hugomimihu

Let's say x is the time in hours.

Since it would take 20 more minutes, so we have 20/60 = 1/3.

TRIP____________speed______time___________distance
Actual___________40________x______________40x
Hypothetical_____30_______x+30/40_________30(x+1/3)

So the distances are equal so

40x = 30(x+ 1/3) 

40x = 30x + 10

10x = 10

x = 1

Now let's plug x in. x * 40 = 40 so 40 miles.

Checking...

40 mph for 40 miles means 1 hour, 30 mph for 40 miles means 1 1/3 hour, and 1 hour is 60 minutes, 1 1/3 hour is 80, 80-60 = 20.

(This is from an answer I previously wrote.)

Don't worry, it's the EXACT same question, word by word.

Let's do this number by number...

There are 10 1's in the ones digits... 01, 11... 91

There are 10 1's in the tens digits. Thus we have 20 for 1's.

There are similarly 20 for 2, 20 for 3...

Thus we have 20(1+2+3+4+5+6+7+8+9) = 20*45 = 900

I believe that is the answer.

I actually was not looking at the AoPS question.

All AoPS questions are stored on my desktop computer only, and I usually go on my laptop.

I assumed since I've seen this exact question many times in the last month.

I do apologize for my error.

Election polls are only somewhat related to probability.

Like Guest and Azalea, these polls give an overview of the population's beliefs using a sample.

You may be swayed into voting for the opponent, but there really is no clear path to probability other than the fact that you might be angry/sad on that day for whatever reason which could affect your vote.

Draw a venn diagram

(this is more of a boxed diagram as I am unable to upload images with my current browser)

cats                                             dogs

|-----------------------|----------------------------|

|                    |             |                            |

|                    |             |                           |

|  14                  |     3       |             6              |

|                    |             |                           |

|-----------------------|----------------------------|

Thus there are 14 + 3 + 6 = 23 people who have a cat OR dog.

I apologize, I read the 38 as 39.

As I am pretty used to AoPS questions I naturally assumed this was the same.

How am I plagarizing?

I drew the diagram myself using asymptote.

The answer is, 6 dogs who have not learned any tricks.

This IS the answer fo the given question.

This is indeed.

I have personally checked.

Here is the proof:

62 have blue: 7+23+16+16 = 30 + 32 = 62

55 have green, 16+16+15 + 8 = 32 + 23 = 55

63 white: 23+15+16 + 9 = 38 + 25 = 63

Any further prrof needed?

The data is indeed correct.

Unless if AoPS is incorrect?

I rendered the image myself, but the numbers come straight from both mine and AoPS' calculations.

If you'll be so kind as to point out the errors?

Total and no-tricks added

Which question do you need the help on most?

We aren't here to do all your AoPS question, but it's fine if you want to ask one.

Here is another AoPS question in which you can peer edit my response

https://web2.0calc.com/questions/at-my-office-people-own-cats-people-own-dogs-and

I can assure you that this is the right answer.