Welcome back.
We're on problem number 15.
And I've tried it as best as I can to draw it.
And they're pretty much saying-- well, I'll read it--
Doug's biology experiment involving timing 12
hamsters in a maze.
Each hamster received at least one practice
before being timed.
The scatter plot above shows the time each hamster took to
complete the maze and the corresponding number of
practices that each hamster received.
Based on the data, which of the following functions best
models the relationship between t, the number of
seconds to complete the maze-- this is the t-axis-- and p,
the number of practices?
This is p, the number of practices.
So we want to find t as a function of p.
So t is a function of p.
So, one, it looks like the hamsters didn't learn much
when they got practice.
No matter how much practice they got, the hamsters, it
looks like they roughly took about the same amount of time.
We could try to draw a line here that fits this curve.
Maybe it would look something like this.
I don't know, something like that.
I mean, it's not going to be-- you could try to be cute and
try to draw something maybe with a little bit of a slope
or anything, but I mean, really, this looks like a flat
line when you look at it.
So what would be the equation of that line?
Well, the equation of that line would be
like 45 or 44 or something.
So if you said t of p is equal to-- and actually, they have a
choice that looks just like that-- t of p is equal to 44.
No matter how many practices the mice got, regardless of
how many, they on average take roughly 44 seconds.
So practice doesn't really help mice much, as opposed to
students preparing for the SAT.
And all of the other ones don't make any sense.
I mean, t of p equals p.
That would be something like this.
Choice A is something like that, that has no sense.
No, sorry, choice A is our answer.
Choice B looks something like that.
Choice C, 44p.
That will be even a super steep.
That makes no sense.
P/44, that's going to be like a really shallow graph.
And then you could have p plus 44.
That would start here and then have a slope of 1, so it would
look like that.
So none of the other ones are even close.
So it's definitely choice A.
t of p is equal to 44.
Last problem.
And I'll do a new color.
Problem 16.
And they drew this thing, so I have a big square.
And then we have a square like that.
Actually, I should just use the line tool,
that would be better.
A square like that.
And then I have a square like that, roughly.
It's not perfectly drawn because these three squares
look the same, and they tell us they're the same.
They tell us that this is W.
And this is L.
W, W, W.
L, L.
The pattern shown above is composed of rectangles.
This pattern is used repeatedly to completely cover
a rectangular region 12 units long and 11 units wide.
So they're covering a region that's 12L long and 10L wide.
So this is like a thumbnail of the floor.
How many rectangles of dimension L by W are needed?
OK.
Well, when they say how many rectangles of dimension L by
W, that's just each of these rectangles
that they drew here.
Right?
Because all of these have dimensions L by W, L by W, L
by W, L by W, L by W, right?
So if we could figure out just how many of these-- this
pattern has 1, 2, 3, 4, 5 of those on it, right?
So if we could just figure out how many of this pattern would
fit onto this, then we're done.
So how can we figure that out?
So do we know a relationship between L and W?
Well, sure.
We see here that two L's are the same thing as three W's.
We know that 2L is equal to three W's.
And since all our dimensions are given in L, let's solve
for W and substitute.
So let's say that W is equal to-- just divide both sides by
3-- W is equal to 2/3 L.
All I said is 2L is the same thing as 3W and I
divided it by 3.
So W is equal to 2/3 L.
So can we represent the height and the width of this
rectangle now in terms of only L's?
Well, sure.
What's the height?
What's the length of this rectangle?
Well, the length is definitely just 2L, right?
L plus L.
That's the length.
And what's the width?
Well, W is what?
It's 2/3 L plus L, so what's the width of this rectangle?
What's 2/3 of something plus 1 whole of that something?
Or 2/3 plus 3/3?
So the width is 5/3 L.
So each of these rectangles is 5/3 L by 2L.
So how many of these rectangles are we going to
have to put onto this floor?
How many total?
Well, going in this dimension they have a length of 2L.
So if we have to-- if they're 2L each, then we're going to
need six of them, right?
We're going to need 6 in this direction.
Because we're going to go a total distance of 12L, and
they're 2L each.
So they're going to be 6 in that direction.
And how many are we going to need in this direction?
Well, we have to go a total distance of 10L.
And the width of each of them is 5/3 L.
So what's 10 divided by 5/3?
So the L's cancel out.
So 10 divided by 5/3 is the same thing as 10 times 3/5.
And that just equals 6.
So we're going to need 6 rectangles in this
direction as well.
So how many total rectangles are we going to need?
Well, 6 times 6 is equal to 36 total rectangles.
And then, how many of these smaller rectangles
are in each of these?
We'll need 36 of this pattern.
And then how many of the
rectangles are in that pattern?
Well, we counted.
There's 5.
So we're going to need 5 times 36 total of these smaller
rectangles.
So 5 times 36 is what?
150 plus 30?
It's 180.
We will need 180 of these smaller rectangles.
So that is choice E.
And we are done with this test three.
I'll see you in test four.