00:03
All right.
00:06
So, let's start by reading the question.
00:09
An experimenter is studying the effects of temperature pressure and a type of catalyst on yield from a chemical reaction.
00:18
Three different temperatures, four different pressures, and five different catalysts are under consideration.
00:23
So let's do this first.
00:26
We'll have t equals three, because we have three different temperatures.
00:31
Of p equals four for pressure and c equals five for catalysts all right so that's the information that's been given so far now for a it says for any particular experimental run it involves a single temperature pressure and catalysts so how many experimental runs are possible in total so how many total experimental runs can we run with this number of each thing well an easier way for me to explain this is going to be with well let's say we wanted the total experimental runs between three and four right so we have temperature one two and three and we have pressure one two three and four right and so for the first pressure i'm sorry first temperature on the left here we need to test one two three four different pressures with just that one temperature and so you can see same with the second one you can see one two three four and all these dots that i'm putting on are the same as one experimental run right so you have to one run one experimental run with the first temperature the first pressure first temperature second first temperature third, fourth, and then same with the second, same with the third.
02:10
And so what you end up seeing is that it ends up just being three times four, or four times three, whichever one you want to do.
02:16
That's how many of these dots you end up with, or that's how many experimental runs you end up with.
02:21
So instead of this, what i can write, let's all out of here.
02:31
Instead of that, i can write n is what i'm going to call number of experimental runs equals t times p times c right because all we're doing is then if we're taking that same idea of the temperatures and pressures all we're doing is adding a third variable right or a third way to test all of them and so you just take all the possibles here and you multiply it by five in this case to get that's how you add on the third variable you just also multiply that so it ends up being three times 4 times 5, which is equal to 60.
03:23
So that is our answer for a.
03:29
Got to write that out front.
03:32
Now we can scroll down here and focus on b.
03:40
So question b asks, how many experimental runs involve the use of the lowest temperature and the two lowest pressures, right? so out of this 60, how many only involve the very lowest pressure, or sorry, temperature, and the two lowest pressures.
04:00
Well, another way to write this is, well, let's just change our tp and c values, right? if we're only concerned about our t values, or one t value, sorry, we can just say t equals 1, p equals lowest two, p values, that's only going to be two, and c, it's going to be five.
04:25
And using our same equation that we got up here, we can write n equals 1 times 2 times 5 equals 10.
04:40
So out of those 60, 10 experimental runs use the lowest temperature and the two lowest pressures.
04:52
So that's using the same principles up here...