Because it was the only major culture there. Japan is an island and Korea is a peninsula. So on one side you have China and on all other sides you have vast ocean. In terms of being influenced, there wasn't any other options.

It isn't the case that someone is always willing to buy at the same time someone wants to sell. What happens is if you want to sell your stock you can either find someone willing to buy it or you put out a sell order that basically is a notice saying "I'm willing to sell Y stocks for X amount of dollars." In which case you sit around and wait till someone is willing to fulfill that order.

On the flip side someone wanting to buy one can either grab one for those immediately willing to be sold or put in a buy order for a certain price.

So when you sell you're either fulfilling one of those buy orders or your putting in a sell order yourself and waiting for someone to buy it.

No. Fatalism makes no statement about purpose or intent. You can be fatalistic and think there is no point or fatalistic and think there is a point. And neither has anything inherently to do with death.

Fatalism is the believe that anything that happens is predetermined and inevitable.

Nihilism is the believe that nothing has inherent meaning or purpose.

Because sin and cos are about ratios, not pure side lengths. For example, 2/1, 4/2, 6/3 are all equal to 2 even though we are dealing with different numbers.

Sin is the same as opposite/hypotenuse and cos is the same as adjacent/hypotenuse.

So the equation is basically:

(opposite/hypotenuse)^(2) + (adjacent/hypotenuse)^(2) = 1

Even if the sides are different, the constraints of a right angled triangle (which is what it is based on, not the unit circle) make all the other sides change such that it still equals 1. Rearranging the equation we get:

opposite^(2)/hypotenuse^(2) + adjacent^(2)/hypotenuse^(2) = 1

opposite^(2) + adjacent^(2) = hypotenuse^(2)

Which is simply the pythagorean theorem.

There is only a finite amount of energy in fuel to be extracted to begin with. That places an upper limit on what your MPG can even be. So it can't simply go up forever without limit. And Whatever that limit is, there are diminishing returns meaning you get less and less an improvement over time.

Ok, and?

It's possible because it isn't impossible. There is no rule in physics or math that says it is impossible, which means it's possible.

And what it is, is basically saying that some subatomic particles can exist in different states at once.

For example, electrons have a property known as spin. Since they have spin they have direction (kind of like how the Earth spins and because of that, has a north and south pole). Since electrons have a direction, an electron can be "up" or "down."

Superposition says its possible for an electron to be put into a state where it is both up and down at the same time, and will only definitely be one (and not the other) when it interacts with another particle.

Said act says:

"that portion of said District included within the present limits of the city of Washington shall continue to be known as the city of Washington"

Washington is a city inside the District of Columbia.

That's why it's "Washington, DC", not "Washington DC"

Because town names are usually a local consideration, whereas a large geographical chunk of an entire nation is a national consideration.

I mean, you would agree that we wouldn't ever give two states the same name, right?

Well, the reason and logic behind it are in the proofs for it, of which there are several. I like this one:

https://upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Thales%27_Theorem.svg/180px-Thales%27_Theorem.svg.png

Since OA = OB = OC, ∆OBA and ∆OBC are isosceles triangles, and by the equality of the base angles of an isosceles triangle, ∠OBC = ∠OCB and ∠OBA = ∠OAB.

Let α = ∠BAO and β = ∠OBC. The three internal angles of the ∆ABC triangle are α, (α + β), and β. Since the sum of the angles of a triangle is equal to 180°, we have:

a + (a + B) + B = 180

2a + 2B = 180

2(a + B) = 180

a + B = 90

Because simply "Northwest" was already in use, historically, to refer to the Northwest Territory of the USA or, even today, the Northwest Territories of Canada.

Ok, but in terms of your question, it is a concept from a science fiction comedy author, not an actual scientific concept anyone expects to happen.

He wasn't and didn't, famously.

As for why he was as successful as he was, simply put, he was a great military leader with a sense of strategy, tactics, and organization, and his army was almost fanatical in terms of their loyalty to him.

There is no confidence that ChatGPT will provide accurate answers. That isn't even the goal of ChatGPT.

ChatGPT is essentially a language prediction model. You provide a prompt. Then, using all of its immense database of collected text, plus its machine learning algorithms, generates what it things should come after that prompt. But it has no conception of what is factually true, it only has strings of information.

For example, if you prompt it with "What is 2 + 2?" It will probably say 4. Not because it us doing a mathematical calculation, or understands what math is, or because it knows 4 is right, but because in all of its training data the text "2 + 2" is overwhelming followed by the text "4".

In fact, more sophisticated models can actually be more prone to giving less correct answers in some situations as illustrated here:

https://www.youtube.com/watch?v=w65p_IIp6JY

The gain is people do business with you versus another bank.

Because that process takes time, up to several days. And if it took several days for people to get money from their check no one would use it. So instead they give you the money immediately while the transaction is verified.

Yes, it allows for these loopholes, but people exploiting this in this manner are far and few between. It'd be more harmful getting rid of this loophole then allowing it.

They don't need food dye and we can leave them out. We choose to put dye to make them look more appealing or more in line with expectations.

It is also the average kinetic energy of the water molecules that is a main driver of volume as well, so the concepts are not unrelated.

>Liquids have a fixed volume regardless of temperature

https://www.researchgate.net/publication/344527033/figure/fig1/AS:944168385916929@1602118693482/Temperature-dependence-of-the-specific-volume-of-ice-and-water-plotted-based-on-Refs-15.ppm

"Flat" in this context means in terms of curvature. Using 2D as an example you can have a piece of paper which is 2D and flat or something like the surface of a balloon which is 2D and curved.

The problem is that, from the perspective of any beings that live on and are constrained by those 2D surfaces, the world just looks "flat" to them in both cases because any 2D beams of light are also constrained to the surface. The balloon case is curved, but it is curved through a third dimension which 2D beings cannot perceive.

Stepping back up into our 3D work, there is an open question as to whether our 3D space is "flat" or "curved" in the 3D sense. If it was curved, it would be curved through a fourth dimension which we cannot directly perceive, so how could we tell?

Stepping back down into 2D, our 2D beings could indirectly determine the curvature of their world through triangles. In the flat 2D world, any triangles they made would have angles whose sum always equals 180 degrees. But in the curved 2D world, you would be able to make triangles whose angles sum to greater than 180 degrees.

This property also works in 3D. If our universe is flat, then triangles all have angles that sum up to 180 degrees and if it is curved then they could sum up to greater than 180 degrees. By picking distant objects (such as far away stars and galaxies) and measuring the relative distances between those objects, we can calculate their angles. Within a certain margin of error, we've calculate that our universe is either flat or has a very very very very small amount of curvature.

Solids dissolve better in hot water because hot water has more space between the molecules to accommodate them. Gasses dissolve worse in hot water for the same reason: the extra space allows the gas to escape.

Yes. You want money tied to the dollar? Keep your dollars.

They gave up that sovereignty when they joined the Union as States.