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400  +  [75D] ==1000 - [25D], solve for D

D ==6 days - after which they will have:

400  +  [75 * 6] ==1000 - [25 *6]

     850     ==     850   followers.

Where are your cards ??!

Here are my attempts, comments/refutations welcome.

First, a counting type approach.

The pack consists of 28 cards, (4 card colours and 7 numbers for each colour).

The number of 5 card combinations that can be drawn will be C(28,5).

Needed are 3 cards with the same number, so 7*C(4,3) = 28 possibilities.

Assuming that the possibility of having 4 cards with the same number is excluded, the remaining 2 cards have to come from 24 remaining cards, (4 cards each of the other 6 numbers), C(24,2) possibilities.

That generates a probability of     \(\displaystyle \frac{28*C(24,2)}{C(28,5)}=\frac{46}{585} \approx 7.86 \%.\)

Second, a probability type approach.

Choose a number and suppose that we draw, in succession, three cards with that number, followed by any two cards with a different number.  

The probability of that sequence will be 

\(\displaystyle \frac{4}{28}\times \frac{3}{27} \times \frac{2}{26}\times \frac{24}{25}\times \frac{23}{24} =\frac{23}{20475}\)

Now there are 7 different numbers to choose from and the sequence can occur in 10 different ways, so the final probability will be

\(\displaystyle 7 \times 10 \times \frac {23}{20475}= \frac{46}{585} \approx 7.86 \%, \text{as earlier}.\)

Any even number can be represented by  2x   where x is any integer

So any odd number could be represented by   2x-1   or   2x+1

2x-1  and   2x+1   are consectutive odd numbers  

There are lots of other pairs that could be used  eg  2x+5  and 2x+7   but the first pair is likely to be the easiest to use.

so

You are told,  

2x+1 = 3(2x-1)

so solve this equation, find x, then find the two numbers and add them together.

OR

you could just do it by trial and error - it is easy.

3x + y = a

2x + 5y = 2a.

Then the first equation x 2 = second equation.

6x + 2y = 2x + 5y

4x = 3y

So if x = 2, then y = 8/3.

Thus 3*2 + 8/3 = a = 26/3

How many miles did Sam drive?

Hello Guest!

\(\dfrac{100mil}{2.4h}\times 8h=333.\overline 3\ mil \\ \color{blue}Sam\ drive\ 333\dfrac{1}{3}\ mil.\)

  !

I assume that when you say "legs" you mean the 3 sides of the triangle. If that is so, then:

I can find only 1 such right triangle:

9^2  +  40^2 = 41^2

Area = (9 x 40) / 2 = 180 u^2

Sum of its 3 sides = 9 + 40 + 41 = 90 u

So, the area is 2 times the sum of the 3 sides of the triangle.

If an an answer is wrong then state why you know this and if possible find the error.

Also, and if it is a genuine attempt at help as this one appears to be, say thanks (which you did  )  then give them a point for their interest and time.

Also, if an question has been asked before, no matter how wrong or ablsent the answers may be, give a link to the original question and request that people answer on the original and ask answerers then leave a note on the repost saying that they have answered.

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Thanks for answering guest.   

Its not right, sorry. Thank you, but can someone still HELP!!!!

The coefficents of the expansion of a trinomial is a lot like what the binomial theorem states about the coefficients of a binomial. 

For example, if you want the coefficient of the a^3*b^2*c term of the expansion of (a+b+c)^6, it is the same as taking 3as, 2bs, and a c, and ordering them which is 6!/(3!*2!*1!). 

The thing is we don't know in this problem is how many y^2 or 2ys are multiplied together to create the y^4 term, so we can split this into 3 scenarios:

2 y^2 terms are multiplied together to get y^4

4 2y terms are multiplied together to get y^4

2 2ys and 1 y^2s are multiplied together to get y^4

The coefficent for the first case would be 6!/(2!*4!)*(-5)^4 = 15 * 625 = 9375

The coefficent for the second case would be 6!/(2!*4!)*2^4*(-5)^2 = 15*16*25 = 6000

The coefficent for the third case would be 6!/(2!*3!*1!)*2^2*(-5)^2 = 60*4*(-125) = -30000 

Adding all the possible cases together we get: -14625 is the coefficient of the y^4 term

Solved this one a few days ago:

Here's the link:

I believe I did say: "might have made a mistake somewhere, why don't you look carefully and read it, instead of just going after the answer"

2(x + y) = 1/2*x*y

4x + 4y - xy = 0

4x + y(4 - x) = 0

y = 4x/(x - 4)

Therefore, x > 4, y  > 4 since x and y must both be positive.

the only positive integer x values that give positive integer y values are    5,6,8,12,and 20

But i just realized that is not what you asked. 

(5,20)    area = 0.5*5*20 = 50

(6,12)    area = 0.5*6*12 = 36

(8,8)      area = 0.5*8*8  = 32

(12,6)    area  is 36

(20,5)    area is 50

so sum of all possible areas is   50+36+32 = 118 units squared.