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1. The volume of the pyramid is 120*sqrt(3).

2. The length of the diagonal is 5*sqrt(2).

Here is a computer count of the all 3's from 1 and up:

Between 1 and 9 = 1
Between 10 and 99 =19
Between 100 and 199 =40 
Between 300 and 323 =27
So: 1 + 19 + 40 + 27 =87 "3's"
So, the dictionary is 323 pages.

We can do this by the long, slow process of counting ...

From 0 through 99 it appears 19 times: 

     3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93

From 100 through 199, it appears another 19 times, for a total of 38 times.

From 200 through 299, it appears another 19 times, for a total of 57 times.

From 300 through 309, it appears another 11 times, for a total of 68 times:

     300, 301, 302, 303, 304, 305, 306, 307, 308, 309

From 310 through 319, it appears another 11 times, for a total of 79 times.

Then there are 320, 321, 322, 323, 324, 325, 326 for another 8 times, for a total of 87 times.

:) yep

whats up my friend hugo

V=4.37 in.^3

There's really no point of trying to make us feel that you are superior, really, none.

It's only your time you're wasting.

Yes, great!

so he counts in intervals of 6, from 15, to 363.

So 6 times x plus 15 = 363

6x + 15 = 363

6x  = 363-15 = 348

x = 348/6 = 58

That's all numbers after 15, so we add one to 58 so 59, I believe.

thank you

See here: https://web2.0calc.com/questions/to-go-to-sleep-oliver-counted-by-6s-starting-from

It has been answereed two years ago:)

Hope this helps, whymenotsmart :P

(363-15)/6  + 1  = ............

uh............................

Is this better?

If you added all the individual  digits of each page together, i.e. 15th page would be considered as 1+5, then you have a book with 1127 pages, which add up to 3401.

Please correct your latex, I cannot see the numbers.

a)  Colin's name is one of ten names. Two names are chosen (with possible repeat). What is the probability that

     Colin's name chosen at least once.

     Let's find the probability that his name is not chosen and then subtract that from 100%.

     There are 9 out of 10 ways to not choose his name the first time and also, since that name is allowed to be

     chosen again, 9 out of 10 ways to not choose his name the second time.  This is:  9/10 x 9/10  =  81/100 

     for a probability of 0.81.

     The probability that his name will be chosen at least once is 1.00 - 0.81  =  0.19.

b)  Same situation but no name can be chosen twice.

     The probability that his name won't be chosen the first time is 9/10. Since there are no repeats, the probability

     that his name won't be chosen the second time is 8/9.  This is 9/10 x 8/9  =  72/90 for a probability of 0.80.

     The probability that his name will be chosen is 1.00 - 0.80  =  0.20.

3 drinks    3 pieces   20 dollars

[$20- (3 pieces * $3 )-5]  = PRICE OF 3 DRINKS