(443,4) = 3, the last three digits of 443⁴⁴³ are 307.

Multiply the weight of one cubic foot by the 3(1/5) cubic feet.  Probably easiest to write 1/5 as 0.2 here, so you have 62.2*3.2 (which is 199.04, as Anonymous noted). 

If this is the equation x = 2 + (1/x) then first multiply through by x to get:

x² = 2x + 1

Rearrange:

x² - 2x - 1 = 0

Solve using the quadratic formula:

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{1}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{1}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{2}}}}\\
{\mathtt{x}} = {\sqrt{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{0.414\: \!213\: \!562\: \!373\: \!095}}\\
{\mathtt{x}} = {\mathtt{2.414\: \!213\: \!562\: \!373\: \!095}}\\
\end{array} \right\}$$

Not quite!

log₄(2x-1) + log₄(3) = log₄((2x-1)*3)

So we should have

(2x-1)*3 = 5x+12

6x - 3 = 5x + 12

x = 15

Check:

$${{log}}_{{\mathtt{4}}}{\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{15}}{\mathtt{\,-\,}}{\mathtt{1}}\right)}{\mathtt{\,\small\textbf+\,}}{{log}}_{{\mathtt{4}}}{\left({\mathtt{3}}\right)} = {\mathtt{3.221\: \!471\: \!747\: \!924\: \!364\: \!5}}$$

$${{log}}_{{\mathtt{4}}}{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{15}}{\mathtt{\,\small\textbf+\,}}{\mathtt{12}}\right)} = {\mathtt{3.221\: \!471\: \!747\: \!924\: \!364\: \!4}}$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{6}}}{{\mathtt{3.14}}}}{\mathtt{\,\times\,}}{\mathtt{29}}\right)} = {\mathtt{88.966\: \!153\: \!896\: \!812^{\circ}}}$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{6}}}{\left({\mathtt{3.14}}{\mathtt{\,\times\,}}{\mathtt{29}}\right)}}\right)} = {\mathtt{3.769\: \!805\: \!197\: \!875^{\circ}}}$$

Use tan(angle) = height(opposite)/distance(adjacent)

So height = distance*tan(angle)

height = 200*tan(35°) m

-9 + (-8) = -9 -8 = -17

Two minuses make a plus, but a plus and minus makes a minus!

What do you mean by eights one whole?

I can only think of door...

If you use the function: 

  $$\mathrm{f(x)=x
^{3/2}}$$

and they value 0 for X it's Y value would be 0 as well and would map to (0,0) in cartesian cordinates aka on a graph.

Did you see my latest drawings?

The answer is basically negative. Negative numbers are numbers that are before 0. You will see negative numbers like in these examples.

Example 1: $$-{\mathtt{1}}$$

Example 2: $$\left(-{\mathtt{1}}\right)$$

If you want to add, use the next example.

Example 3: HINT: Always use this method when you add negative numbers.

$$(-1)+(-7)$$

Then, you just ignore the negative symbols (-). 

So, it is like adding 1 and 7. 

$${\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{7}} = {\mathtt{8}}$$

Now, just put the negative symbol before the 8.

$$-{\mathtt{8}}$$

Now, you can write the answer.

$$\mbox{Answer:\;-8}$$

So,  $$-{\mathtt{8}}$$ Is the answer.

For more information, go to the following link:

It has two vowels in the middle and two consonants at each end......that's all the hints that you get, my friend......!!!!!

Man! Can you give another hint please?

Nope......sorry, DS.....keep thinking.....

$${\frac{{\mathtt{11}}}{{\mathtt{4}}}}{\mathtt{\,-\,}}{\mathtt{3}} = {\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{4}}}} = -{\mathtt{0.25}}$$

That is the answer.