geno3141

3 000 000 (1 + .05)³  =  3000000(1.05)³  =  $3,472,875.00

From the original 20 boxes, since 3 have neither pens nor pencils, let's put those boxes aside. Now we have only 17 boxes.

Of these 17 boxes, some many have only pens, some may have only pencils, and some may have both pens and pencils.

We know that 13 of them have pencils and since every box that we now have has either pens or pencils or both, the 4 boxes that don't have pencils must have pens.

But, since 9 boxes have pens (subtracting 4 boxes from 9 boxes, giving us 5 boxes), 5 of these boxes must be boxes that also have pencils.

If we look inside all the boxes, we will find that 8 boxes have only pencils, 5 boxes have both pens and pencils, and 4 boxes have only pens. (And 3 that have neither pens nor pencils.)

The smallest 3-digit integer is 100, the largest is 999.

Divide 100 by 13; the quotient is 7 and the remainder is 9; this means that the first multiple of 13 that will be at least 100 is 8.

Divide 1000 by 13; the quotient is 76 and the remainder is 12; this means that the last multiple fo 13 that will be smaller than 1000 is 76.

We now need to count the number of numbers starting with 8 and ending with 76.

A short way to do this is to subtract 8 from 76 and add 1 -- 76 - 8 + 1 = 69. (Don't forget to add 1!)

There are 69 positive integer multiples of 13 whose answers have 3 digits.

The greatest common factor is 22.

22 x 17 = 374  and  22 x 29 = 638.

One way to find this to to use the Euclidean algorithm (named in honor of Euclid).

Divide the smaller number into the larger number, and look at the remainder:

638 ÷ 374  =  1, with a remainder of 264  (Actually, you don't care about the quotient, just the remainder).

Since the remainder isn't 0, divide the remainder into the divisor:

374 ÷ 264  =  1, with a remainder of 110.

Since the remainder still isn't 0, divide the remainder into the divisor:

264 ÷ 110  =  2, with a remainder of 44.

Since the remainder still isn't 0, divide the remainder into the divisor:

110 ÷ 44  =  2, with a remainder of 22.

Since the remainder still isn't 0, divide the remainder into the divisor:

44 ÷ 22  =  2, with a remainder of 0.

Now, when the remainder is 0, you are done and your answer (the greatest common factor) is the last divisor; so the greatest common factor is 22.

Let's say that you are arranging them from left to right.

You have 4 choices for the first book, then 3 choices for the next book, then 2 choices, then only 1 choice.

To find the total number of choices, multiply these numbers:  4x3x2x1 = 24 different ways.

(A short way to write  4x3x2x1  is 4!, where "!" means "factorial".)

If you meant the two fractions to be  (x-4)/(x-5)  and  (2x-3)/(x-6),

then the common denominator is (x-5)(x-6).

If your team scores 4 runs in the first three innings, then, at that rate, it will score another 4 runs in the next three innings and another 4 runs in the last three innings:  4 + 4 + 4  = 12 runs scored.

Pasting that into the calculator at this site, I got the answer of 68140.

Use the method of "linear combinations":

-4x - 15y  =  17

 4x - 20y  =  52

Add down the columns to get:

      -35y = 69

          y  =  69/-35

Substitute this value back into either one of the original equations; I'll use the second one:

  4x - 20(69/-35)  =  52

                    4x  =  88/7

                      x  =  22/7

(x + 1)²  =  (x + 1)(x+ 1)

Use FOIL:  First (x and x), Outside (x and 1), Inside (1 and x), Last ( 1 and 1):

x·x + 1·x + 1·x + 1·1

=  x² + 1x + 1x + 1       (Now, simplify by adding 1x + 1x.)

=  x² + 2x + 1