[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.93,0:00:01.52,Default,,0000,0000,0000,,Welcome back.
Dialogue: 0,0:00:01.52,0:00:03.61,Default,,0000,0000,0000,,I tried to start doing problem\Nnumber 10 in the last video,
Dialogue: 0,0:00:03.61,0:00:04.80,Default,,0000,0000,0000,,but I realized I was running\Nout of time, so
Dialogue: 0,0:00:04.80,0:00:06.24,Default,,0000,0000,0000,,let me start over.
Dialogue: 0,0:00:06.24,0:00:07.52,Default,,0000,0000,0000,,Problem number 10.
Dialogue: 0,0:00:07.52,0:00:10.18,Default,,0000,0000,0000,,The Smith Metals Company\Nold machine makes
Dialogue: 0,0:00:10.18,0:00:15.19,Default,,0000,0000,0000,,300 bolts per hour.
Dialogue: 0,0:00:15.19,0:00:23.41,Default,,0000,0000,0000,,Its new machine makes\N450 bolts per hour.
Dialogue: 0,0:00:23.41,0:00:28.08,Default,,0000,0000,0000,,If both machines begin running\Nat the same time, how many
Dialogue: 0,0:00:28.08,0:00:31.42,Default,,0000,0000,0000,,minutes will it take the\Ntwo machines to make a
Dialogue: 0,0:00:31.42,0:00:33.33,Default,,0000,0000,0000,,total of 900 bolts?
Dialogue: 0,0:00:33.33,0:00:34.56,Default,,0000,0000,0000,,So the important thing\Nto realize is
Dialogue: 0,0:00:34.56,0:00:36.63,Default,,0000,0000,0000,,that they said minutes.
Dialogue: 0,0:00:36.63,0:00:39.58,Default,,0000,0000,0000,,So we could convert both of\Nthese rates to minutes now, or
Dialogue: 0,0:00:39.58,0:00:42.12,Default,,0000,0000,0000,,we could say how many hours is\Nit going to take, and then
Dialogue: 0,0:00:42.12,0:00:47.18,Default,,0000,0000,0000,,convert that to minutes after\Nwe have our answer.
Dialogue: 0,0:00:47.18,0:00:49.22,Default,,0000,0000,0000,,Actually, let's do it the second\Nway, let's say how many
Dialogue: 0,0:00:49.22,0:00:51.51,Default,,0000,0000,0000,,hours and then convert\Nthat to minutes.
Dialogue: 0,0:00:51.51,0:00:58.56,Default,,0000,0000,0000,,So let's say we want to\Nproduce 900 bolts.
Dialogue: 0,0:00:58.56,0:01:00.28,Default,,0000,0000,0000,,And how much are we going\Nto produce in each hour?
Dialogue: 0,0:01:00.28,0:01:02.80,Default,,0000,0000,0000,,Well, they're both running\Nat the same time, right?
Dialogue: 0,0:01:02.80,0:01:08.81,Default,,0000,0000,0000,,So in every hour, we're going to\Nproduce 300 plus 450 bolts.
Dialogue: 0,0:01:08.81,0:01:18.26,Default,,0000,0000,0000,,We're going to produce\N750 bolts per hour.
Dialogue: 0,0:01:18.26,0:01:21.50,Default,,0000,0000,0000,,Times, let's say x hours.
Dialogue: 0,0:01:21.50,0:01:24.53,Default,,0000,0000,0000,,The units might confuse you, so\Njust leave out the units.
Dialogue: 0,0:01:24.53,0:01:28.74,Default,,0000,0000,0000,,This is how many hours it takes\Nto produce 900 bolts, so
Dialogue: 0,0:01:28.74,0:01:31.46,Default,,0000,0000,0000,,you divide both sides by 750.
Dialogue: 0,0:01:31.46,0:01:36.62,Default,,0000,0000,0000,,You get x is equal to 900/750.
Dialogue: 0,0:01:36.62,0:01:38.35,Default,,0000,0000,0000,,Let's see what I can do here.
Dialogue: 0,0:01:38.35,0:01:44.04,Default,,0000,0000,0000,,See, if I divide the top and the\Nbottom by 30, the top will
Dialogue: 0,0:01:44.04,0:01:53.39,Default,,0000,0000,0000,,become 30 over-- and then the\Nbottom, 75 divided by 3 is
Dialogue: 0,0:01:53.39,0:01:57.54,Default,,0000,0000,0000,,20-- 75 divided by 3 is 25.
Dialogue: 0,0:01:57.54,0:02:00.28,Default,,0000,0000,0000,,So 30/25.
Dialogue: 0,0:02:00.28,0:02:02.89,Default,,0000,0000,0000,,Then I could-- let's see,\N5 is a common factor.
Dialogue: 0,0:02:02.89,0:02:04.55,Default,,0000,0000,0000,,I can do it all in\None fell swoop.
Dialogue: 0,0:02:04.55,0:02:06.59,Default,,0000,0000,0000,,So that's 6/5.
Dialogue: 0,0:02:06.59,0:02:10.52,Default,,0000,0000,0000,,So it's going to\Ntake 6/5 hours.
Dialogue: 0,0:02:10.52,0:02:11.68,Default,,0000,0000,0000,,That's how long it's\Ngoing to take us.
Dialogue: 0,0:02:11.68,0:02:13.47,Default,,0000,0000,0000,,How many minutes is that?
Dialogue: 0,0:02:13.47,0:02:15.91,Default,,0000,0000,0000,,Every hour is 1 minute--\NI mean, sorry,
Dialogue: 0,0:02:15.91,0:02:17.42,Default,,0000,0000,0000,,every hour is 60 minutes.
Dialogue: 0,0:02:17.42,0:02:18.56,Default,,0000,0000,0000,,It's getting late.
Dialogue: 0,0:02:18.56,0:02:20.70,Default,,0000,0000,0000,,So 6/5 hours.
Dialogue: 0,0:02:20.70,0:02:23.66,Default,,0000,0000,0000,,You just have to multiply it by\N60 to get how many minutes
Dialogue: 0,0:02:23.66,0:02:29.07,Default,,0000,0000,0000,,is equal to-- see, you can\Ncancel this 5, make this a 12.
Dialogue: 0,0:02:29.07,0:02:34.67,Default,,0000,0000,0000,,You get 6 times 12\Nis 72 minutes.
Dialogue: 0,0:02:34.67,0:02:37.73,Default,,0000,0000,0000,,And that is choice B.
Dialogue: 0,0:02:37.73,0:02:38.98,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:02:41.92,0:02:45.05,Default,,0000,0000,0000,,I've been using this yellow\Na while, let me switch.
Dialogue: 0,0:02:45.05,0:02:47.11,Default,,0000,0000,0000,,Problem 11.
Dialogue: 0,0:02:47.11,0:02:49.39,Default,,0000,0000,0000,,The table above gives the values\Nof the linear function
Dialogue: 0,0:02:49.39,0:02:51.62,Default,,0000,0000,0000,,g for selected values of t.
Dialogue: 0,0:02:51.62,0:02:54.13,Default,,0000,0000,0000,,Which of the following\Ndefines g?
Dialogue: 0,0:02:54.13,0:03:01.57,Default,,0000,0000,0000,,OK, so they say t and\Nthey say g of t.
Dialogue: 0,0:03:01.57,0:03:08.28,Default,,0000,0000,0000,,They go from negative 1, 0,\N1, 2, let's see, it's
Dialogue: 0,0:03:08.28,0:03:16.45,Default,,0000,0000,0000,,4, 2, 0, minus 2.
Dialogue: 0,0:03:16.45,0:03:19.09,Default,,0000,0000,0000,,So the one thing I always look\Nat is what g of 0 is because
Dialogue: 0,0:03:19.09,0:03:20.08,Default,,0000,0000,0000,,that tends to be interesting.
Dialogue: 0,0:03:20.08,0:03:21.70,Default,,0000,0000,0000,,Especially when I look at\Nall of the choices.
Dialogue: 0,0:03:21.70,0:03:24.27,Default,,0000,0000,0000,,All of the choices are of this\Nform, they're all of the form
Dialogue: 0,0:03:24.27,0:03:26.22,Default,,0000,0000,0000,,m times t plus B.
Dialogue: 0,0:03:26.22,0:03:28.29,Default,,0000,0000,0000,,Where m is the slope-- if you're\Nfamiliar with linear
Dialogue: 0,0:03:28.29,0:03:30.06,Default,,0000,0000,0000,,equations, you're familiar\Nwith this form.
Dialogue: 0,0:03:30.06,0:03:34.29,Default,,0000,0000,0000,,And so when t equals 0, g of t\Ntells you what the y-intercept
Dialogue: 0,0:03:34.29,0:03:36.04,Default,,0000,0000,0000,,is going to be, right?
Dialogue: 0,0:03:36.04,0:03:43.13,Default,,0000,0000,0000,,So let's see, g of\N0 is equal to 2.
Dialogue: 0,0:03:43.13,0:03:46.71,Default,,0000,0000,0000,,So that tells us that this\Nequation g of t is going to be
Dialogue: 0,0:03:46.71,0:03:51.62,Default,,0000,0000,0000,,equal to the slope times\Nt plus 2, right?
Dialogue: 0,0:03:51.62,0:03:56.17,Default,,0000,0000,0000,,Because when t was 0, all\Nwe had left with was 2.
Dialogue: 0,0:03:56.17,0:03:59.19,Default,,0000,0000,0000,,And so immediately, we can\Ncancel out all but the last
Dialogue: 0,0:03:59.19,0:04:00.92,Default,,0000,0000,0000,,two choices.
Dialogue: 0,0:04:00.92,0:04:05.47,Default,,0000,0000,0000,,So the last two choices, choice\ND is g of t is equal to
Dialogue: 0,0:04:05.47,0:04:07.46,Default,,0000,0000,0000,,minus t plus 2.
Dialogue: 0,0:04:07.46,0:04:10.91,Default,,0000,0000,0000,,And then the last choice\Nis g of t is equal to
Dialogue: 0,0:04:10.91,0:04:13.65,Default,,0000,0000,0000,,minus 2t plus 2.
Dialogue: 0,0:04:13.65,0:04:15.05,Default,,0000,0000,0000,,Let's see which one of\Nthese works, we can
Dialogue: 0,0:04:15.05,0:04:16.67,Default,,0000,0000,0000,,try out some numbers.
Dialogue: 0,0:04:16.67,0:04:19.45,Default,,0000,0000,0000,,So what happens when\Nt is negative 1?
Dialogue: 0,0:04:19.45,0:04:24.76,Default,,0000,0000,0000,,When t is negative 1, this\Nexpression becomes negative 1
Dialogue: 0,0:04:24.76,0:04:25.95,Default,,0000,0000,0000,,times negative.
Dialogue: 0,0:04:25.95,0:04:29.55,Default,,0000,0000,0000,,Negative negative 1 is positive\N1, so this becomes 3.
Dialogue: 0,0:04:29.55,0:04:31.08,Default,,0000,0000,0000,,That's not right.
Dialogue: 0,0:04:31.08,0:04:33.74,Default,,0000,0000,0000,,This one becomes negative\N2 times negative 1 is
Dialogue: 0,0:04:33.74,0:04:36.63,Default,,0000,0000,0000,,positive 2, plus 2.
Dialogue: 0,0:04:36.63,0:04:39.60,Default,,0000,0000,0000,,So this becomes 4.
Dialogue: 0,0:04:39.60,0:04:41.83,Default,,0000,0000,0000,,So we can immediately cancel\Nthis one out because it
Dialogue: 0,0:04:41.83,0:04:45.93,Default,,0000,0000,0000,,didn't-- here, for this g of t,\Ng of negative 1 equaled 3,
Dialogue: 0,0:04:45.93,0:04:47.98,Default,,0000,0000,0000,,and they tell us right here\Nit's supposed to equal 4.
Dialogue: 0,0:04:47.98,0:04:48.76,Default,,0000,0000,0000,,This one worked.
Dialogue: 0,0:04:48.76,0:04:50.30,Default,,0000,0000,0000,,And this is kind of the only\None that still works.
Dialogue: 0,0:04:50.30,0:04:52.75,Default,,0000,0000,0000,,It had a 2 for the y-intercept,\Nand when you
Dialogue: 0,0:04:52.75,0:04:54.66,Default,,0000,0000,0000,,evaluate it for just even\Nthe first point, you
Dialogue: 0,0:04:54.66,0:04:55.65,Default,,0000,0000,0000,,got the right answer.
Dialogue: 0,0:04:55.65,0:04:57.23,Default,,0000,0000,0000,,So that's the answer,\Nthe answer is E.
Dialogue: 0,0:04:59.76,0:05:01.01,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:05:06.65,0:05:08.54,Default,,0000,0000,0000,,OK, survey results.
Dialogue: 0,0:05:08.54,0:05:10.15,Default,,0000,0000,0000,,I guess I should draw this.
Dialogue: 0,0:05:10.15,0:05:14.22,Default,,0000,0000,0000,,I haven't read the question, but\Nit's probably important.
Dialogue: 0,0:05:14.22,0:05:16.44,Default,,0000,0000,0000,,Let's see, there's about\Nfive squares that way.
Dialogue: 0,0:05:19.63,0:05:33.95,Default,,0000,0000,0000,,So that means I have to draw\Nfour lines, that's 1, 2, 3, 4.
Dialogue: 0,0:05:33.95,0:05:36.72,Default,,0000,0000,0000,,And then eight lines\NI have to draw.
Dialogue: 0,0:05:36.72,0:05:39.79,Default,,0000,0000,0000,,1-- that's always the hardest\Npart, just drawing these
Dialogue: 0,0:05:39.79,0:05:49.32,Default,,0000,0000,0000,,diagrams-- 2, 3, 4-- and you're\Nlearning how to count--
Dialogue: 0,0:05:49.32,0:05:59.23,Default,,0000,0000,0000,,5, 6, 7-- almost\Nthere-- and 8.
Dialogue: 0,0:05:59.23,0:06:00.50,Default,,0000,0000,0000,,All righty.
Dialogue: 0,0:06:00.50,0:06:02.56,Default,,0000,0000,0000,,And then they say, these\Nare the grades--
Dialogue: 0,0:06:02.56,0:06:04.44,Default,,0000,0000,0000,,the y-axis is grade.
Dialogue: 0,0:06:04.44,0:06:08.99,Default,,0000,0000,0000,,Grade 9, 10, 11, 12.
Dialogue: 0,0:06:08.99,0:06:12.06,Default,,0000,0000,0000,,The x-axis is distance\Nto school in miles.
Dialogue: 0,0:06:12.06,0:06:16.45,Default,,0000,0000,0000,,1, 2, 3, 4, 5, 6, 7, 8.
Dialogue: 0,0:06:16.45,0:06:17.39,Default,,0000,0000,0000,,And these are the points.
Dialogue: 0,0:06:17.39,0:06:20.22,Default,,0000,0000,0000,,1 comma 10 is right here.
Dialogue: 0,0:06:20.22,0:06:23.33,Default,,0000,0000,0000,,2 comma 9.
Dialogue: 0,0:06:23.33,0:06:25.77,Default,,0000,0000,0000,,2 comma 11.
Dialogue: 0,0:06:25.77,0:06:29.26,Default,,0000,0000,0000,,3 comma 10.
Dialogue: 0,0:06:29.26,0:06:32.38,Default,,0000,0000,0000,,3 comma 12.
Dialogue: 0,0:06:32.38,0:06:36.44,Default,,0000,0000,0000,,4 comma-- let's see,\N4 is at 10 and 11.
Dialogue: 0,0:06:36.44,0:06:40.29,Default,,0000,0000,0000,,5-- they have one point at 11.
Dialogue: 0,0:06:40.29,0:06:45.64,Default,,0000,0000,0000,,6 has three points right\Nhere, 10, 11, and 12.
Dialogue: 0,0:06:45.64,0:06:47.08,Default,,0000,0000,0000,,Let's see.
Dialogue: 0,0:06:47.08,0:06:50.77,Default,,0000,0000,0000,,There's a point here,\Nhere, here.
Dialogue: 0,0:06:50.77,0:06:52.47,Default,,0000,0000,0000,,And then a point\Nhere and here.
Dialogue: 0,0:06:52.47,0:06:54.71,Default,,0000,0000,0000,,Now we can start the problem.
Dialogue: 0,0:06:54.71,0:06:57.49,Default,,0000,0000,0000,,The results of a survey of 16\Nstudents at Thompson High
Dialogue: 0,0:06:57.49,0:06:59.68,Default,,0000,0000,0000,,School are given in\Nthe grid above.
Dialogue: 0,0:06:59.68,0:07:03.30,Default,,0000,0000,0000,,It shows the distance to the\Nnearest mile that students at
Dialogue: 0,0:07:03.30,0:07:05.18,Default,,0000,0000,0000,,various grade levels\Ntravel to school.
Dialogue: 0,0:07:05.18,0:07:07.51,Default,,0000,0000,0000,,So this is miles.
Dialogue: 0,0:07:07.51,0:07:08.76,Default,,0000,0000,0000,,And this is grade.
Dialogue: 0,0:07:10.74,0:07:13.43,Default,,0000,0000,0000,,According to the grid, which\Nof the following is true?
Dialogue: 0,0:07:13.43,0:07:15.01,Default,,0000,0000,0000,,So I'll just read them out.
Dialogue: 0,0:07:15.01,0:07:17.18,Default,,0000,0000,0000,,A, there's only one student\Nwho travels
Dialogue: 0,0:07:17.18,0:07:18.60,Default,,0000,0000,0000,,two miles to school.
Dialogue: 0,0:07:18.60,0:07:20.06,Default,,0000,0000,0000,,Let's see, two miles.
Dialogue: 0,0:07:20.06,0:07:22.05,Default,,0000,0000,0000,,False, there's two students.
Dialogue: 0,0:07:22.05,0:07:24.50,Default,,0000,0000,0000,,There is this guy\Nand this guy.
Dialogue: 0,0:07:24.50,0:07:25.60,Default,,0000,0000,0000,,So it's not A.
Dialogue: 0,0:07:25.60,0:07:28.54,Default,,0000,0000,0000,,Choice B, half of the students\Ntravel less than
Dialogue: 0,0:07:28.54,0:07:31.50,Default,,0000,0000,0000,,four miles to school.
Dialogue: 0,0:07:31.50,0:07:34.25,Default,,0000,0000,0000,,So that's-- less than four miles\Nis everyone to the left
Dialogue: 0,0:07:34.25,0:07:35.45,Default,,0000,0000,0000,,of this line, right?
Dialogue: 0,0:07:35.45,0:07:38.49,Default,,0000,0000,0000,,And this is actually\N1, 2, 3, 4, 5.
Dialogue: 0,0:07:38.49,0:07:43.80,Default,,0000,0000,0000,,5 out of 16 is not half, so\Nwe know it's not choice B.
Dialogue: 0,0:07:43.80,0:07:47.64,Default,,0000,0000,0000,,C, more 12th graders than 11th\Ngraders travel six miles or
Dialogue: 0,0:07:47.64,0:07:49.89,Default,,0000,0000,0000,,more to school.
Dialogue: 0,0:07:49.89,0:07:54.56,Default,,0000,0000,0000,,So they're saying more 12th\Ngraders than 11th graders.
Dialogue: 0,0:07:54.56,0:07:57.11,Default,,0000,0000,0000,,So six miles or more.
Dialogue: 0,0:07:57.11,0:08:00.53,Default,,0000,0000,0000,,So let's see, six miles or more\Nis anything to the right
Dialogue: 0,0:08:00.53,0:08:01.31,Default,,0000,0000,0000,,of this line, right?
Dialogue: 0,0:08:01.31,0:08:03.09,Default,,0000,0000,0000,,That's six miles or more.
Dialogue: 0,0:08:03.09,0:08:05.67,Default,,0000,0000,0000,,There are three 12th graders.
Dialogue: 0,0:08:05.67,0:08:07.22,Default,,0000,0000,0000,,And how many 11th graders\Nare there?
Dialogue: 0,0:08:09.85,0:08:13.14,Default,,0000,0000,0000,,There are two 11th graders.
Dialogue: 0,0:08:13.14,0:08:14.77,Default,,0000,0000,0000,,I think that is correct.
Dialogue: 0,0:08:14.77,0:08:18.28,Default,,0000,0000,0000,,More 12th graders than 11th\Ngraders travel six or more
Dialogue: 0,0:08:18.28,0:08:19.54,Default,,0000,0000,0000,,miles to school.
Dialogue: 0,0:08:19.54,0:08:24.43,Default,,0000,0000,0000,,Six or more miles, three 12th\Ngraders, two 11th graders.
Dialogue: 0,0:08:24.43,0:08:28.42,Default,,0000,0000,0000,,That's our answer,\Nour answer is C.
Dialogue: 0,0:08:28.42,0:08:31.00,Default,,0000,0000,0000,,Next problem.
Dialogue: 0,0:08:31.00,0:08:34.95,Default,,0000,0000,0000,,I don't know if I'll have time\Nfor this one, I'll try.
Dialogue: 0,0:08:34.95,0:08:37.52,Default,,0000,0000,0000,,Problem 13.
Dialogue: 0,0:08:37.52,0:08:42.43,Default,,0000,0000,0000,,How many positive three digit\Nintegers have the hundreds
Dialogue: 0,0:08:42.43,0:08:47.96,Default,,0000,0000,0000,,digit equal to 3 and the units\Ndigit is equal to 4.
Dialogue: 0,0:08:47.96,0:08:51.19,Default,,0000,0000,0000,,So it's going to be\Nlike 3 blank 4.
Dialogue: 0,0:08:51.19,0:08:53.41,Default,,0000,0000,0000,,So how many numbers are here?
Dialogue: 0,0:08:53.41,0:08:57.63,Default,,0000,0000,0000,,Well, how many digits can\Nwe stick in for that?
Dialogue: 0,0:08:57.63,0:09:01.24,Default,,0000,0000,0000,,Well, we could put a\N0, a 1, 2, 3, 4, 5,
Dialogue: 0,0:09:01.24,0:09:03.94,Default,,0000,0000,0000,,6, 7, 8, or 9 there.
Dialogue: 0,0:09:03.94,0:09:06.24,Default,,0000,0000,0000,,We could put any of those\Nin that middle spot.
Dialogue: 0,0:09:06.24,0:09:09.50,Default,,0000,0000,0000,,And there are 10 digits we can\Nput there, so there are 10
Dialogue: 0,0:09:09.50,0:09:10.23,Default,,0000,0000,0000,,possibilities.
Dialogue: 0,0:09:10.23,0:09:12.64,Default,,0000,0000,0000,,There are 10 positive three\Ndigit integers that have the
Dialogue: 0,0:09:12.64,0:09:16.06,Default,,0000,0000,0000,,hundreds digit equal to 3 and\Nthe units digit equal to 4.
Dialogue: 0,0:09:16.06,0:09:17.90,Default,,0000,0000,0000,,That's choice A.
Dialogue: 0,0:09:17.90,0:09:20.74,Default,,0000,0000,0000,,That's one of those problems\Nthat you question yourself
Dialogue: 0,0:09:20.74,0:09:23.14,Default,,0000,0000,0000,,because it seems maybe\Neven too easy.
Dialogue: 0,0:09:23.14,0:09:25.42,Default,,0000,0000,0000,,I'll see you in the\Nnext video.