A cheese shop carries a large stock of 34 kinds of cheese. By the end of the day, 48 cheese sales have been made, and the items sold must be restocked. How many different restocking orders are Possible?

Solution:

1. 48 cheese sales have been made
2. The first sale could have been one of 34 different types of cheese
3. The second sale could also have been one of 34 different types of cheese etc.
4. The 48^th sale could also have been one of 34 different types of cheese
5. Each sale is independent of every other sale, so each event increases the number of possible restocking orders by a factor of 34
6. Therefore, the number of possible restocking orders = 34⁴⁸

Factor the following expression: x^2-9

Solution:

First recognize that this is in the form of (x²-a²), which can always be factored as (x+a)(x-a). If you multiply these two terms, you get x²-ax+ax-a², which is equal to x²-a².

So in this case, we can see that a=3,

so  x²-9

=  x²-3²

= (x+3)(x-3)

How do I rewrite an equation using function rotation?

Solution:

A function is a type of relation, i.e. it relates one set of numbers to another. The function (call it “f”) takes any member of one set (call it “x”) and connects it to a unique member of another set. Symbolically, we write this unique member of the other set as f(x). You can say “f of x” when you see this rotation.

Now, we can write the function as a rule or equation. For example, f(x) = 2x. In this example, each value of x as assigned double its value by the function f.

Simplify : 12 – ( x + 3 ) +10

Solution:

You can simply 12 – ( x + 3 ) +10 by rearranging the terms:

1. 12 –x -3 +10
2. 19-x

Cara made some cookies for her math club bake sale. She sold 3/5 of them in the morning and 1/4 of the remaining cookies in the afternoon. If she sold 200 more cookies in the morning than in the afternoon, how many cookies did she make?

Solution:

1. Let’s call the number of cookies Cara made “x”
2. First she sold three fifths of x(.6x)
3. The remaining amount is two fifths of x(.4x)
4. Then she one fourth of x;two fifths of “x” (.25*.4x = .1x)
5. .6x=.1x+200
6. .5x=200
7. x= 400

I need to know how to do problems like this, I Want to know how to solve, and simplify them, and also finding slopes. Like these kinds of problems (Write the equation, 3x + 5y = 15, in the slope intercept form (y = mx + b))

Here’s how you solve this type of question:

1. Start with an equation like 3x + 5y = 15
2. Move 3x to the other side, so 5y = 15 – 3x
3. Divide both sides by 5, so y = 3 – x
4. Another way of writing this is y = -.6x + 3, or y=mx = b, where m=-0.6 and b = 3
5. If m = -0.6, that means that the slope =-0.6



If 2(x-5)=-11, then x=?

Solution:

• 2(x – 5) = -11
• 2x – 10 = -11
• 2x = -1
• x = -0.5

Determine the next two values in the following pattern of numbers: 1, 4, 9, 61, 52, 63, 94, ___, ___ .

Solution:

This is a well known “trick question”. It’s simply a series of squares with the digits reversed:

1² = 1   => 1

2² = 4   => 4

3² = 9   => 9

4² = 16 => 61

5² = 25 => 52

6² = 36 => 63

7² = 49 => 94

8² = 64 => 46

9² = 81 => 18

How do you find the area of a base on a 3-D rectangle?

Here’s how you solve this type of question:

1. The base of the 3D rectangle is in the shape of a 2D rectangle.
2. Multiply the length of this 2D rectangle by its width to let the area

What is mean?

Solution:

The arithmetic mean is the average.

http://en.wikipedia.org/wiki/Arithmetic_mean