DeSTrOYer303

Is there 20 arrangements if a is 10? 

I did get 715 for the first part, and I did not have trouble with that. For part b, I just don't know whether to approach this problem with casework or some sort of counting technique like stars and bars. One of the hints for part b was to approach the problem by designating variables.

I checked the answer to that question and the answerer did not consider 0 as a valid digit, therefore all of his/her answers were based off of 12 instead of 13.

lol I was the guest who posted above you :D

The probability that a cube has exactly two painted faces is 1/16. This is because if two adjacent sides are colored, then only the 4 cubes along the edge of those two sides are painted twice. 4/64 is 1/16.

The probability that a cube has no painted faces is 9/16. This is because if two adjacent sides are painted, then a total of 16 + 12= 28 cubes are painted on at least one side. We can also see this by subtracting 4 (the cubes overlapping) from 32 total cubes on two faces.

We multiply these two probabilities together because they are dependent events to get 9/256

First, let's start by creating a system of linear equations to solve. We know that both numbers added together equal 30, so we can write the equation x+y=30. [x and y represent our two numbers] 

Now, for our second equation, we look at the second sentence of the problem. If x is doubled and we subtract (3y) we get 5. This can be written as 2x-3y=5.

To solve this equation, we will use substitution. We can move x to the other side of the equals sign in the first equation to get y= -x + 30.

This can be substituted into the second equasion as 2x - 3(-x+30)=5.

If simplified, this leads to 5x-90=5. If we bring 90 to the other side of the equals sign by adding 90 to both sides, we get 5x=95 or x=19. 

Since x= 19, 30-19 = y. This means that y=11. The difference between 19 and 11 is 8.

The second statement is the better statement. People can disagree with the second thesis statement logically by arguing that city council members should rule indefinitely. Also, the first rule is a caustic opinion that is not very formal.

1. Fact.

2. Opinion

3. Fact

4. Fact

5. Opinion

6. Fact

7. Fact. 

8. Opinion

9. Opinion

10. Opinion

If a sentence refers to how someone feels about a topic, then it's an opinion.

Hope this helps :)

Just like CalTheGreat said, the graph of that equation would be exponential, not linear. Therefore it is D, nonlinear.

I looked at desmos and I don't think that there is a standard format linear equation modeled by these points. Maybe they want an exponential function?