geno3141

I am not certain of the use of "repunit" in this problem.

The factors are (10^1 + 1)(10^2 + 1)(10^4 + 1)(10^8 + 1)(10^16 + 1)(10^32 + 1)...

The number of digits in the answer will be the sum of the powers of 10 in the product plus 1.

1 factor --> 2 digits      --> 2^1

2 factors --> 4 digits     --> 2^2

3 factors --> 8 digits     --> 2^3

4 factors --> 16 digits    --> 2^4

5 factors --> 32 digits    --> 2^5

Yes, you are correct!

You'll have to know how much each cargo box weighs. 

The heavier the cargo boxes, the fewer you can carry with you.

√(x²+y²) ≠ x + y       (Except for rare cases.)

For instance: √(3²+4²) = √(9+16) = √25 = 5

But: if √(x²+y²) = x + y, then √(3²+4²) would equal 3 + 4 = 7 (which it doesn't).

Since 1 percent is 0.01, one-half percent is 0.005.

Let x be the interest rate of the $1000 investment; then x + 0.005 will be the interest rate of the $2000 investment.

Formula: (Amount Invested)(Interest Rate) + (Amount Invested)(Interest Rate) = (Interest Earned) 

     (1000)(x) + (2000)(x+0.005) = 160

     1000x + 2000x + 10 = 160

      3000x + 10 = 160

      3000x = 150

      x = 150 / 3000

      x = 0.05    ---> The $1000 is invested at 5%.

Check: ($1000)(0.05) + ($2000)(0.055) = $50 + $110 = $160

I'm assuming that 2.6 x 102 lb of oxygen each year means 2.6 x 10^2.

Also, I'm assuming that 3.9 x 1011 trees means 3.9 x 10^11.

Multiply the two values: (2.6 x 10^2) x (3.9 x 10^11)

                          = (2.6 x 3.9) x (10^2 x 10^11)            Multiply the numbers; add the exponents.

                          = 10.14 x 10^13        

                          = 1.0 x 10^14                                     Round to one decimal.

4³=(2²)³=2^6                   When taking a power to a power, multiply the exponents.

2³·4³=2³·2^6=2^9            When multiplying numbers with the same base, add the                                                    exponents.

Do a (2nd) sin:

15.541 383 331 83

-5(x-3) + 7x = -7             Use the distributive property: -5(x - 3) = -5·x - -5·3 = -5x + 15

-5x + 15 + 7x = -7           Simplify: -5x + 7x = 2x

2x + 15 = -7                    Subtract 15 from both sides.

2x + 15 - 15 = -7 - 15

2x = -22                          Divide by 2.

x = -11 

If you have a problem that looks like this: 12.345 ÷ 67.89

The number that you are dividing by is called the divisor (67.89 is the divisor); the number that you are dividing into is called the dividend (12.345 is the dividend). The answer is called the quotient.

Move the decimal point of the number that you are dividing by (67.89) so that it becomes a whole number; make is 6789.

In this case, you will need to move it 2 places to the right; you will now need to move the decimal point in the other number by 2 places also; make it 1234.5.

You now have: 1234.5 ÷ 6789. Place the decimal point in the quotient directly above the decimal point in the dividend. Divide.

If you have this problem: 1.2 ÷ 34.567.

You need to make the 34.567 into 34567 so move the decimal point 3 places.

Now, move the decimal point of 1.2 be 3 places, making it 1200.

Divide 1200 by 34567, adding a decimal point and zeros after 1200. When you divide, again place the decimal point in the quotient directly above the decimal point in the dividend.

80% as a decimal is 0.80

interpret "of" as "times"

80% of 7.125 ---> 0.80 x 7.125 = 5.7