Authentic voices. Remarkable stories. AOL On Originals showcase the passions that make the world a more interesting place.
Gwyneth Paltrow and Tracy Anderson spend time with women who've overcome hardship, injury, and setbacks to triumph in the face of adversity. We'll hear their inspiring stories firsthand, whether fighting back from a career-ending injury or transforming their lives and bodies through diet and exercise.
Enter the graceful but competitive world of ballet through the eyes of executive producer, Sarah Jessica Parker. This behind-the-scenes docudrama reveals what it takes to perform on the ultimate stage, the New York City Ballet. Catch NYCB on stage at Lincoln Center.
The Future Of Us is a powerful original series from television personality, futurist, filmmaker and techno-philosopher, Jason Silva. In this series, Silva shares his excitement around recent discoveries and inventions.
ACTING DISRUPTIVE takes viewers inside the businesses and passion projects of Hollywood’s top celebrities.
They say every picture tells a story and AOL On's new original series My Ink proves it. Travel along as some of the world's greatest athletes bring their tattoos to life through exclusive interviews and visits to their favorite tattoo parlors.
Explore what it means to be human as we rush head first into the future through the eyes, creativity, and mind of Tiffany Shlain, acclaimed filmmaker and speaker, founder of The Webby Awards, mother, constant pusher of boundaries and one of Newsweek’s “women shaping the 21st Century.”
Discover crowdfunded small business success stories with author, comedian, and entrepreneur Baratunde Thurston.
Go behind-the-scenes with racing's hottest, young talent, 17-year-old Dylan Kwasniewski, as he aspires to make it in the #1 motorsport in America – NASCAR
Follow Scott Schuman, the Sartorialist, from the streets of NYC to the capitals of Europe on his quest to photograph and document the best in culture and fashion.
Iconic potter, designer, author and personality Jonathan Adler shares his unique perspective on creativity. Showcasing the inspiration Jonathan finds in the most unlikely people and places, Inspiration Point will add style, craft and joy to your life.
Serving Innovation gives a fresh look into the stories and passions that motivate some of the most innovative tastemakers in America.
A documentary directed by Alex Winter exploring the Napster downloading revolution; the kids who created it, the bands and businesses that were affected and its impact on the world at large.
Nicole Richie brings her unfiltered sense of humor and unique perspective to life in a new series based on her irreverent twitter feed. The show follows the outspoken celebrity as she shares her perspective on style, parenting, relationships and her journey to adulthood.
We are on the section 8 on the 7th test; we’re almost done on this book. So let’s start problem 1: If 6700=100x6k+7 then k equals what? So let’s divide both sides of this by 100. So you get 100 and cut these two zeroes so you get 67 is equal to 6k plus 7 and I just divide both sides by 100. Subtract 7 from both sides you get 60 is equal to 6k, divide both sides by 6 you get 10=k that’s choice C.
Problem two, if three more than n is a negative number, so n+3 is a negative number that’s what that says. And the five more than n is a positive number, so n+5 is greater than 0. Which of the following could be the value of n? So n+3 is negative, n+5 is greater so n+3 has got to be greater than or has to be less than (-3). This means that n is less than (-3). How do I get that, I subtracted 3 from both sides in this equations, besides if I subtract 5 from both sides of this equation I would get that n is greater than (-5). So you have to be greater than (-5) and less the (-3), what’s the only number that I could take off that’s that. Well and there’s a lot of numbers but a simple one is (-4). Alright (-4) is less than (-3) and if draw a number line this is (-3), (-4) and (-5).
So (-4) is less than (-3) and it’s greater than (-5) so that’s the answer, choice B. And you could try it out with (-4), (-4)+3=(-1), so that works, (-4)+5=1 so that works.
Problem three, in the figure above, the line like that it tells us this is x, this is y and then they tell us, let see in the figure above if x=70 and y=40 and the dotted line bisects the angles with measure x and y degrees what is the volume z? Okay so the dotted line. Instead of drawing dotted line I’m going to drag green lines.
So this green line will bisect this angle so it goes right in between. So if bisects the angle, what is the measure of this angle right here? It’s going to be half of this angle that it bisects it. So this whole thing is 70 so this is going to be 35 degrees. Similarly this other green line is going to bisect y right here. So if it bisects it, what this angle going to be? It’s going to be half of angle y and they tell us angle y is 40 and I wrote that I just wrote over it. So this has to be 20 degrees because it’s half of the full y and they say what is the value of z? Well z is just this whole thing, so if this angle plus this angle so its 55 degrees and that’s choice E.
Problem four, a piece of fruit is to be chosen at random from a basket of fruit, the probability that the piece of fruit chosen will be an apple is 2/5. So apple, the probability of an apple is equal to 2/5. Which of the following could not be the number of pieces of fruit in the basket? So the secret here is, you take 2/5 and whatever 2/5 is times the number of fruit; 2/5 times the number of fruit has to equal the number of apples. And implicitly, I mean there’s not going to be a fractional number of apples in the basket you can’t pick up a piece of an apple.
So this is going to have to be an integer, the number of apples. So 2/5 times sum number is going to be an integer then this number has to be divisible by 5, it make sense. You know if 2/5, if there were 10 fruits then this is going to be equal to 4. If they are 20 fruit then this is going to be, what’s 2/5 of 20? It’s going to be 8 but if there were 6 fruits to or if we thought the number of fruit was 6, 2/5(6) is 12/5 that means that there are 2 2/5 apples that’s not right. So we have to find is the number fruit, it has to be some number divisible by 5. And if you look at the choices, they gave you 20, that’s divisible by 5, 35 is divisible by 5. Its choice C, 52 that’s not divisible by 5 and then the other two choices 70 and 80 are divisible by 5. So only C is not divisible by 5 so that’s our choice that could not be the number of fruit in the basket and you can figure it out. If there are 52 fruits and 2/5 were apples you got a fractional number of apples and that’s not cool.
Next problem, problem five, a square and an equilateral of triangle have equal perimeters. If the square has lengths of side three what is the length of one side of the triangle? So square and a triangle have equal perimeters. And a square has sides of length 3; so 3, 3, 3, 3, so what’s its perimeter? Its 3+3+3+3 that’s 12, the perimeter is 12. Well this triangle is also going to have a perimeter of 12 but it’s going to have amongst 4 sides. Three equal sides because it is only three sides of a triangle. So it’s going to have 12 divided three so it’s going to be 4, 4, 4 and 4. So one side of a triangle has length four and that’s choice C.
Problem six, if x is equal to (-1) and k is greater than zero, which of the following has the greatest value? So choice A, is 2(k)(x), so k is positive, x is (-1) so this is going to be less than zero. So this is going to be a negative number and so we know that’s probably not going to be the answer. So if we look at all of the choices, the only positive choices are going to be the ones where I raised x to an even exponent. Because if I raise x to an odd exponent like let’s see choice C. Choice C is 6kx³=6k(-1³) because x is (-1) so that’s going to be (-6k). And we know k is a positive number. I mean really you can ignore the k, k is just the positive number it’s just kind of a scaling factor and they all have k in them so you just have to worry about the coefficient and the x terms.
So one thing we can, if x has an odd exponent on it, its going to be a negative number. So that’s not going to be the greatest value. So there is only two that has x with a, so you have 4kx², that’s choice B and then you have choice D which is 8kx^4. Well in both of this cases x²=1, (-1²)=1, (-1)^4 = 1 and if k is positive what’s bigger? 8k or 4k, well 8k is going to be bigger and I said they all have k in them so you could kind of ignore k because it’s a positive number. So the answer is choice D. I’ll see you in the next video.