There is no way A can influence E if we know C.

The correct answer is 14 5 or 2 and 4 5.

So that is f of b, right there.

No, that doesn't make sense either.

So here's how this chart will look like,

And then, 54 minus 5 that is 49, and we're done.

And you can multiply it out, in case you're not sure.

Well, phi is equal to A over B, which is equal to A plus B over A we know that A plus B over A is the same thing as

And now, let me play a trick on you.

So this is equal to s a times the Laplace transform of sine of a t.

And remember I said 50 minutes was 5 6 of an hour, so the minutes it takes is a, that a, minus this.

So this path takes her a hours to travel.

So it takes her a hours.

It looks something like that.

Here's one regular expression that captures all the ones on the left and none of the ones on the right.

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First there's a bunch of logic to say that it should be the case that say the a red, a green, and a yellow variables, one of them should be true.

So let's do that, and then we'll confirm that it really is the inverse.

So the intuition is that this is going to be 2x times you know, plus something.

Thrun And the answer for this one is really interesting.

Well, here we have two numbers that add up let's say that a is equal to fj.

Let's call our function gcd. It takes 2 inputst that are integers a and b.

I just have to add the exponents cause I have the same base and I'm taking the product, that's going to be a to the eighth power, and I still have this three out front.

Here I've redrawn our finite state machine for a 1 , and we said before that we were going to make the edges a mapping or a dictionary.

So let me ask you for this relatively complicated Bayes network the following questions.

We can do that with one return statement.

Whereas in contrast, if I use the equals sign and I write A B, then this is a truth assertion.

Now, I haven't shown you how to do something like a , but remember that a is just a a .

All right, next we have a bit of a trick question I'm importing the regular expression library and then I'm calling re.findall on the regular expression a z

A to the fifth literally means a times a times a times a times a.

So this was the situation.

So if we go from a to the first, which is just a, and divide by a, right, so we're just going to go we're just going to divide it by a.

So that gets us to this. x to the 1 power, right?

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What's a to the one? a to the one, we said, was a, and then to get to a squared, what did we do?

So that means that f of x has to be less than positive a or greater than negative a.

So the positive exponents, so you have a to the one, a squared, a cubed, a to the fourth.

And what do we get?

You have to choose either option A or option B. (Laughter)

I said that, because I need a lot of space for what I plan to do.

lot where they say the probability sometimes it's written as probability of a.

That means that the absolute value of f of x, or f of x has to be less than a away from 0.

We're going to reserve a proof for it for an algebra class that you might take in college or in high school.

If I do something to one side of the equation, I have to do it to the other.

Then we want the result to be the value of a that's the bigger one.