Sir-Emo-Chappington

You currently have:

Sine(θ) = 0.9056

Simply apply inverse-sine to both sides to make the angle the "sugject" of this equation. This is commonly shown as "asin"

θ = asin(0.9056)

This is not something are expected to work out by hand, so I hope you have a calculator handy.

Note on most scientific calculators I see, the inverse of Sine is shown as Sine^-1.

θ = Sine^-1(0.9056) = 64.9°

Reminder: "Mode" is the most common, "median" is the middle value, and "mean" is the average

For modal, look at each row and count how often each number happens (Do not mix the same number on different rows together in this counting). Try and find what occurs the most of any number.

You should find that 7 is the only number to occur 3 (or more) times. This happens on row 4. This means the mode is 4|7 which I assume is 47 (Most stem and leaf diagrams have a "key" to explain what each number means).

For median, quite simply this is the "middle" value.

For a rather manual method, look at the diagram you have:

2 |2 3

3 |1 6 8

4 |2 7 7 7

5 |3 4 4 6 6

6 |1 4 4 5

Now start counting from both ends, possibly labeling each number as you go to keep track

2 |2¹ 3²

3 |1³ 6⁴ 8⁵

4 |2⁶ 7⁷ 7⁸ 7⁹

5 |3⁹ 4⁸ 4⁷ 6⁶ 6⁵

6 |1⁴ 4³ 4² 5¹

In this case, there are two middle values: 4|7 and 5|3. When this happens, you want to find the value that's between these two (the average of them). This is (47 + 53)/2 = 50

To quickly check: 50 - 47 = 3, and 53 - 50 = 3. These two numbers must be exactly the same (and they are).

Of course there are faster methods on longer stem and leaf diagrams, but it's all pretty much based on preference and there's no truly "good" method to finding the median quickly.

The total distance of the track is ¹/₄ miles

She travels ⁵/₁₆ of the track

She will travel the total distance of the track, multiplied by how much of the track she actually did. So for example if she did half of a track, you would get half of the total, which is the total multiplied by a half.

The total distance she travels will therefore be: ¹/₄ * ⁵/₁₆

To multiply fractions easily, look at it like this:

$$\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{5}}}{{\mathtt{16}}}}\right) = {\frac{\left({\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{5}}\right)}{\left({\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{16}}\right)}}$$

So the total distance is 5 / 64

Since 5 is a prime number that is not a factor of 64, this is the simplest the fraction can get.

If you want it in numerical form, it's about 0.078 (to 2 d.p.)

Either way works. Ultimately it comes down to preference which is used.

I am inclined to agree however, your method looks nicer. I personally am more familiar with methods that work with the most significant values first and work downwards, but I can see how your method is better adapted to unknown sizes if you are unfamiliar with hexadecimal scales. (You have also just given me a good idea for something I want to change in a program. Cheers)

No problem CPhill

o/ hai

Converting from denary (base-10) to Hexadecimal (base-16): 

We need only three values, as the maximum in three hexadecimal is 4096

A good check to see how many you need is guess the highest, and see if it can fit. For example if we guessed 3 values, then you can see if 16³ is large enough to fit it. Now see about 2 values. 16² is easily not big enough so it will take more than 2 values to fit.

First we see how many of the first significant value we need...

Since the third value is 16² = 256, we must check how many of these fit.

2308 / 256 = 9 [4 remainder]

Now we see how many we need of the next...

With what we got left, let's see how many of the second value we need which are each worth 16. 

4 / 16 = 0 [4 remainder]

And finally let's see how many of the last value we need. This converts pretty easily. This is technically how many "16⁰ = 1"s you can fit into it.

4 / 1 = 4

The result will be:

9 0 4

I think you forgot to give us the choices...

Regardless, you can re-arrange it like so:

12x + y ≤ 3

y ≤ -12x + 3

So basically any graph which has y positions below or equal to this:

27,000,000 / 100,000,000

= 0.27 post-tax profit per share

0.27 / 180 = 0.0015 = 0.15% 

The earnings are 0.15% of it's trading value.

There's quite a lot of different ways of interpretting this question, so apologies if I got this incorrect.

I ordered it around in the way that looked most logical to me:

[[5⁰ / 5^-6]*[1 / 5^-11]] / [[(5²)*4 / (5¹⁰)*2]]

$${\frac{\left[{\frac{{{\mathtt{5}}}^{{\mathtt{0}}}}{{{\mathtt{5}}}^{-{\mathtt{6}}}}}\right]{\mathtt{\,\times\,}}\left[{\frac{{\mathtt{1}}}{{{\mathtt{5}}}^{-{\mathtt{11}}}}}\right]}{\left[{\frac{\left({{\mathtt{5}}}^{{\mathtt{2}}}\right){\mathtt{\,\times\,}}{\mathtt{4}}}{\left[\left({{\mathtt{5}}}^{{\mathtt{10}}}\right){\mathtt{\,\times\,}}{\mathtt{2}}\right]}}\right]}}$$

Some quick formulae to explain my workings:

x⁰ = 1

x^-y = 1 / x^y

1 / (1/x) = x

x^y * x^z = x^y+z

So this equation is = [(1 / (1/5⁶⁾) * (1 / (1/5¹¹))] / [(5²*4) / (5¹⁰*2)]

= [5⁶ * 5¹¹] / [(5²*4) / (5¹⁰*2)]

= 5¹⁷ / [(5²*4) / (5¹⁰*2)]

= 762939453125 / [(25*4) / 9765625*2]

= 762939453125 / 0.00000512

= 149011611938476562.5

= 1.49 * 10¹⁷

Of course I could read it without assuming any of what I did, and just work on the basic principles of what order you should do each function (however even then I must assume where each power "ends", since otherwise you have a crazy looking equation), in which case I get:

5⁰ / 5^-6*1 / 5^-11 / 5²*4 / 5¹⁰*2

$${\frac{\left({\frac{\left({\frac{\left({\frac{{{\mathtt{5}}}^{{\mathtt{0}}}}{\left({{\mathtt{5}}}^{{\mathtt{6}}}{\mathtt{\,\times\,}}{\mathtt{1}}\right)}}\right)}{{{\mathtt{5}}}^{{\mathtt{11}}}}}\right)}{\left(\left({{\mathtt{5}}}^{{\mathtt{2}}}\right){\mathtt{\,\times\,}}{\mathtt{4}}\right)}}\right)}{\left(\left({{\mathtt{5}}}^{{\mathtt{10}}}\right){\mathtt{\,\times\,}}{\mathtt{2}}\right)}}$$

= 5⁰ / 5^-6 / 5^-11 / 5²*4 / 5¹⁰*2

= (((1 / 0.000064) / 0.00000002048) / 100) / 19531250

= ((15625 / 0.00000002048) / 100) / 19531250

= (762939453125 / 100) / 19531250

= 7629394531.25 / 19531250

= 390.625

If I truly do not assume anything ends, then what I get is:

$${{\mathtt{5}}}^{\left({\frac{{\mathtt{0}}}{{{\mathtt{5}}}^{{\mathtt{\,-\,}}\left({\frac{{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{1}}}{{{\mathtt{5}}}^{{\mathtt{\,-\,}}\left({\frac{{\mathtt{11}}}{\left({\frac{{{\mathtt{5}}}^{\left({\mathtt{2}}\right)}{\mathtt{\,\times\,}}{\mathtt{4}}}{\left({{\mathtt{5}}}^{\left({\mathtt{10}}\right)}{\mathtt{\,\times\,}}{\mathtt{2}}\right)}}\right)}}\right)}}}\right)}}}\right)}$$

Which has a fraction with 0 on top, so in short ends up as 5⁰ = 1

She will be getting 374 voters per precinct

And is going to 11 precincts

The total number of expected voters will be how many voters per preseinct multiplied by the number of prescincts she goes to.

Total number of voters = 374 * 11 = 4114

(Of course in reality you would never be able to be that precise in predictions, nor can she make such a prediction off a literal sample size of 1. But I guess that's not relevant to the question :P)