If you're seeing this message, it means we're having trouble loading external resources on our website.

Jeżeli jesteś za filtrem sieci web, prosimy, upewnij się, że domeny ***.kastatic.org** i ***.kasandbox.org** są odblokowane.

Główna zawartość

Aktualny czas:0:00Całkowity czas trwania:9:59

We're on problem 210. A television manufacturer
produces 600 units of a certain model each month at a
cost to the manufacturer of $90 per unit. And all of the produced units
are sold each month. What is the minimum selling
price per unit that will ensure that the monthly profit--
revenue from sales minus manufacturer's cost to
produce-- on the sales of these units will be
at least $42,000. OK. So, they want to know the
minimum selling price. So, let's call that p. So how much are they going
to make per unit? p minus whatever
their cost was. p minus $90. That's how much they
make per unit. And they do that
for 600 units. And they say that this has
to be at least $42,000. So, this has to be greater
than or equal to 42,000. OK. So we get 600p minus--
what's 9 times 6? It's 54. And then we have one,
two, three 0's. 54,000-- Right? 9 times 6. Yep. --is greater than or
equal to 42,000. So then you get 600p. Let's add 54,000
to both sides. Has to be greater than or equal
to 54 plus 42 is 96,000. And just to simplify things,
let's divide both sides by 100. So, you get 6p. If you get two 0's here,
two 0's here. 6p has to be greater than 960. And then p has to be greater
than or equal to-- we don't have to worry about
this because it's a positive number. 6 goes into 96, 16 times, so it
goes into 960, 160 times. So the minimum selling price
is $160 which is choice d. Problem 211. If 4x plus 3y is equal to minus
2, and 3x plus 6 is equal to 0, what is
the value of y? Well this is a quick one. 3x would be equal to minus 6. So x is equal to minus 2. Substitute back here. 4 times minus 2, minus 8 plus
3y is equal to minus 2. Add 8 to both sides. 3y is equal to minus 2 plus 8. Or 3y is equal to 6. y is equal to 2. And so that is choice e. Problem 212. I'll do it in a different
color. 212. The data sets one, two, and
three above are ordered from greatest standard deviation to
least standard deviation in which of the following? OK. So they want us to order
them essentially. Greatest-- So, set one was
72, 73, 74, 75, 76. Set two is 74-- it says 74 a
bunch of times-- 74, 74. And then set three has 62, and
then 74, 74, 74, and then 89. So, standard deviation is how
much, on average, do the numbers vary from the mean. And all of these cases,
the mean is 74. I'm just eyeballing it. Let's see 89 is 15 more. Actually here the
mean isn't 74. So, first of all, every number
here is the mean. So, the standard deviation
is actually 0. So this is going to be-- they
want to know from greatest standard deviation to least
standard deviation. So, 2 is definitely the least
standard deviation. So that leaves us with choices
either b or d. And now have to figure out which
of these have a lower standard deviation. So here we can just eyeball
and say the average is 74. If you average this and this
you get 74, that and that you get 74. So, what's the difference
from 74? Here it's 2. Here it's 1. Here it's 0. Here it's 1. Here it's 2. You just want the magnitude,
how far away you are from 74 each time. And if you were to average these
numbers, you get 2 plus 1, plus 1 plus 2. That's 6 divided by 5. So, you get 6 over 5. You know they square-- you could
even do the variance if you really cared about it, you
could square these numbers. But you just want to get some
measure of, on average, how far is each of the numbers
from the mean. So here's 6 over 5. Let's see 2 plus 1, 3. Yep. 6-- and there's five numbers. And 6 over 5 is the standard
deviation there. What's the mean here? This is interesting. So, 74 to 89. Do I have those numbers right? Yeah. to go from 74 to 89 you
have to go plus-- let me add these up. You get 62-- actually what's
the average of 62 and 89? No, it's not 74. Let's see 2 plus 11 is-- well
I could just take the average-- I just want
to figure out the mean as fast as possible. So 89 and 62. 9 plus 2 is 11. 9 plus 6-- 151. You divide that by 2. The mean of these two
numbers are 75.5. So, at least if you're trying to
figure out the mean, that's going to be the same thing is
the mean of-- so actually let's just do this. It's 151. Let's just take the average
of everything. I tried to be cute, but it's
better to just be brute force. So, 62 plus 89 is 151, plus
74 times 3, divided by 5. Let's see. 74 times 3. 4 times 3 is 12. 7 times 3 is 21. 22. And then 222 plus 151 is 373. And then we're going to
divide that by 5. So, 5 goes into 373-- 7 times 5
is 35, 23, 5 goes into 23 4 times, 4 times 5 is 20. 3. 74.6. So the mean here is 74.6. This is going to have the
largest standard deviation because this is 0.6 from the
means, this is 0.6 from the mean, this is 0.6
from the mean. This number is 12.6
from the mean. And then this number is
14.4 from the mean. So, if you're to average these
numbers, you're going to get a bigger number than 6/5, but
let's just confirm it. So, 12.6 plus 14.4-- oh yeah,
you're definitely going to get a much bigger number because
when you summed all these up, you got a 6. When you just sum up the 12 and
the 14.4 you get-- 15-- you get 27. And then it's going
to get to 29. You divide that by 5. The standard deviation here
is going to be 4. So, 3 has the largest
standard deviation. 2 has the least. So, the
correct answer is d. I should've been able
to eyeball that. I shouldn't have had to go
through all that computation. I took too much time. That wouldn't have been
acceptable on the GMAT. Problem 213. Which of the following is the
lowest positive integer that is the divisible by all
of those numbers? So, it's 2, 3, 4,
5, 6, 7, 8, 8. So the lowest positive
integer that is divisible by all of those. So, one way to think about it is
let's just try to minimize our multiplication. If we're divisible bye 8,
then we don't have to worry about 2 and 4. Being divisible by
8 is enough. Likewise if we're divisible by
9, we don't have to worry about being divisible by 3
because we're definitely going to be divisible by 3. We need to be divisible by 7. If we're divisible by 6-- well,
if we're divisible by 8 and 9 then that means we're
already divisible by 2 and 3. And if we're divisible by 2 and
3 then we don't have to worry about 6. So, we only have to worry
about 5, 7, 8, and 9. So what are those numbers when
you multiply by each other? So if we do 8 times 9 is 72. 8 times 9 is equal to 72, we got
rid of those, times 7 is equal to 2 times 7 is 14. 7 times 7 is 49, plus 1 is 50. And that times 5. 4 times 5 is 20. 5 times 0 is 0. Bring down the 2. 5 times 5 is 25. So, it's 2,520. And that is choice c. And I'm out of time. See you in the next video.