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One way they are the same:

The circumference and area both give information about the size of a circle.

One way they are different:

Circumference is a one-dimensional measurement while area is a two-dimensional measurement.

You still did not address the question of "Guest #13". That is, if this method works for the total number of 3's from 1 to 1,000, which comes to 300 threes, and from 1 to 10,000, which comes to 4,000 threes(of which there is no doubt, since both have been counted by computer programs), then why is it different for the total number of 3's from 1 to 10^12?

Here's one way :

2 / 5     multiply numerator/denominator by 20

40 / 100  =  40%   =   .40   [ or, just .4 ]

"Long division" would also work, but since the denominator is a divisor of 100, this method is easier, IMHO.....!!!!

perimeter of a square = 4 * side length

perimeter of this square = 4(x+3)

perimeter of this square = 4x + 12

\(\frac43\cdot3.14\cdot5\cdot5\cdot5=\frac43\cdot3.14\cdot5^3\approx523.333\)

This looks like the equation for the volume of a sphere! 

h(t) = 16t² + 100t + 3

Assuming t is in seconds,

to find the height of the baseball after 2 seconds, plug in 2 for t.

h(2) = 16(2)² + 100(2) + 3

h(2) = 16(4) + 100(2) + 3

h(2) = 64 + 200 + 3

h(2) = 267 units

In your original method, you suggested that the number matrix be filled out with leading zeros so that all the numbers have the same width. In a set of integers between 0 and 1 * 10^12, this would create a square matrix with zeros clustered at the uper left, like this:

    000000000000

    000000000003

    000000000014

    000000000481

    000000004067

    000000011202

    000000765025

    000006570349

    000052570231

    000569504785

    007221909937

    010323716328

    838219253314

This change makes it easier to understand the problem, but it doesn't change the result, which is true for a set of sequential 1 * 10^12 integers that aren't padded in this way:

                                     0

                                     6

                                   46

                                 426

                               1435

                             55123

                           230105

                         2873680

                       63725050

                     640899375

                   0060833473

                 53442421828

               372859331893

The point? The differing length of the integers between 0 and 1 * 10^12 needs to be taken into account. So the number of threes in the set of integers between 0 and 1 * 10^12 is 1 * 10^12 (height) times 12 (width) divided by 10 (isolate any single digit) divided by two (to account for the missing digits in the upper left of the martix as shown above).

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Why are you here then

-34.

Let N  be the number of sheep after t  years.......so we have....

N  =  4 (3)^t

After 6 years, we have

N  =  4 (3)^6  =  2916

Domain  =  0, 1, 2, 3, 4, 5,  6

Range  =  4, 12, 36. 108, 324, 972, 2916

(48*16) + (2*108)

Multiplication comes before addition.

= (768) + (216)

Now add the numbers together.

= 984

If this is the surface area, the answer will be in square centimeters.

If it is the volume, the answer will be in cubic centimeters.

You can type it in just like that.......

In a problem like this:

2[ x + 5 / (4 - x) + 6(3x) ]

Parenthesees and brackets mean the exact same thing.

It is just easier to see and understand when using a different-looking symbol instead of putting a bunch of sets of parenthesses inside each other.

But if you are talking about in interval notation,

brackets mean "inclusive" and parenthesees mean "exclusive."

The interval [ -5 , 8 )

is all numbers from -5, including -5, up to 8, but not including 8.

thanks!

The perimeter  =  2 (W + L)  ......so

2( x  +  x + 4) < 116      divide both sides by 2

x + x + 4   <   58           subtract 4 from both sides, simplify the left side

2x  <  54                       divide both sides by 2, again

x <  27   ....... so the width is < 27   and the length is < 31

Easy 2

Lol! I was wondering what happened! 

38°  .....I'm done with this one!!!!!

As long as PCQ is a tangent to the circle.....m

So   m

The rest of my answer magically disappeared.....!!!!

(3x)³ * (2x)²  =

3³  * x³  *  2² * x²  =        [ and using a^m * aⁿ  = a^m+n ]

3³ * 2² * x³ * x²   = 

27 * 4  * x⁵   =

108 x⁵

Hmm..did you mean to say 10/18 and 8/22 ?

Because 18/10 means that out of ten students, eighteen of them do running.