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The length of UV is constant no matter how long is the line segment QR.

QR  = 20

UV = 12 

A diagonal.       Sqrt ( 12² + 11² + 9²) = ........

If it is a square centered on the origin....     then   |x| = |y|.  At the corner that intercepts the parabola.....compute the formula of the parabola first.....then......

The brainly site is not correct. I put in your answer the guest and It was wrong.

S=0.1223242434262445262644283446282644492. 37th digit is 2

Great question!  The probability is 4!*4!*4!*4!/12! = 4/5775.

Firstly, the probability is much greater than 5/2^10 (solved it myself already). Secondly, this question is coming from an ongoing math torunament, the MBMT 2020 Online more specficially. Please don't attempt to cheat on math competitions, you are spending 2 minutes to post a question like this while I have had to spend some hours of pure dedicated effort to come up with a solution to the problem. It's really not fair that you are essentailly devaluing the points the question gives for hard workers like me and my team. I will post my solution to this once the competition ends in 3 more days.

ok, no worries, just be careful and maybe learn from this mistake. :)

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.

Attn: theLizzybeth,

I have looked at your history and seen that you have provided many quality answers. I thank you for that.

Jimkey is also a valuable member of this forum.

I share Max's view that Jimkey has had no prior experience with complex numbers. Hence he has been taught that there are no square roots for negative numbers. Certainly, in the real number system, he is correct.

Please be aware that people are at different places in their learning.

Thanks Max ;)

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.

You assume that all the time Hugo.

It is this constant assumption that annoys other people so much.

You did not answer the question. If you were looking at the AOPS question then you did not even TRY to answer this question by yourself.

The AOPS question or the answer should not have been anywhere near you!

For a question like this you can check your answer from the original question given. You did not need to look anywhere else for confirmation, even when you were challenged, you did not check your answer thoroughly.

Angle AIB works out to 41 degrees.

Since, there is an equal chance of winning or losing any bet,

let's have Matthew lose four of those eight bets.  The first four! 

Bet Number      Wager      Win/Lose     Remaining Balance 

                                                                      256.00 

      1                128.00         L                        128.00 

      2                  64.00         L                          64.00 

      3                  32.00         L                          32.00 

      4                  16.00         L                          16.00 

      5                    8.00         W                         24.00  

      6                  12.00         W                         36.00 

      7                  18.00         W                         54.00  

      8                  27.00         W                         81,00 

So... 81 again.  Hmmm, I suspect there might be a pattern. 

_.

In the sequence 1, 5, 4, 1, 3, 2, ..., every term is equal to the absolute value of the difference of the previous two terms.  Find the 1994th term. 

I don't know where you got that 5 but let's continue the sequence: 1, 5, 4, 1, 3, 2,   1, 1, 0,   1, 1, 0,   1, 1, 0,   1, 1, 0,   1, 1, 0 

It starts repeating 110 at the 7th number so there are going to be (1994 – 6) / 3 =  662 & 2/3 groups, so it will be 2/3 of the way through the 663rd group, and 2/3 of the way through any of those groups is a 1.  I'm confident my reasoning is solid so I'm going with a 1. 

_.

You can't count 13, 26, 39, 52, 65, 78, and 91 because they don't have three digits, as the problem required. 

So, subtract those 7 from your 76 and get 69 which is what jimkey got.  I didn't try to figure it up myself. 

_.

how do you know that x = y = z?

two black balls and 5 white balls are placed ina  bag. if amy draws two balls from the bag, what is the proabiblity that they are both white? 

The 1st ball has a 5 out of 7 chance of being white. 

If a white one is drawn, then the 2nd ball has a 4 out of 6 chance of being white. 

The chance of both things happening, multiply them together  5/7 • 4/6  =  20/42  =  10/21  =  about 47.6% 

_.

The 100 people are distributed as follows:

1 man = 10 Breads

9 women =9 x 5 =45 Breads

90 kids    =90 x 1/2 = 45 Breads

People =1 + 9 + 90 =Breads =10 + 45 + 45

100 people  =  100 Breads

Matthew Casertano and Fox Chyatte make a series of bets. In each bet, Matthew sets the stake (the amount he wins or loses) at half his current amount of money. He has an equal chance of winning and losing each bet. If he starts with $256, find the probability that after 8 bets, he will have at least $50.  

Since there's an equal chance of winning or losing, let's alternate them.

Let's start with the worse case scenario, that Matthew loses the first bet. 

Bet Number      Wager      Win/Lose     Remaining Balance 

                                                                      256.00

      1                128.00         L                        128.00 

      2                  64.00         W                       192.00  

      3                  96.00         L                          96.00 

      4                  48.00         W                       144.00  

      5                  72.00         L                          72.00 

      6                  36.00         W                       108,00  

      7                  54,00         L                          54,00 

      8                  27,00         W                         81.00 

_.

The inverse function is the function that "undoes".

We can find the inverse function by setting f(x) as y and solving for x in terms of y.

\(y(2x-1)=x\)

\(2xy-y=x\)

\(y = 2xy-x\)

\( y=x(2y-1) \)

\(x=\frac{y}{2y-1}\)

So the inverse function is \(\frac{x}{2x-1}\)

1. By the Law of Cosines, BC =2*sqrt(14).

2. By the Law of Sines, AC = 12*sqrt(3).

3. B = 15 degrees.