GoldenLeaf

y=mx+b

'm' is the slope (the steepness of the graph)

'b' is the y-intercept (where it hits the y-axis)

'y' is the y-value (height)

'x' is the x-value (length)

So the height is equivalent to the slope times the length plus the y-intercept. Pretty much, you can put in an 'x' value into a y=mx+b problem and get a 'y' value. In this case, the slope of the line is 1/5 and the y-intercept is 1.

Just plug in values, or use the on-site graph maker (there is a button on the bottom of the home page that says Create Graph). Helpful tip, remove the 'y=', or you'll get a dot!

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{36}}^\circ\right)} = {\frac{{\mathtt{10}}}{{\mathtt{x}}}} \Rightarrow {\mathtt{x}} = {\frac{{\mathtt{10}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{2\pi}}}{{sin}}{\left({\frac{{\mathtt{\pi}}}{{\mathtt{5}}}}\right)}}} \Rightarrow {\mathtt{x}} = {\mathtt{17.013\: \!016\: \!167\: \!054\: \!493}}$$

Just plug it in!

$${\mathtt{6\,872}} = {\mathtt{14\,592}}{\mathtt{\,\times\,}}\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{r}}}{{\mathtt{1}}}}\right){\mathtt{\,\times\,}}{\mathtt{11}} \Rightarrow {\mathtt{r}} = {\mathtt{\,-\,}}{\frac{{\mathtt{19\,205}}}{{\mathtt{20\,064}}}} \Rightarrow {\mathtt{r}} = -{\mathtt{0.957\: \!187\: \!001\: \!594\: \!896\: \!3}}$$

I'll try to show some work, but gimme a sec.

As far as I know, we need to isolate the 'r'.

First combine like terms.

$${\mathtt{6\,872}} = {\mathtt{160\,512}}{\mathtt{\,\times\,}}\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{r}}}{{\mathtt{1}}}}\right)$$

Divide 6872 by 160512

$${\frac{{\mathtt{6\,872}}}{{\mathtt{160\,512}}}} = {\mathtt{0.042\: \!812\: \!998\: \!405\: \!103\: \!7}}$$

$${\mathtt{0.042\: \!812\: \!998\: \!405\: \!103\: \!7}} = {\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{r}}}{{\mathtt{1}}}}$$

The 'r/1' can be just 'r'. All that's needed is to subtract 1 from 0.0428129984051037

$${\mathtt{0.042\: \!812\: \!998\: \!405\: \!103\: \!7}}{\mathtt{\,-\,}}{\mathtt{1}} = -{\mathtt{0.957\: \!187\: \!001\: \!594\: \!896\: \!3}}$$

$$-{\mathtt{0.957\: \!187\: \!001\: \!594\: \!896\: \!3}} = {\mathtt{r}}$$

And thus, the work =)

Well, three skiiers on a plane of 17. Considering that one person dies each time, the number decreases by 1 in both the numerator and the denominator.

$$\left({\frac{{\mathtt{3}}}{{\mathtt{17}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{2}}}{{\mathtt{16}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{15}}}}\right) = {\frac{{\mathtt{1}}}{{\mathtt{680}}}} = {\mathtt{0.001\: \!470\: \!588\: \!235\: \!294\: \!1}}$$

The odds are 1/680

This is a compare and contrast problem.

$${\mathtt{5\,000}}{\mathtt{\,\times\,}}{\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{0.085}}}{{\mathtt{12}}}}\right)}^{{\mathtt{48}}} = {\mathtt{7\,016.323\: \!774\: \!833\: \!980\: \!751\: \!8}}$$

$${\mathtt{5\,000}}{\mathtt{\,\times\,}}{\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{0.08}}}{{\mathtt{12}}}}\right)}^{{\mathtt{54}}} = {\mathtt{7\,158.090\: \!240\: \!747\: \!356\: \!130\: \!5}}$$

Thus, Choice 2 is the correct answer.

Okay, I just remembered that I needed to add the '/12' there since we are going my monthly interest I presume?

There is no dividing by a fraction. Thus, you must 'flip' the fraction (or take the inverse) and change the division sign to a multiplication sign. This makes:

$${\frac{{\mathtt{72}}}{\left({\frac{{\mathtt{3}}}{{\mathtt{4}}}}\right)}}$$

Into:

$${\mathtt{72}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{4}}}{{\mathtt{3}}}}\right)$$

This because, similar to subtraction and how subtracting a negative number from a positive number makes it addition, dividing a number that is already being divided just makes the two division signs cancel each other out and become a multiplication sign.

It is wise to make the 72 into a like fraction: That is, make the denominators similar between the two fractions. In order to do this, multiply 72 by 3, and then put that number over 3.

$${\mathtt{72}}{\mathtt{\,\times\,}}{\mathtt{3}} = {\mathtt{216}}$$

$${\frac{{\mathtt{216}}}{{\mathtt{3}}}}$$

This now makes like denominators between the fractions, and thus the whole thing can be put over 9 once the fractions are multiplied together.

$${\frac{\left({\mathtt{216}}{\mathtt{\,\times\,}}{\mathtt{4}}\right)}{{\mathtt{9}}}}$$

Multiply to make it a simpler fraction.

$${\mathtt{216}}{\mathtt{\,\times\,}}{\mathtt{4}} = {\mathtt{864}}$$

$${\frac{{\mathtt{864}}}{{\mathtt{9}}}}$$

Now simplify the fraction. This means dividing 864 by 9.

$${\frac{{\mathtt{864}}}{{\mathtt{9}}}} = {\mathtt{96}}$$

Your final answer is 96.

$${\sqrt{{\mathtt{3}}}} = {\mathtt{1.732\: \!050\: \!807\: \!568\: \!877\: \!3}}$$

$${\frac{{\mathtt{150}}}{{\mathtt{900}}}} = {\frac{{\mathtt{1}}}{{\mathtt{6}}}} = {\mathtt{0.166\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

$${\mathtt{0.166\: \!666\: \!666\: \!666\: \!666\: \!7}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\frac{{\mathtt{50}}}{{\mathtt{3}}}} = {\mathtt{16.666\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

So 16.666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666 (etc. etc. etc.) is your answer.

It makes me feel so evil to put this many 6's in one answer 

EDIT: I think I broke something.