CPhill

Look at this, rosala.....the first few multiples of 3 are:

3  6  9  12  15  18   21   24

And the first few multiples of 6 are:

6 12  18  24  30

So......the first multiples of 3 that are bigger than 3 but are not multiples of 6 are

9  15   21  27

And we only care about the first two........does this make sense??

We can write this as a decimal....it equals (about).....0.5871852583387229

This is a shorthand way of representing a number in scientific notation (it's always a confusing notation, to me!!).   It means:

1.83337 X 10¹⁹  =  18,333,700,000,000,000,000

Nice explanation, ND and a nice "Thank You" from rosala.......rosala, maybe you should send ND some roses, huh??

Points for a good answer and a good "Thank You"

First, let's calculate the speed of the TGV train.

Since there are 3600 seconds in an hour and it travels 89.44 meters/second, it must travel

3600*89.44m = 321,984 meters per hour. We need to divide this by 1000 to get the speed in km = 321.984 km/hr. Note that this is slightly faster than the Japanese train. So, if for instance, our train traveled 321km/hr, it would be the second fastest.

To convert this to mph, note that there are about 1.61 km in a mile. So....

321km/hr * 1 mile / 1.61 ≈ 199mph.

To find out the distance it can travel in 2.5 hrs., we have

Rate * Time = Distance

199mph * 2.5 hrs. = 497.5 miles

OK.......let the montly cost of Cell-U-Later be M...   and let the montly cost of  Ameri-Mobile be (M + q)  where q is some positive quantiy.

Next, let the activation fee  for Ameri-Mobile be A... and let the activation fee for Cell-U-Later be (A + r)  where, again, r is some positive quantity.

So the total cost of Ameri-Mobile after some months is given by:

A + (M + q)n      where n is the number of elapsed months

And the total cost of Cell-U-Later after some months is given by:

(A + r) + Mn      where, again, n is the number of elapsed months

P.S.  ........Ismael should avoid Captain Ahab at all costs.....I hear he's kind of cranky these days after his last run-in with Moby D**k.......

I don't have time to do more than the first one......both answers are incorrect

Matt was going correctly until this point.....

6 – 16 + 30 ÷ 5  ..........then, he added the first three terms and divided the result by 4...this is incorrect....he should have carried out the division, first

Karen makes her error even earlier in the process:

6 – 4( –2) ² + 30 ÷ 5    ..........she then evaluates (-2)²  as (-4)........it should be just 4

Here is the correct series of operations:

6 – 4(3 – 5) ² + 30 ÷ 5 

First, perform the operation inside the parenthesis  (3-5) = (-2)

6 – 4(-2) ² + 30 ÷ 5 ......Now appy the exponent, which gives us

6 – 4(4) + 30 ÷ 5 .........Next, perform the first multiplication 4(4) = 16

6 – 16 + 30 ÷ 5 .........Next, we want to perform the ending division....30/5 = 6

6 – 16 + 6 ..... Now, just add and subtract

-10 + 6    = -4

And that's the answer !!!

I'm at a library, rosala, and this computer is acting rather odd....I told Rose98 that I would do a better job when I got home and could use my trusty laptop !!!!

S_n = (1/2)^1 + (1/2)^2 + (1/2)^3  + ........+ (1/2)^(n-1) + (1/2)^n ..... where the sum ( S_n)  can be found by:

a₁ / (1 - r) ....     where a₁ is the first term = (1/2).... and  r is the geometric ratio between terms = (1/2)

So we have

(1/2) / (1 - 1/2) =  (1/2)/ (1/2)  = 1   

And that's the sum

Very nice Rose98  !!!.....  Good explanation and pic.......thumbs-up and points from me !!!