Oof... you will need 46,656 to get all 6 prizes .... Throw a die.
Each number on the die depicts one of the 6 prizes.
The number of times you throw describes the number of boxes.
Answer:

Step-by-step explanation:
Both expressions are examples of the <em>distributive property</em>, which basically says "if I have <em>this </em>many groups of some size and <em>that</em> many groups of the same size, I've got <em>this </em>+ <em>that</em> groups of that size altogether."
To give an example, if I've got <em>3 groups of 5 </em>and <em>2 groups of 5</em>, I've got 3 + 2 = <em>5 groups of 5 </em>in total. I've attached a visual from Math with Bad Drawings to illustrate this idea.
Mathematically, we'd capture that last example with the equation
. We can also read that in reverse: 3 + 2 groups of 5 is the same as adding together 3 groups of 5 and 2 groups of 5; both directions get us 8 groups of 5. We can use this fact to rewrite the first expression like this:
.
This idea extends to subtraction too: If we have 3 groups of 4 and we take away 1 group of 4, we'd expect to be left with 3 - 1 = 2 groups of 4, or in symbols:
. When we start with two numbers like 15 and 10, our first question should be if we can split them up into groups of the same size. Obviously, you could make 15 groups of 1 and 10 groups of 1, but 15 is also the same as <em>3 groups of 5</em> and 10 is the same as <em>2 groups of 5</em>. Using the distributive property, we could write this as
, so we can say that
.
Answer:
2x + 3y = 12 Is the standard form for linear equations. To determine the slope, solve the equation for y in order to convert to the slope - intercept from7 y = mx + b where is m the slop and b is the y - intercept.
2x + 3y = 12
subtract 2x from both sides.
3y = -2x + 12
Divide both sides by 3.
y= - 2/3 x + 12/3 =
y= - 2/3x + 4
The slope is - 2/3
Answer:
11 and 33
Step-by-step explanation:
The the smaller number be
. Since the other number is 3 times as large as the other, we can represent the large number as
. Because they add up to 44, we have the following equation:

Combine like terms:

Divide both sides by 4:

Substitute
into
to find the larger number:

Therefore, the two numbers are 11 and 33.
Answer: 44.4
Step-by-step explanation:
We are asked to find angle V, so we are going to use our trig ratios to explain this one. They have given us the side opposite of angle v and the hypotunse. angle v. so we are going to be using sine. . SOHCAHTOA.
First, let use the ratio for sine
which equal to 
then we are to take the arcsine or the sine inverse because we are trying to the angle measure not side length. (
(7/10) which gives us 44.4