SAT Prep: Test 2 Section 6 Part 2

WEBVTT
Kind: captions
Language: en

00:00:00.670 --> 00:00:02.990
I think I rushed the end of that
problem just to finish in

00:00:02.990 --> 00:00:05.980
the 10-minute YouTube
time limit.

00:00:05.980 --> 00:00:07.690
And I just want to make sure you
understand because I did

00:00:07.690 --> 00:00:08.850
it all over the place.

00:00:08.850 --> 00:00:12.460
We said, white to
brown is 2:3.

00:00:12.460 --> 00:00:18.510
And then white is equal to
2/3 times the brown.

00:00:18.510 --> 00:00:22.420
And we also said, well the total
number of baskets is

00:00:22.420 --> 00:00:23.770
white plus brown.

00:00:23.770 --> 00:00:26.230
White is 2/3 of the
number of brown.

00:00:26.230 --> 00:00:31.780
So 2/3 brown plus 3/3 brown,
or 1 brown, that equals 5/3

00:00:31.780 --> 00:00:35.300
brown is equal to the total.

00:00:35.300 --> 00:00:40.760
Or we can multiply both sides of
this times 3/5 and say that

00:00:40.760 --> 00:00:45.490
the brown is equal to
the total times 3/5.

00:00:45.490 --> 00:00:48.010
And since we can't have a
fractional number of brown

00:00:48.010 --> 00:00:52.210
eggs, the total has to
be divisible by 5.

00:00:52.210 --> 00:00:54.480
And if you look at the choices,
the only number

00:00:54.480 --> 00:00:57.450
that's not divisible by
5, is choice B, is 12.

00:00:57.450 --> 00:00:59.460
All the other choices are
divisible by 5, so they could

00:00:59.460 --> 00:01:03.060
have been possible choices.

00:01:03.060 --> 00:01:04.849
Let's move on to the next.

00:01:09.390 --> 00:01:13.080
And I will do it in green.

00:01:13.080 --> 00:01:15.740
Seven.

00:01:15.740 --> 00:01:24.850
If 18 root 18, 18 times the
square root of 18 is equal to

00:01:24.850 --> 00:01:32.050
r times the square root of t,
where r and t are positive

00:01:32.050 --> 00:01:37.230
integers-- and we also know
that r is greater than t--

00:01:37.230 --> 00:01:44.150
which of the following can be
the value of r times t?

00:01:47.700 --> 00:01:48.550
So this is is interesting.

00:01:48.550 --> 00:01:55.020
r can't equal t, otherwise
they would both be 18.

00:01:55.020 --> 00:01:59.850
But one interesting thing
that we can try doing.

00:01:59.850 --> 00:02:03.460
Well actually I'm not going to
do it that way, because I

00:02:03.460 --> 00:02:06.810
realize that might be a long
way of doing this problem.

00:02:06.810 --> 00:02:08.949
Let's see, how can we think
about this problem?

00:02:08.949 --> 00:02:11.320
Well, we know that r and t are
positive integers, so what

00:02:11.320 --> 00:02:13.730
could r and t be?

00:02:13.730 --> 00:02:16.330
18 root 18.

00:02:16.330 --> 00:02:18.720
So we could factor this more.

00:02:18.720 --> 00:02:21.360
We could say that this is
the same thing as 18

00:02:21.360 --> 00:02:25.710
times 9 times 2.

00:02:25.710 --> 00:02:28.370
In which case, this is
the same thing as 18.

00:02:28.370 --> 00:02:33.770
The square root of 9 is 3
times 3 times root 2.

00:02:33.770 --> 00:02:36.010
What's 3 times 18?

00:02:36.010 --> 00:02:39.250
That's 54 root 2.

00:02:39.250 --> 00:02:41.830
So this would satisfy
this format.

00:02:41.830 --> 00:02:49.420
So we could say r is 54
and t is 2, in which

00:02:49.420 --> 00:02:51.770
case rt would be 108.

00:02:51.770 --> 00:02:53.640
Let's see if that's a choice.

00:02:53.640 --> 00:02:56.710
And it's a choice, so we're
done, because that could be

00:02:56.710 --> 00:02:59.510
the value of rt.

00:02:59.510 --> 00:03:00.570
Maybe I just stumbled on it.

00:03:00.570 --> 00:03:01.880
I don't know if there's
other choices.

00:03:01.880 --> 00:03:03.370
I won't think too
hard about it.

00:03:03.370 --> 00:03:04.190
But that's the answer.

00:03:04.190 --> 00:03:07.750
I just simplified this a little
bit and I said 18 root

00:03:07.750 --> 00:03:10.220
18 is the same thing
is 54 root 2.

00:03:10.220 --> 00:03:12.060
And so r is 54, t is 2.

00:03:12.060 --> 00:03:16.030
If you multiply them, you get
a 108 and that was choice C.

00:03:16.030 --> 00:03:23.100
Problem number 8, which
I will do in yellow.

00:03:23.100 --> 00:03:24.870
Problem number 8.

00:03:24.870 --> 00:03:30.400
Fancy graph drawn there,
not a graph, a drawing.

00:03:30.400 --> 00:03:32.440
See the triangle,
that's one side.

00:03:35.452 --> 00:03:36.702
That's one side.

00:03:39.800 --> 00:03:41.290
One side.

00:03:41.290 --> 00:03:45.250
Then we have another triangle
inside this triangle.

00:03:45.250 --> 00:03:46.500
Just a triangle.

00:03:51.420 --> 00:03:54.080
Another triangle inside that
triangle and see what they

00:03:54.080 --> 00:03:56.760
wrote in addition to that.

00:03:56.760 --> 00:04:00.520
So this angle is b.

00:04:00.520 --> 00:04:02.990
This angle is c.

00:04:02.990 --> 00:04:05.820
This angle is a.

00:04:05.820 --> 00:04:08.230
This angle is b.

00:04:08.230 --> 00:04:13.160
This is b, and this is a.

00:04:13.160 --> 00:04:16.769
And they want to know, in the
figure above what is the value

00:04:16.769 --> 00:04:21.579
of c in terms of a and b?

00:04:21.579 --> 00:04:24.530
If you've watched my geometry
videos, this to me is the

00:04:24.530 --> 00:04:27.450
angle game because we're just
going to try to figure out as

00:04:27.450 --> 00:04:28.520
many angles as we can.

00:04:28.520 --> 00:04:30.430
And then eventually we'll
hopefully be able to figure

00:04:30.430 --> 00:04:33.260
out what c is.

00:04:33.260 --> 00:04:37.080
So we know this is b, this is
b, and all of these combined

00:04:37.080 --> 00:04:40.200
form this supplementary
angle 180.

00:04:40.200 --> 00:04:45.890
So we know that this angle
right here is 180 minus b

00:04:45.890 --> 00:04:47.420
minus b, so it's minus 2b.

00:04:50.300 --> 00:04:54.980
That's this angle right there
and then what's this angle

00:04:54.980 --> 00:04:56.600
right here?

00:04:56.600 --> 00:04:57.990
What's this angle?

00:04:57.990 --> 00:05:03.560
Well, this angle is 180.

00:05:03.560 --> 00:05:05.530
Well now does that help us?

00:05:05.530 --> 00:05:09.420
Is that going to help me
with this problem?

00:05:09.420 --> 00:05:13.370
This is 180 minus a minus c.

00:05:13.370 --> 00:05:15.500
I don't think that helps
us necessarily.

00:05:15.500 --> 00:05:20.390
This angle right here,
is going to be 180

00:05:20.390 --> 00:05:22.570
minus a minus b.

00:05:25.290 --> 00:05:26.810
I should have drawn
this bigger.

00:05:26.810 --> 00:05:29.120
This angle right here is also--
because we have this

00:05:29.120 --> 00:05:30.280
inner triangle right here.

00:05:30.280 --> 00:05:39.470
That also is going to be
180 minus a minus b.

00:05:39.470 --> 00:05:43.240
This angle here is going to be
180 minus this angle minus

00:05:43.240 --> 00:05:45.030
this angle.

00:05:45.030 --> 00:05:54.190
So it's 180 minus this angle,
which we figured out was 180

00:05:54.190 --> 00:05:55.460
minus a minus b.

00:05:55.460 --> 00:05:57.160
And we just figured out
that because that was

00:05:57.160 --> 00:05:58.620
part of this triangle.

00:05:58.620 --> 00:06:11.770
So it's 180 minus 180 minus a
minus b minus this angle here,

00:06:11.770 --> 00:06:17.710
which is also 180
minus a minus b.

00:06:17.710 --> 00:06:20.820
I mean it's really minus 2 times
180 minus a minus b.

00:06:20.820 --> 00:06:26.390
And if you simplify that, you'll
get 180 minus-- we have

00:06:26.390 --> 00:06:27.020
this twice.

00:06:27.020 --> 00:06:28.260
You could just simplify this.

00:06:28.260 --> 00:06:34.780
It's 2 times 180 plus
2a plus 2b.

00:06:34.780 --> 00:06:36.300
I skipped a couple of steps.

00:06:36.300 --> 00:06:38.090
Because the negative
distributes, then you have two

00:06:38.090 --> 00:06:40.530
a's and 2 b's.

00:06:40.530 --> 00:06:45.330
Then if we simplify this, we get
180 minus 360, so you get

00:06:45.330 --> 00:06:49.330
2a plus 2b minus 180.

00:06:49.330 --> 00:06:53.970
I just simplified this--
is this angle.

00:06:53.970 --> 00:06:56.120
And then we also know that
this angle that we just

00:06:56.120 --> 00:07:07.640
figured out plus b plus
c is equal to 180.

00:07:07.640 --> 00:07:11.170
So let me move up here, I'm
running out of space.

00:07:11.170 --> 00:07:13.520
So if we want to solve for c--
and I don't like this, this

00:07:13.520 --> 00:07:18.510
purple is too dark-- we just
subtract everything from the

00:07:18.510 --> 00:07:19.760
other side.

00:07:21.560 --> 00:07:28.610
So c is going to be equal
to 180 minus 2a

00:07:28.610 --> 00:07:34.400
minus 2b plus 180.

00:07:34.400 --> 00:07:37.220
Because I'm subtracting this
from the other side or that'll

00:07:37.220 --> 00:07:44.650
make it plus 180
minus b again.

00:07:44.650 --> 00:07:56.230
So if we simplify this, so c is
equal to 360 minus 2a and

00:07:56.230 --> 00:07:59.470
then minus 3b.

00:07:59.470 --> 00:08:01.440
Let's see if that's a choice.

00:08:01.440 --> 00:08:05.340
Choice E is 360 minus
2a minus 3b.

00:08:05.340 --> 00:08:07.020
So I haven't made a silly
error, which I

00:08:07.020 --> 00:08:07.670
thought I had made.

00:08:07.670 --> 00:08:11.210
So you figure out this angle
in terms of a and b.

00:08:11.210 --> 00:08:13.140
You figure out this angle
in terms of a and b.

00:08:13.140 --> 00:08:15.590
Then you figure out this angle
in terms of this angle and

00:08:15.590 --> 00:08:16.650
this angle.

00:08:16.650 --> 00:08:19.690
So you just keep using the
angles of a triangle add up to

00:08:19.690 --> 00:08:24.620
180 property of triangles.

00:08:24.620 --> 00:08:25.960
Go to the next page.

00:08:25.960 --> 00:08:27.390
Oh, and now we're on the
free answer questions.

00:08:35.490 --> 00:08:37.580
All right.

00:08:37.580 --> 00:08:39.020
I think we have time
for this one.

00:08:39.020 --> 00:08:40.289
9.

00:08:40.289 --> 00:08:46.120
They say, t to the third
is equal to 351.

00:08:46.120 --> 00:08:49.140
What is 4t to the third?

00:08:49.140 --> 00:08:50.560
So the slow way of doing
this is to try to

00:08:50.560 --> 00:08:51.890
figure out what t is.

00:08:51.890 --> 00:08:55.090
The fast way is, well, 4t to the
third, if t to the third

00:08:55.090 --> 00:08:58.650
is equal to 351, then 4t to the
third, you just multiply

00:08:58.650 --> 00:09:01.290
both sides times 4.

00:09:01.290 --> 00:09:06.380
And so 351 times 4,
4 times 1 is 4.

00:09:06.380 --> 00:09:08.710
4 times 5 is 20.

00:09:08.710 --> 00:09:10.030
3 times 4 is 12.

00:09:10.030 --> 00:09:11.790
1404.

00:09:11.790 --> 00:09:13.100
That's the answer.

00:09:13.100 --> 00:09:16.090
And I have 40 seconds left, so
I'll wait for the next video.

00:09:16.090 --> 00:09:17.340
See you soon.


SAT Prep: Test 2 Section 6 Part 1

WEBVTT
Kind: captions
Language: en

00:00:00.920 --> 00:00:04.080
All right, let's see,
we're on page 471.

00:00:04.080 --> 00:00:06.670
We'll start with
section 6 now.

00:00:06.670 --> 00:00:11.630
So let's do the first problem,
and I will do it in magenta.

00:00:11.630 --> 00:00:13.620
Problem number one.

00:00:13.620 --> 00:00:22.840
3 plus diamond over 2 is
equal to 7 and 1/2.

00:00:22.840 --> 00:00:25.580
And they say, what number,
when used in the place of

00:00:25.580 --> 00:00:27.870
diamond above, makes
the statement true?

00:00:27.870 --> 00:00:30.320
Well, they're just making the
diamond a variable, right?

00:00:30.320 --> 00:00:34.210
So we could just say 3 plus
x over 2-- [? instead ?]

00:00:34.210 --> 00:00:35.790
of an x instead of the diamond,
because that's what

00:00:35.790 --> 00:00:40.960
we're used to-- is equal to--
well, we could write this as a

00:00:40.960 --> 00:00:42.210
decimal if we want, 7.5.

00:00:44.870 --> 00:00:49.870
Multiply both sides by
2, so you get 3 plus

00:00:49.870 --> 00:00:52.790
x is equal to 15.

00:00:52.790 --> 00:00:55.200
x is equal to 12.

00:00:55.200 --> 00:00:56.360
So that's choice D.

00:00:56.360 --> 00:01:00.380
Or we could say diamond is equal
to x is equal to 12.

00:01:00.380 --> 00:01:03.640
OK, problem number two.

00:01:03.640 --> 00:01:05.010
They have this thing drawn.

00:01:05.010 --> 00:01:06.860
Let me draw what they drew.

00:01:06.860 --> 00:01:08.590
I'll do it in a different
color.

00:01:08.590 --> 00:01:12.840
They have, like, a transversal
here, and then they have one

00:01:12.840 --> 00:01:14.090
line that goes like this.

00:01:16.590 --> 00:01:18.040
And then they have another
line that goes

00:01:18.040 --> 00:01:21.070
something like this.

00:01:21.070 --> 00:01:23.290
And then, let's see, they
wrote a bunch of stuff.

00:01:23.290 --> 00:01:34.500
They wrote, this is angle 1, 2,
3, 4, 5, 6, 7, 8, and these

00:01:34.500 --> 00:01:38.360
are lines l and lines m.

00:01:38.360 --> 00:01:43.115
And they say in the figure
above, l is parallel to m.

00:01:43.115 --> 00:01:46.036
All right, parallel lines.

00:01:46.036 --> 00:01:49.900
If l is parallel to m, the sum
of the measures of angles 2

00:01:49.900 --> 00:01:56.390
and 4 must equal the sum of the
measures of which of the

00:01:56.390 --> 00:01:59.450
following pairs of angles?

00:01:59.450 --> 00:02:01.325
So the sum of 2 and 4.

00:02:05.220 --> 00:02:06.480
And actually, we know
another thing.

00:02:06.480 --> 00:02:09.539
We know that 2 and 4 are equal
to each other, right?

00:02:09.539 --> 00:02:11.505
Because they're opposite
angles.

00:02:11.505 --> 00:02:15.360
But anyway, what angles would
be the same as 2 plus 4?

00:02:15.360 --> 00:02:18.730
Well, we can just do what we
learned in geometry class

00:02:18.730 --> 00:02:19.960
about corresponding angles.

00:02:19.960 --> 00:02:24.770
We know that this angle is the
same thing as this angle.

00:02:24.770 --> 00:02:26.520
And we actually know that that
angle is also the same thing

00:02:26.520 --> 00:02:28.970
as this angle, because
they're opposite.

00:02:28.970 --> 00:02:30.290
And that first one, we know that
they are because they're

00:02:30.290 --> 00:02:32.270
corresponding.

00:02:32.270 --> 00:02:33.670
That angle's the same
as this one.

00:02:33.670 --> 00:02:36.650
So 2 plus 4 should be the
same thing as 6 plus 8.

00:02:36.650 --> 00:02:39.720
And all we used is corresponding
angles to say,

00:02:39.720 --> 00:02:40.870
well, 4 is going to
be the same as 8.

00:02:40.870 --> 00:02:41.930
2 is the same as 6.

00:02:41.930 --> 00:02:43.680
And we also know that 6 and
8 are the same, and 2

00:02:43.680 --> 00:02:45.030
and 4 are the same.

00:02:45.030 --> 00:02:48.820
So it's choice D.

00:02:48.820 --> 00:02:50.645
Problem number three.

00:02:59.080 --> 00:03:00.860
Let me draw this table, because
it looks like we'll

00:03:00.860 --> 00:03:03.260
have to use it.

00:03:03.260 --> 00:03:06.950
So I have a box here and then
we draw four lines.

00:03:19.290 --> 00:03:23.570
All right, soon. almost there.

00:03:23.570 --> 00:03:32.170
And then they say, Men,
Women, Total,

00:03:32.170 --> 00:03:39.490
Employed, Unemployed, Total.

00:03:39.490 --> 00:03:46.320
And they wrote in the numbers
27,000-- those are 0's--

00:03:46.320 --> 00:03:57.590
48,000, 21,500, and 50,500.

00:03:57.590 --> 00:04:01.370
In the table above, describing
the Preston City workforce--

00:04:01.370 --> 00:04:04.360
the table is partially filled
in-- based on the information

00:04:04.360 --> 00:04:07.640
in the table, how many women in
the Preston city workforce

00:04:07.640 --> 00:04:08.310
are unemployed?

00:04:08.310 --> 00:04:12.440
So we want to figure out women
that are unemployed.

00:04:12.440 --> 00:04:13.980
We need to figure
out this box.

00:04:17.190 --> 00:04:18.420
So how do we do that?

00:04:18.420 --> 00:04:21.050
Well, first we can figure out
the women that are employed

00:04:21.050 --> 00:04:24.020
because there's 48,000
workers.

00:04:24.020 --> 00:04:25.990
27,000 are men.

00:04:25.990 --> 00:04:29.745
So we just subtract 27,000 from
48,000, so there's going

00:04:29.745 --> 00:04:34.540
to be 21,000 women.

00:04:34.540 --> 00:04:38.090
And then if there's 21,000
women-- I just subtracted--

00:04:38.090 --> 00:04:43.270
and-- no, sorry, there's 21,000
employed women, because

00:04:43.270 --> 00:04:45.140
we're in the Employed column--
and there are

00:04:45.140 --> 00:04:47.500
21,500 total women.

00:04:47.500 --> 00:04:49.380
Well, then we just
subtract again.

00:04:49.380 --> 00:04:52.960
21,500 minus 21,000.

00:04:52.960 --> 00:04:58.610
There must be 500 unemployed
women in Preston City, and

00:04:58.610 --> 00:05:01.210
that's choice A.

00:05:01.210 --> 00:05:02.830
OK, problem number four.

00:05:02.830 --> 00:05:04.900
And I will switch from
this kind of

00:05:04.900 --> 00:05:07.320
nauseating color, I think.

00:05:12.540 --> 00:05:16.370
A group of students washed
cars to raise money.

00:05:16.370 --> 00:05:24.230
The net amount, A, in dollars
raised by washing k cars, is

00:05:24.230 --> 00:05:27.750
given by the function-- oh,
well, they tell us, A of k.

00:05:27.750 --> 00:05:32.310
So this is how much you've made
after washing k cars, is

00:05:32.310 --> 00:05:36.580
4k minus 30.

00:05:36.580 --> 00:05:39.980
If the group washed 15
cars, what is the

00:05:39.980 --> 00:05:43.300
net amount they raised?

00:05:43.300 --> 00:05:46.000
Well, this seems unbelievably
easy, because they tell you

00:05:46.000 --> 00:05:57.800
that k is 15, so A of 15 is
equal to 4 times 15, minus 30.

00:05:57.800 --> 00:06:01.000
4 times 15 is 60, minus 30.

00:06:01.000 --> 00:06:02.410
That just equals 30.

00:06:02.410 --> 00:06:04.200
They raised $30.

00:06:04.200 --> 00:06:06.860
That's choice E.

00:06:06.860 --> 00:06:08.560
If I was taking the SAT, I would
have paused, just to

00:06:08.560 --> 00:06:10.060
make sure I didn't
miss something.

00:06:10.060 --> 00:06:11.240
I'm actually pausing
now to make sure I

00:06:11.240 --> 00:06:11.950
didn't miss a trick.

00:06:11.950 --> 00:06:12.810
But I think that's it.

00:06:12.810 --> 00:06:16.250
That's kind of one of those
freebie quick questions.

00:06:16.250 --> 00:06:18.802
OK, problem number five.

00:06:18.802 --> 00:06:22.110
And I'll switch colors
for variety.

00:06:22.110 --> 00:06:35.650
If xr is equal to v, and v is
equal to kr, and we also know

00:06:35.650 --> 00:06:39.010
that rv does not equal 0,
which also tells us that

00:06:39.010 --> 00:06:41.560
neither you of these numbers
can equal 0, which of the

00:06:41.560 --> 00:06:43.740
following is equal to k?

00:06:43.740 --> 00:06:47.710
And all of the choices have
just x's and some numbers.

00:06:47.710 --> 00:06:52.016
So we want to write
k in terms of x.

00:06:52.016 --> 00:06:55.006
So xr is equal to v, and
v is equal to kr.

00:07:01.790 --> 00:07:09.190
So we know that xr is equal to
kr, and since we know that r

00:07:09.190 --> 00:07:13.990
does not equal 0, we can divide
both sides of this

00:07:13.990 --> 00:07:16.285
equation by r and
they cancel out.

00:07:16.285 --> 00:07:20.060
And we get x is equal to
k, or k is equal to x.

00:07:20.060 --> 00:07:23.080
So that is choice D.

00:07:23.080 --> 00:07:25.690
Well, they're giving us a lot
of quick problems, but I

00:07:25.690 --> 00:07:26.150
that's good.

00:07:26.150 --> 00:07:29.300
I can fit a lot into
one video.

00:07:29.300 --> 00:07:30.550
OK, problem number six.

00:07:33.000 --> 00:07:37.780
The eggs in a certain basket
are either white or brown.

00:07:37.780 --> 00:07:42.690
If the ratio of white eggs to
brown eggs-- I should probably

00:07:42.690 --> 00:07:46.410
do it in those colors, but I'm
not to confuse you-- the ratio

00:07:46.410 --> 00:07:53.190
of white to brown is
equal to 2 over 3.

00:07:53.190 --> 00:07:56.670
Each of the following could be
the number of eggs in the

00:07:56.670 --> 00:08:00.440
basket, except-- so this
is a tricky one.

00:08:00.440 --> 00:08:05.150
So the ratio of white to
brown is 2:3, right?

00:08:08.550 --> 00:08:12.025
White to brown is equal
to 2 over 3.

00:08:12.025 --> 00:08:18.740
Or another way we could say it
is, white is equal to 2/3

00:08:18.740 --> 00:08:22.790
times the brown eggs.

00:08:22.790 --> 00:08:26.590
And so the total eggs in the
basket are going to be white

00:08:26.590 --> 00:08:27.840
plus brown.

00:08:30.590 --> 00:08:36.714
And so we could write, this w,
it as 2/3 of the number of

00:08:36.714 --> 00:08:38.590
brown eggs is the white eggs--
that's what we figured out

00:08:38.590 --> 00:08:42.030
here-- plus the brown eggs.

00:08:42.030 --> 00:08:44.720
So the total number of baskets
is-- let's see, what's 2/3

00:08:44.720 --> 00:08:48.140
plus-- 1 is the same thing
is 3/3, right?

00:08:48.140 --> 00:08:50.680
The total number of baskets
is 5/3 times the

00:08:50.680 --> 00:08:51.930
number of brown eggs.

00:08:54.730 --> 00:08:57.540
We know we can't have a
fractional number of eggs, so

00:08:57.540 --> 00:09:00.065
we know that this has to
be a whole number.

00:09:08.120 --> 00:09:13.420
If we said 5/3B, this is the
first choice is equal to 10,

00:09:13.420 --> 00:09:15.290
could that be a choice?

00:09:15.290 --> 00:09:22.370
Let's see, B would have to be
3/5 times 10, which would be--

00:09:22.370 --> 00:09:26.330
this cancels out-- that
works, right?

00:09:26.330 --> 00:09:29.270
Because then B would be
6, so that could work.

00:09:32.200 --> 00:09:35.250
Well, I think we already
know, right?

00:09:35.250 --> 00:09:38.790
The total number of baskets
has to be divisible by 5.

00:09:38.790 --> 00:09:44.660
Because B is equal to the total
number times 3 over 5.

00:09:44.660 --> 00:09:48.010
I just used this equation, 5/3B
is equal to the total.

00:09:48.010 --> 00:09:48.980
Multiply both sides
[? by the ?]

00:09:48.980 --> 00:09:50.230
reciprocal, you get this.

00:09:50.230 --> 00:09:55.630
And the only choice that's not
divisible by 5 is choice B.

00:09:55.630 --> 00:09:57.980
Hope I didn't rush it, but I had
to finish under the wire.

00:09:57.980 --> 00:09:59.420
I'll see


SAT Prep: Test 2 Section 6 Part 3

WEBVTT
Kind: captions
Language: en

00:00:00.750 --> 00:00:01.460
Welcome back.

00:00:01.460 --> 00:00:07.040
We are on problem number 10.

00:00:07.040 --> 00:00:09.420
I'm trying to do as many
problems as possible, because

00:00:09.420 --> 00:00:09.935
today is Thanksgiving.

00:00:09.935 --> 00:00:12.750
And I want to build up an
appetite to really take down

00:00:12.750 --> 00:00:14.650
that turkey.

00:00:14.650 --> 00:00:18.130
Anyway, they say, what is the
coordinate of the point on a

00:00:18.130 --> 00:00:22.140
number line that is exactly
halfway between the points

00:00:22.140 --> 00:00:26.800
with coordinates 53 and 62?

00:00:26.800 --> 00:00:28.840
So the point that's halfway
between those two is just

00:00:28.840 --> 00:00:30.980
going to be the average
of these two points.

00:00:30.980 --> 00:00:31.840
So what's the average?

00:00:31.840 --> 00:00:35.910
It's 53 plus 62 over 2.

00:00:35.910 --> 00:00:37.590
And that's what?

00:00:37.590 --> 00:00:47.460
5 plus 6 is 111,
so it's 115/2.

00:00:47.460 --> 00:00:51.240
That equals 57.5.

00:00:51.240 --> 00:00:52.080
So that's the answer.

00:00:52.080 --> 00:00:53.980
And this is one of those ones
we have to fill it in.

00:00:53.980 --> 00:00:56.350
57.5 is half way between
the two.

00:00:56.350 --> 00:00:57.900
And at first, I was
little taken aback

00:00:57.900 --> 00:00:59.270
because of the decimal.

00:00:59.270 --> 00:01:00.700
I was thinking maybe is an
integer number line.

00:01:00.700 --> 00:01:01.450
But they don't say that.

00:01:01.450 --> 00:01:03.580
So on a regular number line,
you can have decimals.

00:01:03.580 --> 00:01:08.220
So this is the point
that is exactly

00:01:08.220 --> 00:01:09.270
halfway between the two.

00:01:09.270 --> 00:01:11.180
This is the coordinate
of the point.

00:01:11.180 --> 00:01:13.780
Number 11.

00:01:13.780 --> 00:01:16.100
A certain triangle has
two angles that

00:01:16.100 --> 00:01:17.750
have the same measure.

00:01:17.750 --> 00:01:20.730
If the lengths of the two sides
of the triangle are 50

00:01:20.730 --> 00:01:24.610
and 30, what is the least
possible value for the

00:01:24.610 --> 00:01:26.160
perimeter of the triangle?

00:01:26.160 --> 00:01:29.555
All right, so we've
got a triangle.

00:01:33.120 --> 00:01:36.740
And we know that two
of these sides are

00:01:36.740 --> 00:01:38.570
the same angle, right?

00:01:38.570 --> 00:01:41.270
And we know, from geometry, if
the two base angles are the

00:01:41.270 --> 00:01:43.190
same, then that means that these
two sides are going to

00:01:43.190 --> 00:01:44.670
be the same.

00:01:44.670 --> 00:01:49.870
And they tell us that two of
the sides are 50 and 30.

00:01:49.870 --> 00:01:53.610
So either this could be 50
and this could be 30.

00:01:53.610 --> 00:01:55.240
Or this could be 30 and
this could be 50.

00:01:55.240 --> 00:01:56.990
Because this can't
be 50 and 30.

00:01:56.990 --> 00:01:58.470
These have to be
the same thing.

00:01:58.470 --> 00:02:00.080
So we want to know the
least possible

00:02:00.080 --> 00:02:01.590
value of the perimeter.

00:02:01.590 --> 00:02:04.080
So if we want the smallest
possible value for the

00:02:04.080 --> 00:02:07.385
perimeter, we want
more 30 sides and

00:02:07.385 --> 00:02:09.440
less 50 sides, right?

00:02:09.440 --> 00:02:11.810
So why don't we make
this side 30?

00:02:11.810 --> 00:02:13.970
Because then, this side
will be 30, and this

00:02:13.970 --> 00:02:15.600
side will be 50.

00:02:15.600 --> 00:02:18.600
And the other option would
have been to do this.

00:02:18.600 --> 00:02:21.190
50, 50, and 30.

00:02:21.190 --> 00:02:23.010
But clearly, this would have
had a larger perimeter,

00:02:23.010 --> 00:02:24.300
because we would have
used 50 twice

00:02:24.300 --> 00:02:25.790
instead of using 30 twice.

00:02:25.790 --> 00:02:27.170
So this has a smaller
perimeter.

00:02:27.170 --> 00:02:27.860
And what is the perimeter?

00:02:27.860 --> 00:02:29.650
It's 60 plus 50.

00:02:29.650 --> 00:02:32.230
It's 110.

00:02:32.230 --> 00:02:35.920
That is the smallest perimeter
we could have.

00:02:35.920 --> 00:02:37.170
Next problem.

00:02:40.750 --> 00:02:42.310
Problem number 12.

00:02:42.310 --> 00:02:44.695
I don't want to use
the whiteboard.

00:02:44.695 --> 00:02:46.460
There's something psychological
about a

00:02:46.460 --> 00:02:47.020
blackboard, I think.

00:02:47.020 --> 00:02:49.430
It makes it more engaging.

00:02:49.430 --> 00:02:59.380
All right, if x squared minus y
squared is equal to 77, and

00:02:59.380 --> 00:03:04.550
x plus y is equal to 11,
what is the value of x?

00:03:04.550 --> 00:03:06.490
So this is something that some
people-- oh my God, I've got a

00:03:06.490 --> 00:03:07.600
system soon. of equations.

00:03:07.600 --> 00:03:08.650
Or I've got a quadratic.

00:03:08.650 --> 00:03:10.110
What is it?

00:03:10.110 --> 00:03:11.290
All you have to do
is factor this.

00:03:11.290 --> 00:03:12.850
What is x squared
minus y squared?

00:03:12.850 --> 00:03:15.410
Well, a squared minus b
squared is, a plus b

00:03:15.410 --> 00:03:16.410
times a minus b.

00:03:16.410 --> 00:03:20.280
Or, in this case, x squared
minus y squared, that's just x

00:03:20.280 --> 00:03:26.880
plus y times x minus
y is equal to 77.

00:03:26.880 --> 00:03:28.960
And the biggest clue on why you
can do that immediately,

00:03:28.960 --> 00:03:31.770
is that they told you what
x plus y is, right?

00:03:31.770 --> 00:03:33.680
So we know that x
plus y is 11.

00:03:33.680 --> 00:03:39.310
So 11 times x minus
y is equal to 77.

00:03:39.310 --> 00:03:42.776
So now we know, divide
both sides by 11.

00:03:42.776 --> 00:03:47.415
x minus why is equal
to 7, right?

00:03:51.310 --> 00:03:52.490
Now, we have a very

00:03:52.490 --> 00:03:54.040
straightforward system of equations.

00:03:54.040 --> 00:03:55.610
And we want to solve
for x, right?

00:03:55.610 --> 00:03:57.860
So we can let the
y's cancel out.

00:03:57.860 --> 00:04:00.370
Let's take that top one down
here and just rewrite it.

00:04:00.370 --> 00:04:04.250
x plus y is equal to 11.

00:04:04.250 --> 00:04:05.290
Add the two equations.

00:04:05.290 --> 00:04:07.690
x plus x is 2x.

00:04:07.690 --> 00:04:10.500
Minus y plus y is 0.

00:04:10.500 --> 00:04:13.330
y is equal to 18, right?

00:04:13.330 --> 00:04:15.360
7 plus 11 is 18.

00:04:15.360 --> 00:04:17.640
2x is equal to 18.

00:04:17.640 --> 00:04:21.120
x is equal to 9 Done.

00:04:21.120 --> 00:04:22.370
Next problem.

00:04:27.190 --> 00:04:31.595
OK, we are on problem
number 13.

00:04:31.595 --> 00:04:34.500
Tamara cut a circular pizza into
wedge shaped pieces, one

00:04:34.500 --> 00:04:36.030
of which is shown above.

00:04:36.030 --> 00:04:38.010
The tip of each piece is at
the center of the pizza.

00:04:38.010 --> 00:04:40.820
And the angle of the tip is
always greater than 20

00:04:40.820 --> 00:04:43.870
degrees, but less
than 30 degrees.

00:04:43.870 --> 00:04:49.980
OK, what is one possible value
for the number of pieces into

00:04:49.980 --> 00:04:53.120
which the pizza is cut?

00:04:53.120 --> 00:04:55.210
OK, so this is interesting.

00:04:55.210 --> 00:04:59.270
So we have a pizza pie, although
it could just be a

00:04:59.270 --> 00:05:00.730
regular pie.

00:05:00.730 --> 00:05:05.300
And each of her slices
goes to the center.

00:05:13.540 --> 00:05:18.300
And this angle right here--
so let's call it theta.

00:05:18.300 --> 00:05:27.486
It's going to be-- it's greater
than 20 degrees.

00:05:27.486 --> 00:05:31.800
And it's less than 30
degrees, right?

00:05:31.800 --> 00:05:32.760
Well, let me ask a question.

00:05:32.760 --> 00:05:37.520
If theta was 20 degrees,
how many slices

00:05:37.520 --> 00:05:39.950
could she have cut?

00:05:39.950 --> 00:05:42.710
Well, there's 360 degrees
in a circle, right?

00:05:45.430 --> 00:05:50.260
So if every slice is 20
degrees-- Well, 20 goes into

00:05:50.260 --> 00:05:52.930
360 how many times?

00:05:52.930 --> 00:05:55.550
20 goes into 360,
18 times, right?

00:05:55.550 --> 00:05:58.390
2 into 36 goes 18 times.

00:05:58.390 --> 00:06:02.740
So if every slice is 20 degrees,
it'd be 18 slices.

00:06:02.740 --> 00:06:06.490
Similarly, if every slice was
30 degrees-- 30 degrees goes

00:06:06.490 --> 00:06:09.100
into 360, how many times?

00:06:09.100 --> 00:06:10.560
Well, it goes into it 12 times.

00:06:10.560 --> 00:06:12.566
12 slices.

00:06:12.566 --> 00:06:13.060
you

00:06:13.060 --> 00:06:16.760
So we know that the slices
are larger than 20 and

00:06:16.760 --> 00:06:18.090
less than 30, right?

00:06:18.090 --> 00:06:25.080
So the slices are going
to be greater than 12

00:06:25.080 --> 00:06:27.680
and less than 18.

00:06:27.680 --> 00:06:29.860
And so you, literally,
can pick any number.

00:06:29.860 --> 00:06:37.690
The answer could be 13, 14,
15, 16, or 17 slices.

00:06:37.690 --> 00:06:41.520
Any of those numbers would be
a suitably correct answer.

00:06:41.520 --> 00:06:43.120
That sometimes confuses
people, but

00:06:43.120 --> 00:06:43.990
you should be confident.

00:06:43.990 --> 00:06:46.330
Any of these numbers that
you put down will work.

00:06:46.330 --> 00:06:48.140
Maybe you want to put the
middle one just to be

00:06:48.140 --> 00:06:48.570
comfortable.

00:06:48.570 --> 00:06:53.590
I think that would be
a 25 degree slice.

00:06:53.590 --> 00:06:54.840
Next problem.

00:06:58.820 --> 00:07:02.670
14.

00:07:02.670 --> 00:07:09.962
We have this sequence a,
3a, dot, dot, dot.

00:07:09.962 --> 00:07:11.212
[SNEEZES]

00:07:15.160 --> 00:07:17.832
The first term in the
sequence above is a.

00:07:17.832 --> 00:07:20.840
I just went for a hike at a
place called Windy Hill, and

00:07:20.840 --> 00:07:22.980
it was freezing.

00:07:22.980 --> 00:07:25.560
The first term in the sequence
above is a, and each term

00:07:25.560 --> 00:07:29.130
after the first is 3 times
the preceding term.

00:07:29.130 --> 00:07:33.370
If the sum of the first five
terms, is 605, what is the

00:07:33.370 --> 00:07:34.180
value of a?

00:07:34.180 --> 00:07:37.330
So the first five terms-- well,
that's just going to be

00:07:37.330 --> 00:07:45.965
a, 3a, and then the next
one's going to be 9a.

00:07:45.965 --> 00:07:48.336
The next one is going
to be 27a.

00:07:48.336 --> 00:07:50.100
The next one is going
to be 81a, right?

00:07:50.100 --> 00:07:53.920
That's the first five terms.
So you add them all up.

00:07:53.920 --> 00:07:57.430
3 plus 9 is 12.

00:07:57.430 --> 00:07:58.800
This is where I always
mess up.

00:07:58.800 --> 00:08:00.390
3 plus 9 is 12.

00:08:00.390 --> 00:08:04.530
12 plus 27 is 39.

00:08:04.530 --> 00:08:12.960
39 plus 81-- 9 plus 1 is 10.

00:08:12.960 --> 00:08:15.150
And then 1 plus 3 is 120.

00:08:15.150 --> 00:08:17.830
So that equals 120a.

00:08:17.830 --> 00:08:19.690
So these are the first
five terms, right?

00:08:19.690 --> 00:08:22.530
Each one is 3 times
the preceding one.

00:08:22.530 --> 00:08:28.850
And the sum of these
is equal to 605.

00:08:28.850 --> 00:08:31.330
What is the value of a?

00:08:31.330 --> 00:08:36.650
a is equal to 605/120.

00:08:36.650 --> 00:08:38.289
And let's see, can
we simplify this?

00:08:38.289 --> 00:08:47.300
Sure, if we divide the top and
the bottom by five, how many

00:08:47.300 --> 00:08:49.610
times does 5 goes into 120?

00:08:49.610 --> 00:08:52.950
It goes into it 24 times.

00:08:52.950 --> 00:08:55.440
Are these divisible by 3?

00:08:55.440 --> 00:08:56.160
No.

00:08:56.160 --> 00:08:58.170
I think that's in simplest
terms, because you can't

00:08:58.170 --> 00:08:59.960
divide by 2.

00:08:59.960 --> 00:09:02.500
Can't divide by 3.

00:09:02.500 --> 00:09:08.460
121 times 5 is 605.

00:09:08.460 --> 00:09:12.940
So I think that is the simplest
form that you can do

00:09:12.940 --> 00:09:15.130
this problem.

00:09:15.130 --> 00:09:16.100
I'm running out of time.

00:09:16.100 --> 00:09:17.350
So I will wait to
do next the next

00:09:17.350 --> 00:09:18.400
problem in the next video.

00:09:18.400 --> 00:09:19.650
See


SAT Prep: Test 2 Section 6 Part 4

WEBVTT
Kind: captions
Language: en

00:00:00.940 --> 00:00:03.940
I just realized that when I just
did problem number 14, I

00:00:03.940 --> 00:00:06.220
got a weird answer because,
once again, I

00:00:06.220 --> 00:00:08.130
cannot add and multiply.

00:00:08.130 --> 00:00:11.250
But just redoing it just so
you get the right answer.

00:00:11.250 --> 00:00:13.300
Number 14.

00:00:13.300 --> 00:00:18.440
Oh, they give you a,
3a, dot, dot, dot.

00:00:18.440 --> 00:00:22.500
And they say that each term is
3 times the previous term.

00:00:22.500 --> 00:00:26.690
So the next term is going
to be 9a and so forth.

00:00:26.690 --> 00:00:30.710
They say the sum of the first
five terms is 605.

00:00:30.710 --> 00:00:32.670
And so what is a?

00:00:32.670 --> 00:00:34.460
Well, what are the
first five terms?

00:00:34.460 --> 00:00:41.490
It's a, 3a, 9a, 27a-- I'm just
multiplying by 3 every time.

00:00:41.490 --> 00:00:42.880
81a.

00:00:42.880 --> 00:00:46.040
And this is always the part
that I will mess up.

00:00:46.040 --> 00:00:47.270
This is 1a.

00:00:47.270 --> 00:00:48.870
So 1 plus 3 is 4.

00:00:48.870 --> 00:00:51.570
4 plus 9 is 13.

00:00:51.570 --> 00:00:59.550
13 plus 7 is 20, plus 1 is 21.

00:00:59.550 --> 00:01:04.349
And then 4 plus 8, 121a is equal
to-- and they say, it

00:01:04.349 --> 00:01:05.910
equals 605.

00:01:05.910 --> 00:01:09.190
The sum of the first
five terms, 605.

00:01:09.190 --> 00:01:16.370
a is equal to 605/121,
and that is 5.

00:01:16.370 --> 00:01:20.360
Much easier when you
can add properly.

00:01:20.360 --> 00:01:22.150
That's all I had for this video
because I just had to

00:01:22.150 --> 00:01:23.700
correct my mistake.

00:01:23.700 --> 00:01:26.020
See you in the next problem.


SAT Prep: Test 2 Section 6 Part 5

WEBVTT
Kind: captions
Language: en

00:00:00.970 --> 00:00:01.920
Where are we?

00:00:01.920 --> 00:00:10.950
We are on problem 15.

00:00:10.950 --> 00:00:11.220
Let's see.

00:00:11.220 --> 00:00:12.890
They have a bunch of
triangles drawn.

00:00:12.890 --> 00:00:16.550
So let me get the line tool and
see what I can do about

00:00:16.550 --> 00:00:17.380
drawing these.

00:00:17.380 --> 00:00:24.880
I've got a big triangle, looks
something like that.

00:00:24.880 --> 00:00:28.040
It's the big triangle, and
there's this altitude to that

00:00:28.040 --> 00:00:31.790
drops down like that.

00:00:31.790 --> 00:00:34.230
And there's a smaller triangle
within it that looks

00:00:34.230 --> 00:00:35.480
something like this.

00:00:41.545 --> 00:00:46.940
A smaller triangle and then
this is a 90 degree angle

00:00:46.940 --> 00:00:47.410
right here.

00:00:47.410 --> 00:00:49.550
It's perpendicular.

00:00:49.550 --> 00:00:58.220
q, s, p, v.

00:00:58.220 --> 00:00:59.530
Oh my God no, I messed up.

00:01:05.000 --> 00:01:06.370
I should have done this
ahead of time.

00:01:06.370 --> 00:01:08.350
I'm wasting your time.

00:01:08.350 --> 00:01:10.320
Bear with me, I drew
this line wrong.

00:01:10.320 --> 00:01:13.790
This line is something
different.

00:01:13.790 --> 00:01:15.370
That line looks like this.

00:01:21.430 --> 00:01:22.840
All right, now I'm
back in business.

00:01:31.190 --> 00:01:33.220
t and then r.

00:01:33.220 --> 00:01:36.375
It took me almost two minutes
just to draw this thing.

00:01:36.375 --> 00:01:38.810
And it says, note, figure
not drawn to scale.

00:01:38.810 --> 00:01:42.840
It says, in triangle
pqr above, qs over

00:01:42.840 --> 00:01:50.800
qv is equal to 1/3.

00:01:50.800 --> 00:02:02.410
And it says, pt over
pr is equal to 3/4.

00:02:02.410 --> 00:02:04.670
What is the value
of the fraction?

00:02:04.670 --> 00:02:14.890
And they want to know area of
triangle pst over area of

00:02:14.890 --> 00:02:18.150
triangle pqr?

00:02:18.150 --> 00:02:18.680
Now let's see what we can do.

00:02:18.680 --> 00:02:19.910
I haven't been thinking
just yet.

00:02:19.910 --> 00:02:21.680
I've just been drawing
and writing.

00:02:21.680 --> 00:02:30.740
So they say, qs over qv, over
this whole thing, is 1/3.

00:02:30.740 --> 00:02:32.360
Fair enough.

00:02:32.360 --> 00:02:41.180
And they say, pt over
pr is equal to 3/4.

00:02:41.180 --> 00:02:41.690
OK.

00:02:41.690 --> 00:02:42.305
Fair enough.

00:02:42.305 --> 00:02:45.480
So, area of pst over
area of pqr.

00:02:45.480 --> 00:02:47.610
So what's the area of pst?

00:02:57.350 --> 00:03:03.470
That would be just the base
times the height times 1/2.

00:03:03.470 --> 00:03:06.120
And we'll see the 1/2's cancel
out, we don't have to do them,

00:03:06.120 --> 00:03:07.470
but I'll do it just
to figure it out.

00:03:07.470 --> 00:03:17.940
So it's 1/2 pt times sv.

00:03:20.510 --> 00:03:35.040
And then area of pqr
is going to be 1/2.

00:03:35.040 --> 00:03:42.760
So it's this whole thing,
pr times qv.

00:03:48.500 --> 00:03:53.640
So the area of this triangle pst
over the area of triangle

00:03:53.640 --> 00:04:04.920
pqr is just going to be 1/2 pt
times sv over 1/2 times the

00:04:04.920 --> 00:04:05.820
area of pqr.

00:04:05.820 --> 00:04:07.150
So it's over this.

00:04:07.150 --> 00:04:12.250
1/2 pr times qv.

00:04:12.250 --> 00:04:13.590
Let's see what we could
figure out.

00:04:13.590 --> 00:04:15.540
We definitely see the
1/2's cancel out.

00:04:18.410 --> 00:04:21.350
Do we know what pt over pr is?

00:04:21.350 --> 00:04:24.740
Let me see, pt over pr.

00:04:24.740 --> 00:04:27.840
They give it right here.
pt over pr is 3/4.

00:04:27.840 --> 00:04:31.960
So this term is equal to 3/4.

00:04:31.960 --> 00:04:39.910
So this is equal to 3/4
times sv over qv.

00:04:39.910 --> 00:04:41.220
And now we're at a conundrum.

00:04:41.220 --> 00:04:43.430
We know what qv is.

00:04:43.430 --> 00:04:47.580
But we only know qs,
we don't know sv.

00:04:47.580 --> 00:04:49.200
Let me ask you a question.

00:04:49.200 --> 00:04:57.920
If qs over qv, over this whole
thing, is 1/3-- so this pink

00:04:57.920 --> 00:05:03.580
distance right here is 1/3 of
this entire length, right?

00:05:03.580 --> 00:05:06.530
Because this distance over the
entire distance is 1/3.

00:05:06.530 --> 00:05:12.340
Then sv over qv so then this
is going to be 2/3.

00:05:12.340 --> 00:05:14.600
If this is 1/3, this'll
be 2/3.

00:05:14.600 --> 00:05:20.730
So then we know that sv
over the whole thing

00:05:20.730 --> 00:05:21.870
is going to be 2/3.

00:05:21.870 --> 00:05:24.980
So this is 2/3.

00:05:24.980 --> 00:05:27.970
And then 3/4 times 2/3,
well the 3's cancel

00:05:27.970 --> 00:05:29.220
out, and you get 2/4.

00:05:29.220 --> 00:05:33.530
It equals 1/2, and you
just fill it in.

00:05:33.530 --> 00:05:35.490
Next problem.

00:05:35.490 --> 00:05:36.640
Hope you get that.

00:05:36.640 --> 00:05:39.020
Most of it we just figured out
what the areas were and just

00:05:39.020 --> 00:05:39.890
substituted.

00:05:39.890 --> 00:05:43.980
And then we just have to figure
out what sv over qv is,

00:05:43.980 --> 00:05:47.110
given qs over qv.

00:05:47.110 --> 00:05:51.580
We figured out that
sv over qv is 2/3.

00:05:51.580 --> 00:05:54.685
I hope I did not confuse you.

00:05:54.685 --> 00:05:58.360
It's Thanksgiving and it's not
a good day to confuse people.

00:05:58.360 --> 00:06:04.560
OK number 16.

00:06:04.560 --> 00:06:17.840
Let the function h be defined by
h of x is equal to 14 plus

00:06:17.840 --> 00:06:21.380
x squared over 4.

00:06:21.380 --> 00:06:30.510
If h of 2m is equal
to 9m, what is one

00:06:30.510 --> 00:06:32.930
possible value of m?

00:06:32.930 --> 00:06:36.940
Well let's just figure
out what h of 2m is.

00:06:36.940 --> 00:06:44.000
So h of 2m is equal to, just
using this definition of its

00:06:44.000 --> 00:06:49.440
function, 14 plus-- we're taking
h of 2m, so it's 2m

00:06:49.440 --> 00:06:54.080
squared over 4.

00:06:54.080 --> 00:06:55.790
And we also know that
this is equal to 9m.

00:06:59.850 --> 00:07:01.680
And let's see what we can
do to simplify it.

00:07:01.680 --> 00:07:06.920
So we could say 14 plus
4m squared over 4.

00:07:06.920 --> 00:07:07.740
Just squaring both of these.

00:07:07.740 --> 00:07:09.790
This is equal to 9.

00:07:09.790 --> 00:07:11.766
This cancels out.

00:07:16.730 --> 00:07:17.890
Oh, that was equal to 9m.

00:07:17.890 --> 00:07:19.570
Sorry.

00:07:19.570 --> 00:07:23.200
And now we're left with 14 plus
m squared is equal to 9m.

00:07:23.200 --> 00:07:24.280
We're left with a quadratic.

00:07:24.280 --> 00:07:25.370
It might not be obvious
to you.

00:07:25.370 --> 00:07:27.270
Let's subtract 9m from
both sides and

00:07:27.270 --> 00:07:28.100
rearrange a little bit.

00:07:28.100 --> 00:07:34.860
You get m squared minus 9m
plus 14 is equal to 0.

00:07:34.860 --> 00:07:37.500
All I did is I took this 9m,
put it on this side,

00:07:37.500 --> 00:07:39.360
subtracted 9m from both
sides, and put the

00:07:39.360 --> 00:07:41.210
m squared out front.

00:07:41.210 --> 00:07:44.740
Now we have a quadratic and we
need to solve-- figure out

00:07:44.740 --> 00:07:48.280
where this expression intersects
the x-axis, or

00:07:48.280 --> 00:07:50.740
figure out the roots
of this quadratic.

00:07:50.740 --> 00:07:52.090
And we can factor this.

00:07:52.090 --> 00:07:55.580
If you remember your factoring
from later Algebra I or some

00:07:55.580 --> 00:07:56.120
Algebra II.

00:07:56.120 --> 00:08:03.100
This would be m minus 7 times
m minus 2 is equal to 0.

00:08:03.100 --> 00:08:04.120
And how did I figure that out?

00:08:04.120 --> 00:08:06.880
Well I had to figure out two
numbers that when I multiply

00:08:06.880 --> 00:08:10.450
them, equals positive 14, and
that when I add them, is equal

00:08:10.450 --> 00:08:12.440
to negative 9.

00:08:12.440 --> 00:08:18.840
So 7 times 2 is 14, or
negative 7 times

00:08:18.840 --> 00:08:20.390
negative 2 is also 14.

00:08:20.390 --> 00:08:21.740
And we know it's negative
because it has to go to

00:08:21.740 --> 00:08:23.000
negative 9.

00:08:23.000 --> 00:08:24.380
And that's just a review
of what you

00:08:24.380 --> 00:08:25.230
learned in algebra class.

00:08:25.230 --> 00:08:26.740
If this was confusing,
you might

00:08:26.740 --> 00:08:28.930
want to review factoring.

00:08:28.930 --> 00:08:31.500
Anyway, m minus 7 times m
minus 2 is equal to 0.

00:08:31.500 --> 00:08:35.860
That means that m is
equal to 7 or 2.

00:08:35.860 --> 00:08:38.780
And you can fill in either one
of those, because they say

00:08:38.780 --> 00:08:42.400
what is one possible
value for m?

00:08:42.400 --> 00:08:45.910
I have a minute left, so and I
only have two problems left.

00:08:45.910 --> 00:08:47.940
Well, that's good for one extra
video, so I'll see you

00:08:47.940 --> 00:08:49.540
in the next video.


SAT Prep: Test 2 Section 6 Part 6

WEBVTT
Kind: captions
Language: en

00:00:00.790 --> 00:00:01.480
Welcome back.

00:00:01.480 --> 00:00:03.970
So I did this ahead of time, so
as to not waste your time

00:00:03.970 --> 00:00:04.775
drawing it.

00:00:04.775 --> 00:00:08.560
The question says, a merchant
sells three types of clocks

00:00:08.560 --> 00:00:10.500
that chime as indicated
by the check marks

00:00:10.500 --> 00:00:11.890
in the table above.

00:00:11.890 --> 00:00:16.610
What is the total number of
chimes of the inventory of

00:00:16.610 --> 00:00:18.860
clocks in the 90-minute
period?

00:00:18.860 --> 00:00:26.780
And we're talking about
7:15 to 8:45.

00:00:26.780 --> 00:00:28.405
So let's just make sure we
understand this chart.

00:00:28.405 --> 00:00:31.700
So we have clocks of
type a, b, and c.

00:00:31.700 --> 00:00:33.730
This is the number of
each of those clocks

00:00:33.730 --> 00:00:36.830
that the store has.

00:00:36.830 --> 00:00:39.540
Now these n times on the nth
hour, that means when it turns

00:00:39.540 --> 00:00:41.680
7 o'clock, it's going to
chime seven times.

00:00:41.680 --> 00:00:45.895
When it turns 8 o'clock, it's
going to chime eight times, et

00:00:45.895 --> 00:00:47.190
cetera, et cetera.

00:00:47.190 --> 00:00:49.200
This is once on the hour,
so right at the hour

00:00:49.200 --> 00:00:51.150
does just one chime.

00:00:51.150 --> 00:00:52.785
And then these do once
on the half hour.

00:00:56.230 --> 00:01:06.360
So let's see, we have
clock a times 10.

00:01:06.360 --> 00:01:09.880
And how many times is each of
the clock a's going to chime

00:01:09.880 --> 00:01:11.570
between this period?

00:01:11.570 --> 00:01:15.340
Well, it does n times
on the nth hour.

00:01:15.340 --> 00:01:18.780
So between 7:15 and 8:45,
there's only one hour that

00:01:18.780 --> 00:01:21.660
happens, which is 8 o'clock.

00:01:21.660 --> 00:01:26.220
And at 8 o'clock it's going
to chime n times.

00:01:26.220 --> 00:01:30.965
It's going to chime eight
chimes at 8 o'clock.

00:01:33.470 --> 00:01:35.730
And it also does one
on the half hour.

00:01:35.730 --> 00:01:37.100
So what half hours are there?

00:01:37.100 --> 00:01:42.230
Well there's 7:30 and there's
8:30 that pass up.

00:01:42.230 --> 00:01:43.520
So there are two half hours.

00:01:43.520 --> 00:01:46.420
It's going to chime at 7:30
and 8:30, each of these.

00:01:46.420 --> 00:01:51.910
So then plus 2, once at 7:30
and once at 8:30, times 10,

00:01:51.910 --> 00:01:54.750
because there's ten clocks.

00:01:54.750 --> 00:02:01.190
Let's see, b times 5 clocks,
n times on the nth hour.

00:02:01.190 --> 00:02:06.660
Well, once again that's eight
chimes at 8:00, and it doesn't

00:02:06.660 --> 00:02:08.639
do anything else.

00:02:08.639 --> 00:02:10.419
So times 5.

00:02:10.419 --> 00:02:14.260
And then finally c times
three clocks.

00:02:14.260 --> 00:02:16.380
It doesn't do this n
times the nth hour.

00:02:16.380 --> 00:02:17.740
It does once on the hour.

00:02:17.740 --> 00:02:22.880
It's going to do it
once at 8 o'clock.

00:02:22.880 --> 00:02:28.410
And then once on the half
hour, so plus 1 at

00:02:28.410 --> 00:02:34.350
7:30 plus 1 at 8:30.

00:02:34.350 --> 00:02:38.550
So that's 3 times
three clocks.

00:02:38.550 --> 00:02:39.070
So what's this?

00:02:39.070 --> 00:02:41.180
It's 8 plus 2.

00:02:41.180 --> 00:02:43.110
Eight chimes plus two chimes.

00:02:43.110 --> 00:02:46.190
So that's ten chimes per
clock times 10 is

00:02:46.190 --> 00:02:48.360
equal to a 100 chimes.

00:02:48.360 --> 00:02:50.770
Eight chimes per clock
times five clocks

00:02:50.770 --> 00:02:52.930
is equal to 40 chimes.

00:02:52.930 --> 00:02:57.360
And then three chimes per clock
times three clocks is

00:02:57.360 --> 00:03:00.010
equal to 9.

00:03:00.010 --> 00:03:02.910
You add all this up together,
and the whole store in this

00:03:02.910 --> 00:03:07.250
time period, if I haven't made
a mistake, will chime 149 or

00:03:07.250 --> 00:03:11.850
there'll be 149 chimes of the
inventory of clocks in this

00:03:11.850 --> 00:03:14.210
90-minute period.

00:03:14.210 --> 00:03:15.460
Next question.

00:03:20.070 --> 00:03:24.440
So they draw a bunch
of random things.

00:03:24.440 --> 00:03:26.300
I'll just replace them with
numbers because that's easier

00:03:26.300 --> 00:03:33.020
for me to think, or letters
a, b, c, d, and e.

00:03:33.020 --> 00:03:34.930
I mean those pictures
are useless.

00:03:34.930 --> 00:03:37.410
They say, if the five cards
shown above are placed in a

00:03:37.410 --> 00:03:43.320
row so that the shaded box, but
I'll call that c, so that

00:03:43.320 --> 00:03:47.510
c is never at either end, how
many different arrangements

00:03:47.510 --> 00:03:48.700
are possible?

00:03:48.700 --> 00:03:51.250
Well, this is how I
think about it.

00:03:51.250 --> 00:03:55.140
c is the most restricted.

00:03:55.140 --> 00:03:59.550
Let's say that we're placing
them in order.

00:03:59.550 --> 00:04:01.790
Let's say these are the spots.

00:04:01.790 --> 00:04:02.620
They're in a row.

00:04:02.620 --> 00:04:06.560
1, 2, 3, 4, 5.

00:04:06.560 --> 00:04:08.870
And when we come along,
we have c.

00:04:08.870 --> 00:04:10.660
We know that c can't be
placed here, and it

00:04:10.660 --> 00:04:11.570
can't be placed here.

00:04:11.570 --> 00:04:15.920
So it can only be placed in
one of these three spots.

00:04:15.920 --> 00:04:18.480
So there's three possible
situations

00:04:18.480 --> 00:04:21.000
where c can be placed.

00:04:21.000 --> 00:04:25.890
Let's say you place c in one
of these three spots.

00:04:25.890 --> 00:04:28.280
Now it's our turn to place a.

00:04:28.280 --> 00:04:30.880
How many spots are
left to place a?

00:04:30.880 --> 00:04:33.550
Well, one of these three is
going to be taken by c.

00:04:33.550 --> 00:04:37.820
But then a can be in any
of the other four.

00:04:37.820 --> 00:04:41.720
So then there's four
possibilities for a.

00:04:41.720 --> 00:04:44.840
And then once you place a, then
for b, well two of the

00:04:44.840 --> 00:04:46.650
spots are going to be
taken up in b, so

00:04:46.650 --> 00:04:47.850
there's three spots left.

00:04:47.850 --> 00:04:50.380
So there's three possibilities
for b.

00:04:50.380 --> 00:04:53.990
And then there's only
two openings for d.

00:04:53.990 --> 00:04:56.220
And then there's
only one for e.

00:04:56.220 --> 00:05:00.100
So if you multiply this out,
you get 3 times 4 is 12.

00:05:00.100 --> 00:05:02.910
12 times 3 is 36.

00:05:02.910 --> 00:05:05.700
36 times 2 is 72.

00:05:05.700 --> 00:05:12.480
So there are 72 possible
arrangements where the middle

00:05:12.480 --> 00:05:16.470
card or that grey card is never
placed at either end.

00:05:16.470 --> 00:05:18.220
That's how I always think about
these because you just

00:05:18.220 --> 00:05:20.250
think about placing them-- well
this first one can only

00:05:20.250 --> 00:05:21.560
go in three-- well
you get the idea.

00:05:21.560 --> 00:05:23.570
Hopefully you get the idea.

00:05:23.570 --> 00:05:25.510
Well, that's this section,
so I will see

00:05:25.510 --> 00:05:27.160
you in the next section.

00:05:27.160 --> 00:05:28.410
Have fun.


SAT Prep: Test 2 Section 3 Part 6

WEBVTT
Kind: captions
Language: en

00:00:00.890 --> 00:00:03.720
One problem left, problem
number 20.

00:00:03.720 --> 00:00:07.770
There are 75 more
women than men

00:00:07.770 --> 00:00:09.710
enrolled in Linden College.

00:00:09.710 --> 00:00:14.260
If n men enrolled, then in terms
of n, what percentage of

00:00:14.260 --> 00:00:15.866
those enrolled are men?

00:00:19.690 --> 00:00:27.870
Well, they're saying that n is
men, so n is equal to number

00:00:27.870 --> 00:00:32.610
of men, right?

00:00:32.610 --> 00:00:33.480
They tell us that.

00:00:33.480 --> 00:00:38.310
And there are 75 more women
than men, right?

00:00:38.310 --> 00:00:40.140
So what is equal to the
number of women?

00:00:42.760 --> 00:00:46.680
We know that there are 75 more
women than men, so it

00:00:46.680 --> 00:00:51.220
must be n plus 75.

00:00:51.220 --> 00:00:52.920
I think I'm coming down
with something.

00:00:52.920 --> 00:00:56.320
And then they say well, in terms
of n, what percentage of

00:00:56.320 --> 00:00:58.630
those enrolled are men?

00:01:05.190 --> 00:01:07.320
So if we want to know the
fraction that are men, it's

00:01:07.320 --> 00:01:09.690
the number of men over the
total number of students.

00:01:09.690 --> 00:01:12.080
So the total number of students
is going to be the

00:01:12.080 --> 00:01:13.840
men plus the women.

00:01:13.840 --> 00:01:20.810
So the men is n plus the women
is n plus 75, right?

00:01:20.810 --> 00:01:22.730
So this tells us the fraction
that are men.

00:01:22.730 --> 00:01:30.360
So this is n over 2n plus 75.

00:01:30.360 --> 00:01:33.000
This would be some decimal
number, and if I want to

00:01:33.000 --> 00:01:41.040
convert this to a percentage,
I'd multiply it times 100 and

00:01:41.040 --> 00:01:42.415
add a percent sign right here.

00:01:42.415 --> 00:01:47.260
And if I wanted to rewrite that,
it would be 100n over 2n

00:01:47.260 --> 00:01:50.780
plus 75 percent.

00:01:50.780 --> 00:01:55.521
And that is choice e.

00:01:55.521 --> 00:01:57.800
I have all this extra time I
don't know what to do with.

00:01:57.800 --> 00:02:01.540
I guess I will let you use
it more productively then

00:02:01.540 --> 00:02:03.080
watching me do nothing
on a video.

00:02:03.080 --> 00:02:06.800
I'll see you in the
next SAT Section.


SAT Prep: Test 2 Section 3 Part 5

WEBVTT
Kind: captions
Language: en

00:00:00.670 --> 00:00:02.120
We are in the home stretch.

00:00:02.120 --> 00:00:07.150
Problem number 17 on page 463.

00:00:07.150 --> 00:00:09.390
Oh, I like these with these
strange operations.

00:00:09.390 --> 00:00:18.190
Let the operation up arrow be
defined as a up arrow b is

00:00:18.190 --> 00:00:26.780
equal to a plus b over a minus
b, for all numbers in a and b,

00:00:26.780 --> 00:00:29.230
where a does not equal b.

00:00:29.230 --> 00:00:30.190
And why do they to
have to say that?

00:00:30.190 --> 00:00:32.250
Well, because otherwise, our
denominator would be 0.

00:00:34.890 --> 00:00:45.180
So we know that 1 up 2 is equal
to 2 up x, what is x?

00:00:47.750 --> 00:00:48.920
So let's set up the equation.

00:00:48.920 --> 00:00:50.640
So what is 1 up arrow 2?

00:00:50.640 --> 00:00:54.140
So that's 1 plus 2
over 1 minus 2.

00:00:54.140 --> 00:00:57.960
So it's 1 plus 2
over 1 minus 2.

00:00:57.960 --> 00:01:03.230
I just used this formula,
1 is a, 2 is be, right?

00:01:03.230 --> 00:01:04.750
What's 2 up arrow x?

00:01:04.750 --> 00:01:09.560
That's 2 plus x over
2 minus x.

00:01:12.810 --> 00:01:15.900
So 1 plus 2 is 3.

00:01:15.900 --> 00:01:20.340
1 minus 2 is negative 1.

00:01:20.340 --> 00:01:28.530
So it's negative 1 is equal to
2 plus x over 2 minus x, and

00:01:28.530 --> 00:01:32.020
of course this is just
equal to negative 3.

00:01:32.020 --> 00:01:34.540
And now we can multiply both
sides of this equation by 2

00:01:34.540 --> 00:01:37.560
minus x, because we know that x
can't be equal to 2, because

00:01:37.560 --> 00:01:39.330
it says a can't be equal to b.

00:01:39.330 --> 00:01:40.820
So we know we're not multiplying
both sides of this

00:01:40.820 --> 00:01:42.590
equation by 0.

00:01:42.590 --> 00:01:44.180
2 minus x.

00:01:44.180 --> 00:01:45.730
That's all I'm doing, I'm
just multiplying both

00:01:45.730 --> 00:01:47.440
sides by 2 minus x.

00:01:50.200 --> 00:01:53.700
On the left-hand side, I
get negative 3 minus 3,

00:01:53.700 --> 00:01:57.130
times 2 minus x.

00:01:57.130 --> 00:01:59.870
And on the right-hand side, the
2 minus x's cancel out,

00:01:59.870 --> 00:02:02.560
and I get 2 plus x.

00:02:02.560 --> 00:02:04.390
And then I distribute the 3.

00:02:04.390 --> 00:02:11.009
Minus 6 plus 3x is equal
to 2 plus x.

00:02:11.009 --> 00:02:12.310
And let's see, where
do I want my x's?

00:02:12.310 --> 00:02:14.150
Let's add 6 to both sides.

00:02:14.150 --> 00:02:17.360
3x is equal to 8 plus x.

00:02:17.360 --> 00:02:19.070
Subtract x from both sides.

00:02:19.070 --> 00:02:21.950
2x is equal to 8.

00:02:21.950 --> 00:02:24.540
x is equal to 4.

00:02:24.540 --> 00:02:26.590
Choice A.

00:02:26.590 --> 00:02:29.050
OK, problem number 18.

00:02:29.050 --> 00:02:32.530
I'm going to switch colors, too,
because this color is not

00:02:32.530 --> 00:02:34.710
appealing to me.

00:02:34.710 --> 00:02:36.830
Let's see, green.

00:02:36.830 --> 00:02:41.880
18, looks like this involves
money, so green is good.

00:02:41.880 --> 00:02:45.050
During a sale, a customer can
buy one shirt for x dollars.

00:02:45.050 --> 00:02:47.330
So 1 for x.

00:02:49.990 --> 00:02:54.120
Each additional shirt
costs z dollars less

00:02:54.120 --> 00:02:56.480
than the first shirt.

00:02:56.480 --> 00:02:59.650
soon.

00:02:59.650 --> 00:03:11.130
So additional z less than first.
For example, the cost

00:03:11.130 --> 00:03:13.990
of the second shirt
is x minus z.

00:03:13.990 --> 00:03:15.570
All right, fair enough.

00:03:15.570 --> 00:03:18.030
Which of the following
represents the customer's cost

00:03:18.030 --> 00:03:20.910
in dollars for n shirts bought
during the sale?

00:03:27.340 --> 00:03:32.280
So the first shirt is
going to cost x.

00:03:32.280 --> 00:03:33.475
The first shirt's
going to cost x.

00:03:33.475 --> 00:03:35.860
And then how many
shirts are left?

00:03:35.860 --> 00:03:39.390
Well, there's n minus 1 shirts,
that aren't the first

00:03:39.390 --> 00:03:41.880
shirt, right?

00:03:41.880 --> 00:03:44.360
They buy 1 shirt at x and then
they're going to buy n minus 1

00:03:44.360 --> 00:03:46.230
at the other price.

00:03:46.230 --> 00:03:49.710
And then the other price
is x minus z.

00:03:49.710 --> 00:03:56.990
Because it's not like the third
shirt costs z less than

00:03:56.990 --> 00:03:58.925
the second, and then the fourth
shirt costs z less

00:03:58.925 --> 00:04:02.110
than-- they all cost z less
than the first, right?

00:04:02.110 --> 00:04:05.910
So every other shirt
costs x minus z.

00:04:05.910 --> 00:04:08.960
So we have n minus
1 other shirts.

00:04:08.960 --> 00:04:12.210
The first one costs x, then we
have n minus 1 shirts that

00:04:12.210 --> 00:04:16.140
cost x minus z dollars.

00:04:16.140 --> 00:04:18.410
And did they draw it
right like that?

00:04:18.410 --> 00:04:21.320
Yes, that is choice A.

00:04:21.320 --> 00:04:23.220
I thought maybe they might have
multiplied it out and

00:04:23.220 --> 00:04:25.300
we'd have to look for something
similar, but they

00:04:25.300 --> 00:04:28.160
give it just the way it is.

00:04:28.160 --> 00:04:33.070
All right, next problem.

00:04:33.070 --> 00:04:43.060
Problem number 19.

00:04:43.060 --> 00:04:44.510
I don't need to draw
it neatly.

00:04:44.510 --> 00:04:46.110
I can draw this thing
freehand.

00:04:49.360 --> 00:04:57.070
OK, so this is P, 30
degrees, Q, and R.

00:04:57.070 --> 00:05:00.960
In the figure above, QR is the
arc of a circle with center P.

00:05:00.960 --> 00:05:12.870
If the length of QR is 6 pi,
what is the area of sector P?

00:05:12.870 --> 00:05:15.440
So this length is 6 pi,
so they want to know

00:05:15.440 --> 00:05:18.220
what this area is.

00:05:18.220 --> 00:05:21.870
Well, the important realization
is is that this is

00:05:21.870 --> 00:05:23.440
part of a larger circle.

00:05:23.440 --> 00:05:27.940
So if I were to draw the entire
circle like that, and

00:05:27.940 --> 00:05:32.290
then I would draw-- let me do
it in a different color.

00:05:32.290 --> 00:05:43.750
This is part of a larger circle,
where this is P, Q, R,

00:05:43.750 --> 00:05:46.100
and 30 degrees.

00:05:46.100 --> 00:05:47.830
And this 30 degrees is important
because it tells us

00:05:47.830 --> 00:05:50.180
what fraction of the larger
circle this is.

00:05:50.180 --> 00:05:52.440
Well, how many degrees are there
in a total circle? you

00:05:52.440 --> 00:05:53.570
Well there are 360, right?

00:05:53.570 --> 00:05:56.330
If we were to go all the way
around, there's 360.

00:05:56.330 --> 00:06:00.990
So the fraction that this is
of the full circle is 30

00:06:00.990 --> 00:06:04.400
degrees over 360.

00:06:04.400 --> 00:06:09.550
And this is 1/12.

00:06:09.550 --> 00:06:10.540
I haven't drawn it to scale.

00:06:10.540 --> 00:06:13.760
The way I drew it, it looks more
like 60 degrees, but you

00:06:13.760 --> 00:06:16.970
should be able draw 12 pies
of 30 degrees here.

00:06:16.970 --> 00:06:20.110
I hope I'm not confusing you,
because there are 360 degrees

00:06:20.110 --> 00:06:21.170
in the circle.

00:06:21.170 --> 00:06:27.520
So if this slice is 1/12 of the
whole circle, then this

00:06:27.520 --> 00:06:34.980
arc length, this 6 pi right
here, is going to be 1/12 of

00:06:34.980 --> 00:06:36.540
the entire circumference.

00:06:36.540 --> 00:06:37.830
So what's the circumference?

00:06:37.830 --> 00:06:41.340
The circumference is going
to be 12 times this.

00:06:41.340 --> 00:06:45.160
So the circumference
is 12 times 6 pi,

00:06:45.160 --> 00:06:49.950
which equals 72 pi.

00:06:49.950 --> 00:06:56.520
If the circumference is 72
pi, what is the radius?

00:06:56.520 --> 00:06:57.770
What's the formula?

00:06:57.770 --> 00:07:02.200
Circumference is equal
to 2 pi r.

00:07:02.200 --> 00:07:06.290
So we could say that also
is equal to 72 pi.

00:07:06.290 --> 00:07:11.810
So you could divide both sides
by pi, and then divide both

00:07:11.810 --> 00:07:13.450
sides by 2.

00:07:13.450 --> 00:07:17.490
And you have the radius
is equal to 36.

00:07:17.490 --> 00:07:21.170
So this radius right here-- let
me do it in a different

00:07:21.170 --> 00:07:25.260
color-- this radius
is equal to 36.

00:07:25.260 --> 00:07:29.220
All I did is I figured out this
arc length is 1/12 of the

00:07:29.220 --> 00:07:30.940
entire circumference.

00:07:30.940 --> 00:07:33.610
And so the entire circumference
is 72 pi.

00:07:33.610 --> 00:07:35.260
And then I used that to
figure out that the

00:07:35.260 --> 00:07:39.000
radius must be 36.

00:07:39.000 --> 00:07:42.390
Now we want to know the area
of just this piece.

00:07:42.390 --> 00:07:44.310
So we could just figure out the
area of the whole thing

00:07:44.310 --> 00:07:46.980
and then divide by 12, because
this is 1/12 the area of the

00:07:46.980 --> 00:07:48.260
circle as well.

00:07:48.260 --> 00:07:49.720
So what's the area?

00:07:49.720 --> 00:07:54.580
Area is equal to pi r squared.

00:07:54.580 --> 00:08:00.050
That equals pi times 36
squared-- I'm going to write

00:08:00.050 --> 00:08:01.220
36 times 36.

00:08:01.220 --> 00:08:03.320
I don't want multiply
big numbers.

00:08:03.320 --> 00:08:06.230
And then that's the area of the
whole thing, is pi times

00:08:06.230 --> 00:08:08.190
36, times 36.

00:08:08.190 --> 00:08:11.820
So the area of just this
fraction will be the area of

00:08:11.820 --> 00:08:16.880
the whole thing divided by 12.

00:08:16.880 --> 00:08:18.760
And the reason why I didn't
multiply it out is because I

00:08:18.760 --> 00:08:19.580
can actually cancel.

00:08:19.580 --> 00:08:22.600
I can say, well, this
is 3, this is 1.

00:08:22.600 --> 00:08:25.330
So it's pi times 3, times 36.

00:08:25.330 --> 00:08:26.570
And what's 3 times 36?

00:08:26.570 --> 00:08:31.940
90 plus 18 is 108, so
it equals 108 pi,

00:08:31.940 --> 00:08:35.539
which is choice A.

00:08:35.539 --> 00:08:38.850
Let's see if I can squeeze
in the last problem.

00:08:38.850 --> 00:08:41.799
Probably not.

00:08:41.799 --> 00:08:45.890
Actually, I will save the last
problem for a video of its

00:08:45.890 --> 00:08:47.640
own, because I only have
a minute left.

00:08:47.640 --> 00:08:48.890
See


SAT Prep: Test 2 Section 3 Part 4

WEBVTT
Kind: captions
Language: en

00:00:00.690 --> 00:00:07.680
All right, we're now on problem
number 15 on page 463.

00:00:07.680 --> 00:00:09.050
Let's see, they have a chart.

00:00:09.050 --> 00:00:16.010
And it says, city and noon
temperature in Farenheit.

00:00:16.010 --> 00:00:17.260
So I'll just write
temperature.

00:00:22.650 --> 00:00:42.670
And city A is 50 degrees, B is
33, C is 27, D is t degrees, E

00:00:42.670 --> 00:00:55.870
is 68 degrees, F is 44 degrees,
and G is 40 degrees.

00:00:55.870 --> 00:00:56.610
All right.

00:00:56.610 --> 00:01:00.100
Now, so the question says, the
table above shows the noon

00:01:00.100 --> 00:01:02.580
temperature for seven cities
designated A through G.

00:01:02.580 --> 00:01:08.890
All right, if the median noon
temperature-- so the median--

00:01:08.890 --> 00:01:16.800
is 40 degrees, then the noon
temperature for city D could

00:01:16.800 --> 00:01:19.120
be any of the following
except?

00:01:19.120 --> 00:01:20.420
So the median means what?

00:01:20.420 --> 00:01:21.920
It means the middle number.

00:01:21.920 --> 00:01:24.680
It means if we were to rearrange
all of these numbers

00:01:24.680 --> 00:01:28.190
from smallest to highest, the
40 would be the middle.

00:01:28.190 --> 00:01:32.140
So let's rearrange all the
numbers, I guess, except for t

00:01:32.140 --> 00:01:33.110
from smallest to highest,
because we

00:01:33.110 --> 00:01:34.450
don't know what t is.

00:01:34.450 --> 00:01:44.630
So let's see, the smallest
is 27, then we go to 33.

00:01:44.630 --> 00:01:47.240
Then we have 40.

00:01:47.240 --> 00:01:51.790
Then we have 44.

00:01:51.790 --> 00:01:54.310
Then we have 50.

00:01:54.310 --> 00:01:55.950
Then we have 68, right?

00:01:55.950 --> 00:01:58.800
I should have written six
numbers down, and I wrote six

00:01:58.800 --> 00:01:59.910
numbers down, right?

00:01:59.910 --> 00:02:04.140
And they're saying
the median is 40.

00:02:04.140 --> 00:02:06.610
So in order for the median to
be 40, this needs to be the

00:02:06.610 --> 00:02:08.050
middle number, right?

00:02:08.050 --> 00:02:09.240
The middle number.

00:02:09.240 --> 00:02:12.070
That means there need to be just
as many numbers smaller

00:02:12.070 --> 00:02:17.000
than 40 as there are numbers
larger than 40, right?

00:02:17.000 --> 00:02:19.460
Just the way I drew it right
now, it doesn't look like the

00:02:19.460 --> 00:02:20.060
median, right?

00:02:20.060 --> 00:02:22.690
Because there's only two numbers
less than it and

00:02:22.690 --> 00:02:25.140
there's three numbers
greater that it.

00:02:25.140 --> 00:02:27.470
So I think you see where
this is going.

00:02:27.470 --> 00:02:30.750
t has to be someplace here.

00:02:30.750 --> 00:02:34.420
t has to be someplace less than
40 degrees in order for

00:02:34.420 --> 00:02:37.890
40 to be the median number.

00:02:37.890 --> 00:02:41.030
So let's see, it says-- and
actually, t could be less than

00:02:41.030 --> 00:02:41.950
or equal to 40.

00:02:41.950 --> 00:02:45.750
Because even if we had another
40 here, then 40 would still

00:02:45.750 --> 00:02:46.770
be the median, right?

00:02:46.770 --> 00:02:48.850
Because if you put all the
numbers in order-- you know,

00:02:48.850 --> 00:02:51.870
you have seven numbers-- the
fourth highest number would

00:02:51.870 --> 00:02:52.560
still be 40.

00:02:52.560 --> 00:02:55.310
So t has to be less than
or equal to 40.

00:02:55.310 --> 00:02:57.640
So if we look at the choices,
A is 29, well

00:02:57.640 --> 00:02:59.050
that satisfies it.

00:02:59.050 --> 00:03:02.260
B is 35, that satisfies it.

00:03:02.260 --> 00:03:04.220
C is 39, satisfies it.

00:03:04.220 --> 00:03:05.440
D is 40.

00:03:05.440 --> 00:03:06.120
And then we look at E.

00:03:06.120 --> 00:03:10.110
E is 42, so that does
not satisfy it, so

00:03:10.110 --> 00:03:13.650
our choice is E.

00:03:13.650 --> 00:03:15.600
All right, problem number 14.

00:03:15.600 --> 00:03:20.780
This one looks exciting,
and I will do it

00:03:20.780 --> 00:03:23.220
in an exciting color.

00:03:23.220 --> 00:03:26.420
So let me see if I
can draw this.

00:03:26.420 --> 00:03:31.290
So I have a line on the top and
then I have a line that

00:03:31.290 --> 00:03:33.240
goes straight down like that.

00:03:36.650 --> 00:03:43.330
And then this thing goes
something like this and it

00:03:43.330 --> 00:03:46.570
goes something like this.

00:03:46.570 --> 00:03:50.580
Can I draw this right,
draw this even.

00:03:50.580 --> 00:03:54.460
And then it goes-- well, close
enough, I think, to what they

00:03:54.460 --> 00:03:56.490
have on the drawing.

00:03:56.490 --> 00:03:58.850
And let me fill in all
the information.

00:03:58.850 --> 00:04:02.790
So it says these are right
angles, this is a right angle.

00:04:02.790 --> 00:04:04.400
The length of this is 6.

00:04:04.400 --> 00:04:06.420
The length of this is 6.

00:04:06.420 --> 00:04:08.110
The length of this is 6.

00:04:08.110 --> 00:04:16.680
And then it tells us that
these are 30 degrees.

00:04:16.680 --> 00:04:19.750
And it says, what is the
perimeter of the figure above?

00:04:19.750 --> 00:04:21.190
So in order to figure out the
perimeter-- we you know this

00:04:21.190 --> 00:04:23.060
side, we know this side, we know
this side-- we need to

00:04:23.060 --> 00:04:25.540
figure out these two
sides, right?

00:04:25.540 --> 00:04:26.790
These two sides.

00:04:26.790 --> 00:04:29.080
So once we know those,
then we're set.

00:04:29.080 --> 00:04:31.460
And you could do some fancy
things here if you wanted to

00:04:31.460 --> 00:04:32.600
go in the wrong direction.

00:04:32.600 --> 00:04:34.490
But you'd get the right answer,
you could make a 30,

00:04:34.490 --> 00:04:39.200
60, 90 triangle here and here
and figure out this side and

00:04:39.200 --> 00:04:41.070
then figure out the hypotenuse
et cetera, et cetera.

00:04:41.070 --> 00:04:43.030
But the real trick of this is
just kind of seeing the

00:04:43.030 --> 00:04:44.020
negative image here.

00:04:44.020 --> 00:04:47.020
Trying to see kind of what
hasn't been drawn.

00:04:47.020 --> 00:04:49.430
And I'll show you what I mean.

00:04:49.430 --> 00:04:56.160
If we draw-- let's just draw
a little line here.

00:04:56.160 --> 00:04:59.280
I think now you'll start
to see what I'm doing.

00:04:59.280 --> 00:05:04.960
If we have a line here,
what's this angle?

00:05:04.960 --> 00:05:07.170
Well, this whole thing is a
right angle, it's 90 degrees,

00:05:07.170 --> 00:05:09.340
so this angle would
be 60, right?

00:05:09.340 --> 00:05:10.330
And so would this angle.

00:05:10.330 --> 00:05:13.130
This angle would also
be 60 degrees.

00:05:13.130 --> 00:05:15.630
And so would this
angle, right?

00:05:15.630 --> 00:05:18.000
Because they have to add up to
180, and if two of them are

00:05:18.000 --> 00:05:19.580
60, the third one's
going to be 60.

00:05:19.580 --> 00:05:23.580
So what do we know about this
triangle right here?

00:05:23.580 --> 00:05:25.000
Well, it's an equilateral
triangle.

00:05:25.000 --> 00:05:26.520
All the sides are the
same because all the

00:05:26.520 --> 00:05:27.990
angles are the same.

00:05:27.990 --> 00:05:29.220
Well, we know one
of the sides.

00:05:29.220 --> 00:05:31.470
We know this side we made up
because it's going to be the

00:05:31.470 --> 00:05:34.060
same length as this
side up here.

00:05:34.060 --> 00:05:36.010
So this is going to be 6.

00:05:36.010 --> 00:05:38.480
Well, if that side is 6, then
all of the sides of this

00:05:38.480 --> 00:05:43.400
equilateral triangle are going
to have to be 6, right?

00:05:43.400 --> 00:05:43.950
And then we're done.

00:05:43.950 --> 00:05:46.610
Now we just have to add
up all the sides.

00:05:46.610 --> 00:05:51.340
So it's 6 plus 6 plus 6
plus 6 plus 6, right?

00:05:51.340 --> 00:05:52.090
We ignore this one.

00:05:52.090 --> 00:05:54.010
This isn't part of the
perimeter, the perimeters are

00:05:54.010 --> 00:05:57.170
the purple sides, so it's one,
two, three, four, five, sixes,

00:05:57.170 --> 00:06:01.180
so 5 times 6 equal to 30.

00:06:01.180 --> 00:06:02.430
Choice D.

00:06:05.480 --> 00:06:15.930
All right, problem number 15.

00:06:15.930 --> 00:06:28.420
m is the greatest prime
factor of 38.

00:06:28.420 --> 00:06:40.690
n is the greatest prime
factor of 100.

00:06:40.690 --> 00:06:43.780
What is the value of m plus n?

00:06:43.780 --> 00:06:48.220
Well, without knowing a trick
here-- a trick hasn't just

00:06:48.220 --> 00:06:50.440
jumped into my head-- let's just
try to factor them, do

00:06:50.440 --> 00:06:51.690
the prime factorization.

00:06:56.100 --> 00:06:59.350
And actually the easiest way to
do the prime factorization

00:06:59.350 --> 00:07:03.930
is, well-- look, we want to get
the greatest prime factor,

00:07:03.930 --> 00:07:05.020
and this one is actually
pretty easy.

00:07:05.020 --> 00:07:08.430
Because you have two, and
then it's 2 times what?

00:07:08.430 --> 00:07:10.670
2 times 19.

00:07:10.670 --> 00:07:11.240
We're done.

00:07:11.240 --> 00:07:12.350
That was pretty easy, right?

00:07:12.350 --> 00:07:16.140
2 times 19, 19 is the greatest
prime factor of 38.

00:07:16.140 --> 00:07:20.130
100 might take us a little
bit more time, right?

00:07:20.130 --> 00:07:22.740
Because it's 2 times 50.

00:07:22.740 --> 00:07:24.070
100 is 2 times 50.

00:07:24.070 --> 00:07:27.120
50 is 2 times 25.

00:07:27.120 --> 00:07:28.920
25 is 5 times 5.

00:07:28.920 --> 00:07:30.290
Actually, that didn't take
us much time, either.

00:07:30.290 --> 00:07:32.520
This is just a straight-- I
thought there might be a trick

00:07:32.520 --> 00:07:33.860
here-- but this is just
a straight prime

00:07:33.860 --> 00:07:34.910
factorization problem.

00:07:34.910 --> 00:07:39.620
So the greatest prime
factor of 100 is 5.

00:07:39.620 --> 00:07:48.420
You add them together, 19
plus 5 is equal to 24.

00:07:48.420 --> 00:07:52.090
And that is choice C.

00:07:52.090 --> 00:07:55.490
OK, let's see if I have time to
fit in problem number 16.

00:07:55.490 --> 00:07:57.030
Otherwise I'll do it
in the next video.

00:08:00.030 --> 00:08:02.820
Line L has a positive slope
and passes-- let me draw

00:08:02.820 --> 00:08:05.220
coordinate axes.

00:08:05.220 --> 00:08:09.870
So that's my y-axis, that's my
x-axis, and I'm going to drawn

00:08:09.870 --> 00:08:10.995
another line in a
different color.

00:08:10.995 --> 00:08:13.360
Let's see, has a positive
slope-- so that means it's

00:08:13.360 --> 00:08:16.850
going to go from the bottom
left to the top right.

00:08:16.850 --> 00:08:19.790
And it goes through
the point 0, 0.

00:08:19.790 --> 00:08:22.400
So this is line l.

00:08:22.400 --> 00:08:25.380
Line l looks something
like that.

00:08:25.380 --> 00:08:27.630
So this is line l.

00:08:30.820 --> 00:08:34.520
If line k is perpendicular to
line l, which of the following

00:08:34.520 --> 00:08:35.190
must be true?

00:08:35.190 --> 00:08:38.409
So it intersects at a
perpendicular angle.

00:08:38.409 --> 00:08:40.429
So line k is going to look
something-- let me do it in a

00:08:40.429 --> 00:08:43.159
different color-- line k is
going to look something like

00:08:43.159 --> 00:08:43.710
this, right?

00:08:43.710 --> 00:08:44.960
It's perpendicular.

00:08:53.570 --> 00:08:55.400
I have a feeling that this is
going to go into something

00:08:55.400 --> 00:08:57.390
that you just need to know.

00:08:57.390 --> 00:09:00.110
The perpendicular-- if you know
the slope of something,

00:09:00.110 --> 00:09:01.950
let's say line l's slope.

00:09:01.950 --> 00:09:09.490
Let's say l is y is equal to mx
plus b, but we know it goes

00:09:09.490 --> 00:09:12.240
through the intercept, so
it's actually just mx.

00:09:12.240 --> 00:09:19.210
Then we know that line k, right
here, is going to have

00:09:19.210 --> 00:09:22.760
the negative inverse of
the slope of line l.

00:09:22.760 --> 00:09:27.880
So it's going to be negative
1 over mx and then plus b.

00:09:27.880 --> 00:09:31.030
This could intersect right here,
we don't know because

00:09:31.030 --> 00:09:33.380
they didn't tell us it goes
through the origin.

00:09:33.380 --> 00:09:35.830
So we don't know what
b is. b could be 0.

00:09:35.830 --> 00:09:38.590
But the bottom line is, the only
thing we do know is that

00:09:38.590 --> 00:09:43.470
if this number is positive,
this number

00:09:43.470 --> 00:09:44.430
is going to be negative.

00:09:44.430 --> 00:09:46.880
And they told us that this
is positive, right?

00:09:46.880 --> 00:09:50.860
And let's see, choice a, line
k passes through 0, 0.

00:09:50.860 --> 00:09:51.330
No, no.

00:09:51.330 --> 00:09:52.850
Oh, it's C, choise C.

00:09:52.850 --> 00:09:54.440
Line k has a negative slope.

00:09:54.440 --> 00:09:57.070
And that's all we know.

00:09:57.070 --> 00:09:58.850
See you in the next video.


SAT Prep: Test 1 Section 6 Part 2

WEBVTT
Kind: captions
Language: en

00:00:00.640 --> 00:00:01.450
All right.

00:00:01.450 --> 00:00:04.730
We're now on problem number
5, on page 408.

00:00:04.730 --> 00:00:07.440
And they have this little
drawing here, and it says, on

00:00:07.440 --> 00:00:12.350
the disk shown above, a player
spins the arrow, this little

00:00:12.350 --> 00:00:14.660
blue arrow.

00:00:14.660 --> 00:00:17.430
A player spins the
arrow twice.

00:00:17.430 --> 00:00:25.010
The fraction a/b is formed,
where a is the number of the

00:00:25.010 --> 00:00:34.760
sector where the arrow stopped
after the first spin, and b is

00:00:34.760 --> 00:00:36.600
a number of the sector where
the arrow stopped after the

00:00:36.600 --> 00:00:37.850
second spin.

00:00:42.750 --> 00:00:46.070
On every spin, each of the
numbered sectors has an equal

00:00:46.070 --> 00:00:48.010
probability of being
the sector on

00:00:48.010 --> 00:00:49.350
which the arrow stops.

00:00:49.350 --> 00:00:51.780
What is the probability that
the fraction a/b is

00:00:51.780 --> 00:00:52.410
greater than 1?

00:00:52.410 --> 00:00:58.330
So they want to know the
probability that a/b is

00:00:58.330 --> 00:01:00.850
greater than 1.

00:01:00.850 --> 00:01:04.420
Well, the first thing you need
to realize is, this is just a

00:01:04.420 --> 00:01:07.020
random number generator.

00:01:07.020 --> 00:01:09.720
The probability that any number
between 1 and 6 is

00:01:09.720 --> 00:01:12.820
equal, so this could just be
a roll of a six sided die.

00:01:12.820 --> 00:01:17.820
And saying well, if I roll a
six sided die twice, what's

00:01:17.820 --> 00:01:22.110
the probability that the first
roll is going to be larger

00:01:22.110 --> 00:01:23.150
than the second roll, right?

00:01:23.150 --> 00:01:26.060
Because in order for this
fraction to be greater than 1,

00:01:26.060 --> 00:01:28.820
the numerator has to
be greater than the

00:01:28.820 --> 00:01:29.510
denominator, right?

00:01:29.510 --> 00:01:32.700
Or, you could just take a/b is
greater than 1, and multiply

00:01:32.700 --> 00:01:34.626
both sides by b.

00:01:34.626 --> 00:01:38.650
And that's the same thing as
the probability that a is

00:01:38.650 --> 00:01:41.460
greater than b.

00:01:41.460 --> 00:01:44.120
So we can set up a little table
and we could say, well,

00:01:44.120 --> 00:01:46.800
what's the probability of
getting each of these numbers

00:01:46.800 --> 00:01:47.840
on the first roll?

00:01:47.840 --> 00:01:51.160
And then given that probability,
or given that you

00:01:51.160 --> 00:01:54.640
got, let's say, a 2 on the first
roll, what are the odds

00:01:54.640 --> 00:01:57.090
that the second roll is going
to be less than the first

00:01:57.090 --> 00:01:58.190
roll, right?

00:01:58.190 --> 00:02:12.610
So let's say spin, call this
a spin, 1, 2, 3, 4, 5, 6.

00:02:12.610 --> 00:02:16.525
What's the probability of
getting each of these spins?

00:02:25.610 --> 00:02:27.210
I'm just making up
notation as I go.

00:02:27.210 --> 00:02:29.390
But, hopefully this is
making sense to you.

00:02:29.390 --> 00:02:30.550
So the probability of
getting any one of

00:02:30.550 --> 00:02:31.890
these is 1/6, right?

00:02:36.700 --> 00:02:39.810
They all have an equal
probability of happening.

00:02:39.810 --> 00:02:42.560
1/6.

00:02:42.560 --> 00:02:52.876
Now, given each of these, what's
the probability that

00:02:52.876 --> 00:02:59.170
soon. your second spin is going
to be less than the

00:02:59.170 --> 00:03:00.500
first spin?

00:03:00.500 --> 00:03:02.830
This is the second spin, b.

00:03:02.830 --> 00:03:04.290
Actually let's put an a here.

00:03:04.290 --> 00:03:07.000
The probability of a.

00:03:07.000 --> 00:03:08.720
That'll probably make
more sense to you.

00:03:08.720 --> 00:03:10.990
And then we want to know the
probably that the second spin,

00:03:10.990 --> 00:03:14.080
b, is less than a.

00:03:14.080 --> 00:03:18.690
Well, if I got a 1 the first
time, what's the probability

00:03:18.690 --> 00:03:21.980
that I get a number less
than 1 out of these?

00:03:21.980 --> 00:03:24.310
Well, is there any number
less than 1?

00:03:24.310 --> 00:03:25.650
There's 1, but that's not
even less than 1.

00:03:25.650 --> 00:03:29.700
That's equal to 1, so there's a
0 chance that I get a number

00:03:29.700 --> 00:03:31.610
less than 1, right?

00:03:31.610 --> 00:03:34.670
Because there is no number less
than 1 that I can get.

00:03:34.670 --> 00:03:38.320
If I got a 2, well there's only
one number less than 1

00:03:38.320 --> 00:03:39.310
out of the six, right?

00:03:39.310 --> 00:03:40.470
That's 1.

00:03:40.470 --> 00:03:41.720
So there's a 1/6 chance.

00:03:44.190 --> 00:03:45.110
A 3.

00:03:45.110 --> 00:03:48.610
If I got a 3 on the first spin,
I can only get a 1 or 2

00:03:48.610 --> 00:03:50.200
on the second spin, right?

00:03:50.200 --> 00:03:52.470
So that's a 2/6 chance.

00:03:52.470 --> 00:03:54.440
2/6.

00:03:54.440 --> 00:03:56.600
If I got a 4, I could
get a 1, 2, or 3.

00:03:56.600 --> 00:03:57.530
That's a 3/6.

00:03:57.530 --> 00:03:59.500
I think you see the
pattern here.

00:03:59.500 --> 00:04:03.360
There's a 4/6 chance of getting
something less than 5.

00:04:03.360 --> 00:04:07.570
And there's a 5/6 chance of
getting something less than 6.

00:04:07.570 --> 00:04:13.230
And so, what's the combined
probability now for each of

00:04:13.230 --> 00:04:13.860
the scenarios?

00:04:13.860 --> 00:04:18.410
So what is the probability that
I get a 1, and then I get

00:04:18.410 --> 00:04:19.950
something less than 1?

00:04:19.950 --> 00:04:22.220
Well, you just have to multiply
these probabilities.

00:04:22.220 --> 00:04:23.530
So that's a 0.

00:04:23.530 --> 00:04:26.590
What's the probability that I
get a 2, and then something

00:04:26.590 --> 00:04:28.170
less than 2?

00:04:28.170 --> 00:04:33.045
It's 1/6 times 1/6
which is 1/36.

00:04:33.045 --> 00:04:34.960
The probability that
I get a 3, and then

00:04:34.960 --> 00:04:36.760
something less than 3?

00:04:36.760 --> 00:04:37.600
Multiply them.

00:04:37.600 --> 00:04:39.350
It's 2/36.

00:04:39.350 --> 00:04:41.230
I think you see the pattern
here again.

00:04:41.230 --> 00:04:48.210
3/36, 4/36, and then 5/36.

00:04:48.210 --> 00:04:50.670
5/36 is the probability
to get a 6, and then

00:04:50.670 --> 00:04:53.450
something less than a 6.

00:04:53.450 --> 00:04:58.760
So in general, the probability
that I get my first spin is

00:04:58.760 --> 00:05:01.990
greater than my second spin is
going to be the sum of these

00:05:01.990 --> 00:05:02.910
probabilities, right?

00:05:02.910 --> 00:05:07.610
Because any one of these
scenarios would satisfy a

00:05:07.610 --> 00:05:08.500
being greater than b.

00:05:08.500 --> 00:05:10.830
So I just add up these
probabilities.

00:05:10.830 --> 00:05:14.780
So the denominator for
all of them is 36.

00:05:14.780 --> 00:05:17.220
It says 0/36, right?

00:05:17.220 --> 00:05:25.620
So it's essentially 1 plus
2 plus 3 plus 4 plus 5.

00:05:25.620 --> 00:05:27.530
Now let me add carefully
because this is where I

00:05:27.530 --> 00:05:31.460
historically mess up my
problems. 1 plus 2 is 3.

00:05:31.460 --> 00:05:33.770
3 plus 3 is 6.

00:05:33.770 --> 00:05:35.990
6 plus 4 is 10.

00:05:35.990 --> 00:05:37.510
10 plus 5 is 15.

00:05:37.510 --> 00:05:42.990
So that equals 15/36.

00:05:42.990 --> 00:05:45.360
And that is choice you a.

00:05:47.890 --> 00:05:49.440
Move on to the next problem.

00:05:56.900 --> 00:05:59.160
We're on problem number 6.

00:05:59.160 --> 00:06:02.670
Which of the following tables
shows a relationship in which

00:06:02.670 --> 00:06:05.350
w is proportional to x?

00:06:05.350 --> 00:06:07.190
All right, so let's just
write them all out.

00:06:07.190 --> 00:06:22.180
So choice a, if we have wx, so
they have 1, 3, 2, 4, 3, 5.

00:06:22.180 --> 00:06:24.250
So w is proportional to x.

00:06:24.250 --> 00:06:26.190
Well, that also means that
x is going to be

00:06:26.190 --> 00:06:28.200
proportional to w, right?

00:06:28.200 --> 00:06:31.400
So in this case x is 3 times.

00:06:31.400 --> 00:06:34.750
So here we have times 3.

00:06:34.750 --> 00:06:35.350
0, 3.

00:06:35.350 --> 00:06:38.950
Here we have times 2 and
here we have times 5/3.

00:06:38.950 --> 00:06:42.000
So we're multiplying by a
different factor every time.

00:06:42.000 --> 00:06:44.960
So w is not proportional
to x and x is not

00:06:44.960 --> 00:06:46.630
proportional to w.

00:06:46.630 --> 00:06:49.020
I'm just trying to figure out
what do I have to multiply w

00:06:49.020 --> 00:06:49.920
by to get x?

00:06:49.920 --> 00:06:51.810
What would I have to multiply
x by to get w?

00:06:51.810 --> 00:06:54.730
They all have to be the same
in order for these two

00:06:54.730 --> 00:06:55.810
variables to be proportional.

00:06:55.810 --> 00:06:58.450
So choice a is not right.

00:06:58.450 --> 00:07:00.450
Choice b.

00:07:00.450 --> 00:07:05.710
w, x, 3/9.

00:07:08.270 --> 00:07:14.120
Let's see what I'm doing,
3, 9, 4, 16, 5, 25.

00:07:14.120 --> 00:07:18.130
It looks like, in every scenario
here, we squared w to

00:07:18.130 --> 00:07:20.430
get x or w is the square
root of x.

00:07:20.430 --> 00:07:21.720
But they're not proportional
because here we

00:07:21.720 --> 00:07:23.610
multiplied by 3.

00:07:23.610 --> 00:07:26.500
Here we multiplied by 4, and
here we multiplied by 5.

00:07:26.500 --> 00:07:30.400
So once again, it's not
going to be choice b.

00:07:30.400 --> 00:07:30.840
c.

00:07:30.840 --> 00:07:33.910
I will change colors
for variety.

00:07:33.910 --> 00:07:36.060
I changed it to brown.

00:07:36.060 --> 00:07:46.150
C w, x, 5, 10, so I
multiplied by 2.

00:07:46.150 --> 00:07:47.740
This is what I'm
multiplying by.

00:07:47.740 --> 00:07:50.080
It's not 10 times 2.

00:07:50.080 --> 00:07:54.120
6 to 18, I multiplied by 3.

00:07:54.120 --> 00:07:55.290
I already know this
is wrong, right?

00:07:55.290 --> 00:07:57.190
I multiplied by two
different factors.

00:07:57.190 --> 00:07:58.570
It's not choice c.

00:07:58.570 --> 00:08:01.300
Choice d.

00:08:01.300 --> 00:08:02.080
w.

00:08:02.080 --> 00:08:04.030
I did one of the later choices,
just to make sure we

00:08:04.030 --> 00:08:05.280
do a lot of work.

00:08:05.280 --> 00:08:08.510
Choice d is 7 to 21.

00:08:08.510 --> 00:08:11.480
I multiplied by 3 to do that.

00:08:11.480 --> 00:08:14.030
8 to 24, times 3.

00:08:14.030 --> 00:08:16.350
Looks good so far.

00:08:16.350 --> 00:08:19.860
9 to 27, multiplied by 3

00:08:19.860 --> 00:08:23.500
So, in every case, I multiplied
by the same factor.

00:08:23.500 --> 00:08:28.290
So w is proportionate to x and
x is proportionate to w.

00:08:28.290 --> 00:08:31.340
So d is our choice.

00:08:31.340 --> 00:08:33.409
I will see you in
the next video.

00:08:33.409 --> 00:08:35.763
And we don't have to worry about
e because we know that d

00:08:35.763 --> 00:08:36.659
is our choice.

00:08:36.659 --> 00:08:38.080
I'll see