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cuz its awesome

I'll try (3), too

Here's the same figure as in the answer to (2)

Using reasoning from the other two answers, P cannot fall into area ABFE, because then, any triangle DPC is greater than any triangle APB.  P also cannot fall into area EID because all triangles BPC would be greater than all triangles APB.

If P falls into any of the regions IFC, ICG of IGD, all triangles APB will have greater areas than either triangles BPC or CPD. And these areas are 3/8 of the square ABCD = 37.5%.....so that's the probabilty that tiangle APB will have a greater area than either BPC or CPD.

9+10 = 21 

$${{\mathtt{3}}}^{-{\mathtt{3}}} = {\frac{{\mathtt{1}}}{{\mathtt{27}}}} = {\mathtt{0.037\: \!037\: \!037\: \!037\: \!037}}$$

This is what i got.

Honestly, i don't know.

I've always hated negative number they always trick me with the operations.

I'm glad this went from Down-hill to up. :)

Lol Melody can cook Pi!

Any sexist comments are bad.

log x + logx^2 + log x^3

Notice that the last two terms can be written as

2log x     and   3log x      so we have

log x + 2log x + 3logx  =

(1 + 2 + 3) log x  =

6 log x

Yay. Thanks you CPhill.

Very, very nice MG1.......!!!!!

A BIG 3 points from me.....

I'll also take a stab at (2)

Consider square ABCD below:

This square is divided into 8 equal areas. It is clear that P cannot fall anywhere into rectangle ABFE because, although triangle APB and and triangle DPC would have equal bases, DPC would always have a greater height, and thus, a greater area.

It's also clear that P cannot fall into area IFC......To see this, note that if P fell on AC, its distance from AD and AB would be exactly the same. But, if P falls in area IFC, its distance from AD would always be greater than its distance from AB. Thus, triangles APB and APD formed by having P fall into this region would have equal bases, but APD would always have a greater height than triangle APB.

For the same reason, P cannot fall into area EID, because all triangles BPC would have greater heights than triangles APB.

So, P can only fall into region CID. Here triangles APB, BPC, CPD and DPA will all have the same bases, but APB  will have a height greater than the other three.

And since  CID is 25% of the area of the square, the probabilty that APB is greater than the other three mentioned triangles is ≈ 25%

dood its 9+10=19 ok not that hard bro

You're welcome. 

:)

Thnx man.

well explained.

$${\frac{{\mathtt{475}}}{{\mathtt{19}}}} = {\mathtt{25}}$$

25 do.

Hi thumb, :)

There are 5 steps to answering this:

Step 1) How many seconds are in an hour? You know there's 60 seconds in a minute, and 60 minutes in a hour.

$${\mathtt{60}}{\mathtt{\,\times\,}}{\mathtt{60}} = {\mathtt{3\,600}}$$

Step 2) Find out how many in a day. There's 24hr in a day.

$${\mathtt{3\,600}}{\mathtt{\,\times\,}}{\mathtt{24}} = {\mathtt{86\,400}}$$

Step 3) So that's how many in a day, now there's 365 days in a year.

$${\mathtt{86\,400}}{\mathtt{\,\times\,}}{\mathtt{365}} = {\mathtt{31\,536\,000}}$$

Step 4) There's 10 years in a decade 

$${\mathtt{31\,536\,000}}{\mathtt{\,\times\,}}{\mathtt{10}} = {\mathtt{315\,360\,000}}$$

Step 5 ) That's your answer 315360000 seconds.

-MathsGod1

The sum is 250.

Take 850/2000, which is 0.425 or 42.5%.

good, just remember to renew the formula by saying the ancient words before 28 days expire

Improper Fraction: $${\frac{{\mathtt{157}}}{{\mathtt{50}}}}$$

Proper Fraction: 3 and 7/50

yay! thanks, Chris!! :)

I did all of that yesterday, now I'm doing math.

nope. that process is too challenging (if youre a newb) or too easy (if youre a pro). This formula is hard for EVERYONE!!!!!!!!!!!

Or I could do some more math...?

O.o 

It's true I am MathsBoy.

I'll attempt to answer (1)

Shown below is square ABCD

Notice that if point P falls anywhere within rectangle EFCD, then the triangle APB will have a greater area than triangle DPC because each will have an equal base, but APB will have a greater height than DPC. And since rectangle EFCD is 1/2 of the area of the square, then the probability of P falling into this area is ≈ 1/2. So, the probability that APB > DPC   ≈ 1/2. [Of course, there is the slight possibility that P falls exactly on EF, which would make both triangles equal in area.......thus the need for the " ≈  "    symbol  !!!  ]