hectictar

Hmmm good point....

$1.015^{n}(4000) = 1.04^{n}(3542)$

Divide both sides by 4000.

$1.015^{n} = 1.04^{n}(\frac{3542}{4000})$

Divide both sides by 1.04^n

$\frac{1.015^{n}}{1.04^{n}}=\frac{3542}{4000}$

That is:

$(\frac{1.015}{1.04})^{n}=\frac{3542}{4000}$

$(\frac{1.015}{1.04})^{n}=0.8855$

n equals the log base (1.015/1.04) of 0.8855, but since most calculators can only do base 10 or base e, we will need to use a change of base formula.

This page talks about the change of base formula: http://www.purplemath.com/modules/logrules5.htm

That tells you that:

n = [ln 0.8855]/[ln (1.015/1.04)]

Just plug that into a calculator to get that

n ≈ 4.998

1/75 * 4

= 4/75

(5/3)^-2

A negative exponent means to move the term to the denominator and get rid of the negative sign.

= $\frac{1}{(5/3)^{2}}$

That is the same thing as:

= $\frac{1}{5^{2}/3^{2}}$

=$\frac{1}{25/9}$

=$1 / \frac{25}{9}$

Keep, change, flip

=$1 * \frac{9}{25}$

=$\frac{9}{25}$

You can reduce the numerator and denominator by 8.

40/8 = 5

72/8 = 9

so

40/72 = 5/9

The total number of hours minus the number of hours she didn't walk equals the number of hours she walked.

24 - 8 = 16

4) 16 hours

4x + 7 = 3(x-2)

Distribute.

4x + 7 = 3x - 6

Subtract 3x from both sides.

1x + 7 = -6

Subtract 7 from both sides.

x = -13

holy cow 

(-8)(-9) - 7