geno3141

1 petabyte = 1 x 10^15 bytes

1 zettabype = 1 x 10^21 bytes.

To go from zettabytes to petabytes, multiply by 10^6.

To go from petabytes to zettabytes, divide by 10^6.

If you replace x with -5 and y with -11 into both equations, the values work in both equations.

Therefore (-5, -11) is a solution. 

The idea is that halves of equal are equal.

The bisector of an angle produces two angles, each one-half the size of the original angle.

Since the original angles are congruent, they are equal in size.

Haves of two equal-sized angles are equal in size.

Therefore, the angles created by the bisecting of two congruent angles are themselves congruent.

(-2.3·10^13)·(0.8·10^-28)

=  (-2.3·0.8)·(10^13·10^-28)        Rearrage, since you can multiply in any order.

=  (-1.84)·(10^-15)                        When you multiply numbers with the same base, just add exponnents.

=  -1.84 · 10^-15

Since 1 inch = 2.54 cm

--->  (1 in)²  -= (2.54 cm)²

--->  1 in²  =  6.4516 cm²

So:  375 in²  =  375 x 6.4516 cm²  =  2419.35 cm²

Happy -- that's a really neat way to do it!

Can you explain what you did and why it works so the process can be applied to other problems?

1000 =  500e^(.05x)

Divide both sides by 500:  2  =  e^(.05x)

Take the ln of both sides:  ln(2)  =  ln( e^(.05x) )

Since the ln( e^z )  =  z:  ln(2)  =  .05x

Divide both sides by .05:  x  =  ln(2) / .05

Use a calculator to get a decimal approximation.

To find the number of pounds, divide the total number of ounces by 16:

38 / 16  =  2 .375 pounds or 2 pounds 6 ounces.

To write 2 pounds 6 ounces as a mixed number, it becomes 2 and 6/16 pounds which is 2 3/8 pounds.

The actual interest rate depends upon the number of times that the investment is compounded per year.

Assuming that it is compounded once per year, using the compound interest formula:

       A  =  P(1 + r)^t

with A = 2 (representing twice the initial value),     P = 1 (representing the initial value),     and t = 15:

      2  =  1(1 + r)^15

--->   2  =  (1 + r)^15

Taking the 15th root of both sides:

--->  2^(1/15)  =  1 + r

--->  1.04729  =  1 + r

--->  0.04729  =  r

If you have a problem in which the compounding is more than once per year, or is compounded continuously, repost...

For part a:

There are 9 positions in the identifying number and each position can hold any one of ten digits, so there are 

   10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10    or     10^9   =   1,000,000, 000 possibilities.

For part b:

I have no idea what the 120 stamps refer to; perhaps someone else can answer that ...