All Answers 358091 Answers

If you think about it, a regular hexagon is just comprised of six equilateral triangles.

The area of one of these triangles is given by

(1/2)s^2 *(√3/2) = (√3/4)*(s^2)   where s is the side length of the hexagon

So.....6 times this is just

(3/2)(√3) s^2

Are there any sequences between the prime numbers ?

p = 41 + n(1+n)   for n = 0,1,...,39

@@ End of Day Wrap      Wed 10/12/14       Sydney,   Australia         Time 7:00 pm          ♬

Hi all,

As is normal, there were many questions and many answers.  Our answerers were CPhill, SevenUp, Alexa4life, Jbow4, Zegroes, GoldenLeaf, Geno3141, TayJay, Shnaiab29544, Happy7, Alan, Heureka, Rosala, Usaijohann, Tiddle, Landry, iLoveMilk, and flflvm97.  Thank you - without you there would be no forum.  If questions were not answered then they would stop being posted very quickly.:) 

Again many quesions were not answered. If you still need an answer please follow my directions from yesterday's wrap.

There was some excitment this morning as Zegroes returned and was at his cheeky best.  Nauseated and zegroes were 'sparing'.

Anyway, here are some interest posts;

1) Happy's tribute to many on the forum.  Thanks Happy   

I don't get it......is this some secret code??

Melody......I tried to figure out GL's solution methods to these "solution" problems.....he must have "guessed and checked".......maybe he knows some easier method......!!!!

Thurs 11/10/14

1) SevenUp tells us we can expect a play  

y=5x-11

2x+3y=18

Solve the system of equations by substitution.

simplify

$$\\2\times x \quad + \quad 3\quad \times\underbrace{y}_{=5x-11}=18 \\\\
2\times x \quad + \quad 3\quad \times (5x-11)=18\\\\
2\times x \quad + \quad 3\times 5x - 3\times 11 = 18$$

2x + 15x - 33 = 18

17x                 = 18 + 33

17x                 = 51

    x                 = 51 / 17

    x                 = 3

y = 5*x   - 11

y = 5*(3) - 11

y = 15     - 11

y = 4

Where did your numbers come from Golden Leaf?  You need to show how you get your answers.

40% OF X + 70% OF Y = 60% OF (X+Y)

X+Y=30

Y=30-X

so

0.4X   +   0.7(30-X)   = 0.6*30

0.4X   +   21 - 0.7X   = 18

-0.3X   = -3

x          =-3/-0.3

       X  =  10

10ml of the 40% solution are needed. 

Adding or subtracting any real quantity from infinity still results in infinity......it doesn't play by "normal" mathematical rules because it's a "concept,"  not a "number"

I like the way geno did this one.......however..... what if we forgot (or didn't know) that the x coordinate of the vertex occurs mid-way between the roots?? Here's an alternative approach - though maybe not as "neat"

We have

0 = a(10)^2 + b(10) + c

0 = a(34)^2 + b(34) + c

Subtracting the first equation from the second, we get

0= a(34^2 - 10^2) + b(34 - 10)  simplify

0 = a(1056) + b(24)    rearrange

-b(24) = a(1056)       divide both sides by 24

-b = a(44) = 44a

Now.....suppose that we do remember that the x coordinate of the vertex is given by

x = -b / 2a    so we have

x = 44a / 2a  =  22   .....and that's the x coordinate of the vertex

And now we can continue the problem just as geno did by finding the value of "a," etc.  !!!

24u^2-72u+54

The first thing that i notice is that it can be divided through by 3

$$3(8u^2-24u+18)$$

Now I need 2 numbers that mult to 8*18      (that is positive so they must both be pos or both neg)

And they need to add to -24                        (so they must both be negative)

I am going to try and shough you what I am thinking

8*18=2*2*2*3*3*2=2*2*3      *  2*3*3       =12*12

and 12+12=24 that is great

so the numbers are -12 and -12

now replace -24u with -12u-12u

$$3[8u^2-12u-12u+18]$$

Now factorise in pairs

$$\\=3[4u(2u-3)-6(2u-3)]\\\\
=3(4u-6)(2u-3)\\\\$$

Don't faint.......there's only me to revive you, and I'm afraid it's a long trip to Sydney.....!!!

A mild swoon WILL be permitted, however.....

24u^2-72u+54

Testing some factors, we have

(6u - 9)(4u - 6)   ......wow.....guessed it correctly right off the bat....!!!  ......highly unusual....

Two times a month means that every paycheck covers a two-week period....so.....

2 weeks x 50 hrs per week x $8.25/ hr  = $825 per every two weeeks

Double this to get the monthly amount.

How did you do it Landry?

We must put a notch somewhere - My answer was the most succinct.  

I think I am going to faint.  

I think you pressed 10*exp3  instead of just just exp3

I am pretty sure that is what you would have done.   

They have won 8/14 of their games

Thus (8/14) x 21 = (4/7) x 21 = 4 x 3 = 12 games

they have 12 winning games after playing 21 matches

given

W=8

L=6

T=W+L=14(2*7)

also ratio(W:L)=8:6=4:3(4+3=7)

Good one Chris   LOL

Hi Nauseated - I didn't tell you you could post that picture of me!!

Drawing three cards and then returning these cards and reshuffling does not influence the rest of the problem.

The problem of getting three spades by drawing three cards:

  You must get a spade on the first card: the probability is 13/52 because there are 13 spades and 52 cards

    and you must get a spade on the next card:  12/51 because there are 12 spades left and 51 cards left

      and you must get a spade on the third card:  11/50  because there are 11 spades left and 50 cards left

  The total probability is 13/52 x 12/51 x 10/50  (you multiply when you have an 'and' situation).

The problem of getting a ten, a king, and a two (in that order):

  You must get a ten on the first card:  4/52  (four tens and 52 cards)

    and you must get a king on the second card:  4/51  (four kings and 51 remaining cards)

      and you must get a two on the third card:  4/50  (four twos and 50 remaining cards)

  The total probability is 4/52 x 4/51 x 4/50

This was an excellent question flflvm97.

If you mean 1/4%:

1/4% means 1/4 of 1%

which is 1/4 of 0.01

which is 1/4 x 0.01

which is 0.25 x 0.01   =   0.0025

Here  is a little exerpt from Dr. Who that you may enjoy. Digits of pi. 

Using the 50 fish that were caught to represent all the fish in the lake, we can set up this proportion:

14 / 50  =  x / 7500

Can you finish this?