In order to find the decimal equivalent of a percentage, the number that makes up the percent has to be divided by 100. However, since it is division by a power of 10, we can accomplish the same thing, by moving the decimal point 2 places to the left, thus making the number smaller. For this problem, that looks like this:

A face card constitutes a Jack, Queen, or King, and there are twelve in a deck, so the probability of drawing a face card is .

There are thirteen spades in the deck, so the probability of drawing a spade is .

Keep in mind that there are also three cards that fit into both categories: the Jack, Queen, and King of Spades; the probability of drawing one is

Thus the probability of drawing a face card or a spade is:

Although we have different bases, we know that .

Therefore,

.

Finally, we factor out to get

.

Least common multiple is the smallest number that is divisible by two or more factors. Since are prime numbers and can't be broken down to smaller factors, we just multiply them to get as our answer.

When multplying exponents, we need to make sure we have the same base.

Since we do, all we have to do is add the exponents.

The answer is .

Rewrite all three fractions in terms of their least common denominator, which is :

;

remains as is;

The sequence begins

Subtract the first term from the second term to get the common difference :

Setting and ,

If this common difference is added a few more times, a pattern emerges:

...

All of the denominators end in 4 or 9, so none of them can be divisible by 20. Therefore, none of the terms will be integers.

When adding exponents, you want to factor out to make solving the question easier.

We can factor out to get

.

Now we can add exponents and therefore our answer is

.

The formula for of interior angles based on a polygon with a number of side n is:

Each Interior Angle = (n-2)*180/n

= (7-2)*180/7 = 128.57 degrees

AB = 10 ’

BC = AC – AB = 25’ – 10’ = 15’

CD = 2 * AB = 2 * 10’ = 20 ’

AD = AB + BC + CD = 10’ + 15’ + 20’ = 45’