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I assume you're sayng that all the cars differ in at least one aspect......so...there are 24 "different" cars, thusly:

(H, W,2)          (V, W,2)            (F, W, 2)          (C, W,2) 

(H, W,4)          (V, W,4)            (F, W, 4)          (C, W,4)                   

(H, R, 2)          (V, R,2)             (F,  R,  2)         (C, R, 2)

(H, R, 4)          (V, R 4)             (F, R,  4)          (C, R, 4)  

Notice that there are 4 ways  to  pair the  Hondas with a "different" Volvo, "different" Ford  or "different" Cadillac.  So, 4 + 4 + 4 = 12

And there are 4 ways  to pair the Volvos wth a "different" Ford or "different' Cadillac. {We've already paired each with a "different" Honda.} So 4 + 4 = 8

And since we've already paired the Fords with a "different" Honda or Volvo, we have 4 ways that we can pair them with a "different" Cadillac.

So there are 12 + 8 + 4 = 24 "different" pairings

And the total number of possible pairs made by selecting any 2 cars from 24  = C(24,2) = 276

So 24 / 276 = 2/23 = about an 8.7% chance of pairing two "different" cars......

x=.20(500)

x=100

Nevermind. The answer is 5.5. 

The angle of depression is given by...

tan^-1(10,000/ 50,000)   =  tan^-1(1 / 5) = about 11.31°

thats good you like them CPhill!

and btw id definitely take the key with me......especially after that "stupid idiot" thing!LOL

NO!!!    { All we need is one counter-example........ }

√7 + √7  ≠   2 (7)      prove this for yourself.....

Probability of a straight.....There are 10 ways to do this within the ranks. {The ace can be the high or low card.} And within each rank, we are choosing any 1 of 4 cards.  Note that we are including the straight flushes and royal flushes, here.

So.....there are C(10,1)*[C(4,1)]^5  = 10,240 possibilities

For the flush, we want to choose any 5 of the 13 ranks. And we have 4 ways to make each of these flushes.....all diamonds, all spades, all hearts or all clubs.  Here again, we are including the royal and straight flushes.

So......there are  C(13, 5) * C(4,1) = 5148 possibilities

Thus....the straight is almost twice as likely to occur......

Let A be the probability of drawing a white ball first, then a red one second, and then a white one last.

Let B be the probability of drawing a red ball first, then a white one second, and then a red one last.

So, P(A or B)  = 

[4/9 x 5/8 x 3/7 =  60/504 ] + [ 5/9 x 4/8 x 4/7 = 80/504 ]  =

[60 + 80 ] / 504  = 140/504 =  5/18 = about 27.8%

Using order of operations

Parenthesis

exponents

multiplication

division

addition

subtraction

0+50*1-60-60*0+10

no parenthesis

exponents

there is multiplication: 0+50-60-0+10

no division

there is addition: 50-60-10

there is subtraction: -120 

Answer: -120

HAHAHA!!!  Love those "trick pics," rosala!!!  .....especially the "BIG BIRD" and those bridesmaids sitting on the chairs......

We're glad that you're back, but your life seems pretty busy, at the moment .....  

P.S. ------  ALWAYS take the key WITH you!!!   LOL!!!!!

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Math may be boring but someones gotta do it, otherwise you wouldnt have a lot of stuff that exists today and is taken granted for.

This is the Eq: 7h-8=41

First you have to get the h on its own side and everything else on the other, which in this problem would mean adding 8 to both sides of the equal sign making it: 7h = 49

Secondly you cant times 7 by h so in order to remove that you need to devide the 7 from both sides meaning it will be: h = 7

Theres your answer: h = 7

Think of the first summation as the position of the first ball.  It can only go into boxes 1 to 7, because the 2nd ball will be in another box to the "right" of it, and the third ball will be to the "right " of that.

It might have been better to write the summations as follows, where each summation refers to each ball:

.

Its a Never-Ending Number that starts with 3.14 and is commonly stated as that number used to help figure out the radius and area upon other things of a circle.

We can also do this with one variable.

Let x be the son's age 4 years ago,

Then his father's age 4 years ago  = 7x

And years later, - 4 years from now -  the father will be 3 times older than his son. So we have.....

3(x + 8)  = 7x + 8    simplify

3x+ 24  = 7x + 8

4x = 16

So the son's age 4 years ago was 4

And his father was 7(4)  = 28

And 4 yeara later the son is 8 and the father is 32.

Here's a picture Melody:

The copper colour is the z = 2x² - 3y² surface.  The red blob is the point A = (2, 1, 5).  The blue mesh is the plane tangential to the surface at A (z = 8x - 6y - 5).  

The black line is the unit length vector lying in the tangential plane in the direction of steepest descent.

I took Bertie's solution for the vector in the horizontal plane, found where the end of this would meet the tangential plane, scaled the resulting vector from A to this point to be of unit length and plotted the black line to represent the unit vector in the tangential plane.

The black line goes from (2, 1, 5) to (1.92, 1.06, 4.01)  (approximately).

.

If 10 students are taking algebra and drafting  and 24 are taking algebta, then 24 - 10 = 14 are taking algebra only.

So   11 + 14 = 25 are taking algebra and drafting, but not both.

Hi MG

I write the wrap when I get things to a good spot for me at the end of the day (occassionally i miss a day)

Now this can be late afternoon sydney time or if there is a real lot of questions or I have been busy with other thngs it can be early the next morning.

I put the Sydney time that I write it on the top of each wrap so you can take a look and see.

Today I wrote it at 11:30 pm as I recall.   (which is still quite late)

BUT yesterday I wrote it a 4am the next morning.   (which was REALLY late)

Ideally I'd like to write it at about 8 pm

I think you live in Great Britain which means you are 10 hous behind Sydney, that is why it seems early to you :)

Take a look at the times on the top of each post 

Here is a great time site - you will like it. 

You'd have four.

Unless there is a trick to this question?

Like Jeff brought his own apple.

Thank you for explaining the double sigma notations Alan      (I didn't understand that before)

BUT

I did this with 9C3   Choose three boxes our of 9 and put an identical ball in each one.  9C3 = 84

Now,  your summation gives the same result but I don't understand the logic that you used to derive the sum in the first place.  (where on Earth did you pluck 7 from ??? )

Can you try and explain the logic that you used please?

Hmmm...

Is it me or was this posted earlier than usual.

In Uk, I see the wrap around evening but in London its only 3pm?

5   I didn't share mine with Jeff.  He ate his own.