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Cool! I never knew there was a method to it - Always just used intuition :)

xy  =  3x  + 2y  + z

xy - 3x  =  2y  + z

x ( y - 3)  =  2y + z

           2y + z

x =    _______

            y -  3

2^9  =  512

Subtract  this from  729  = 217

2^7 = 128

Subtract this from 217  =  89

2^6  =  64

Subtract this from  89  =  25

2^4  = 16 

Subtract this from 25  = 9

2^3  =  8

Subtract this from 9  = 1

2^0  = 1

So  writing  backwards we have

Powers of 2       0 1 2  3  4   5  6  7  8  9

                          1 0 0  1  1   0  1 1   0  1

Reverse the part in red

729₁₀ = 1011011001₂

A) I'm not sure, but I think 𝑝̂ is the percentage. The fraction for this would be 14581 / 107109, the decimal being 0.136132... :)

The percentage would be 100 times the decimal, so that's around 13.613 % people positive :D

B) Here, we just find 13.613 percent of 11.69 million people. That would be 13.613 / 100    *    11,690,000 = an estimate of around 1,591,359 people positive :D

This is solving for x. :)

xy = 3x + 2y + z, right? So, we can divide both sides by y to get

x = (3x + 2y + z) / y :D

Is that it? Do we need to do anything more?

Binary is fun.

The answer is 1011011001 :D

oops forgot to log in, I'm CentsLord xD

I think I would like that site if you find it again!  I used a quarter and a pen....then scanned in......ugh. 

Thanks, EP!!!!

I've been looking for an online Venn diagram maker....I once found a good one but it disappeared   !!!!

Cool! it's always interesting to have multiple ways to solve a question.

Thanks, CentsLord and LuckyDucky   !!!

Here's my approach  :

Bob has finished   (8/10) = 4/5 of the race  and Carol has finished (6/10) =3/5  of the race when Anna finishes

So....in 4/5  of the race  he has as 200 meter lead on Carol

So...in each (1/5) of the race  he gains 200 /4  = 50 meters on Carol

So....for the last 1/5  of the race he picks up another 50m on Carol

So....when he crosses the finish line, he is  200 + 50  =  250 m  ahead of Carol

The average, which is the median in this case, has been removed. That would be 85 :D

I got the same answer. 

w0t? BTW there are 8 options for the first position. I'm not sure I understood the last few lines, but I could be wrong!

First, we need to place "123" in the string of 7 digits. There are 5 ways to do that.

Now, we have to place 8 digits in the first digit, at 0 cannot be one. So far, there are 5 * 8 = 40 ways.

Now, we simply have to place digits in the remaining 3 digits. There are 9³ = 729 ways to do that. 

Therefore, there are 40 * 729 = 29160 phone numbers :D

Haha No problem

Oops just ignore this 

000/7 = 142 numbers that have at least 1 factor of 7

1000/49 = 20 numbers that have at  an additional factor of 7

1000/343 =  2 numbers that have a third factor of 7

Then we get 142 + 20 + 1 = 163

So n = 163

Let's say Anna finished in 1000 seconds (1 meter per second). Therefore, she finished in 1000 seconds.

Bob's speed is 80% of Anna's, as he had run 80% of the distance Anna did in the same amount of time. Therefore, his speed is 0.8 meters per second.

Using the same logic, Carol's speed is 0.6 meters per second.

Bob must've finished in 1000 / 0.8 = 1250 seconds. 

Going back to Carol. From the beginning of the race to when Bob finished (after 1250 seconds), Carol must have gone 0.6 m * 1250 sec = 750 meters, behind Bob by 1000 - 750 = 250 m.

So, Carol was behind Bob by 250 m when he finished :D

THERE....you had it     arctan (7/15) = 25.016^o  ~ 25.0 ^o

Here is a Venn diagram:

Lol Thanks!

The hero we need AND deserve :D