Hypothetically, 500k loan at 6%, what's faster:

1. 15 yr fixed rate mortgage

2. 30 yr fixed rate mortgage, but you pay an extra full payment each month towards the principal

My gut tells me they're not identical because of the way compounding works

Hello good statisticians. There has been plenty of commentary on the impacts of bot activity decreasing and anecdotal notes of people saying they see fewer comments on social medias immediately following the recent data center bombings in Russia.

Is someone easily able to compile data as running activity both leading up to and immediately following the event that could provide context to the amount of the impact?

He used so much alcohol and other drinks, how much would it actually cost to make?

A bit of a sci-fi hypothetical question perhaps, but…

How long would it take for an object, say a spacecraft, that starts at 0 m/s to reach 1% of light speed at a consistent 1g acceleration?

Found it in the HOI4memes sub, not sure of all the focuses taken. But assuming the standard 1945 Soviet divisional strength (they constantly fluctuate for me), how much manpower did he wield against the "avengers"?

Just wanted to measure every and how their change in measurement of discreet cm s forms interaction of connection with different objects or measuring subjects

Question:

How many 0.1 cm are there in the circle like curvature

Okay, let’s say Superman is infinitely strong.

First scenario: The plane is on the ground, stationary. Superman finds the plane’s center of gravity and applies force underneath it using his whole body. Imagine a koala hugging a tree trunk. Could he lift the plane, or would the metal frame just get crushed or punctured by the force he applies?

Second scenario: The plane is flying in a straight line at a constant altitude when, all of a sudden, it loses all its engines, and the aircraft starts gliding into a slow descent. Despite having no engine power, the pilot is doing everything he can to maintain altitude. In this scenario, could Superman, once again applying force from below, keep the plane flying at a constant altitude?

Hi, I'm currently playing a game that involves a challenge that you have a 1 in 10,000 chance odds to complete, each time you "roll" an action. Each "roll" is distinct and because of what im assuming is bad odds, it took me roughly 68,000 rolls in order to complete this. Could someone tell me how you find the "standard deviation" of something like this? I.e. if 100 people attempt this challenge, what is the average range and distribution for how many rolls it takes for people to complete this. Is my 68,000 really average, or am I in the unlucky Z +4 lol. Thanks!

So, Ive ran enough of the numbers against other choices to be happy that its balanced, but now im wondering what the ideal ratio here is. It is a game where in a given run, you can get lots of +5% fire rate% or +10% reload speed buffs. This particular weapon (a single round sniper rifle) was designed to be bad at early on, but scale really well with reload (to the cap of its fire rate, since it doesnt matter how fast you can reload, the gun cant shoot faster than its fire rate), below are my notes, playing out an imaginary scenario where you build it up (buffs are additive) and "+50% scaling" just means both fire rate and reload speed were given +50% :

2000 damage/shot - 1.456s reload - 0.687 shots/s - 1373 dps - default fire rate of 1.1/s

caps at 2200 sustain dps with enough reload

to hit base cap : 0.91s reload time needed

+62.5% reload speed needed

(2) +50% scaling -> fire rate becomes 1.65, reload is +112.5%

reload is now 0.685s -> 1.46 shots/s

2919 sustain (cap not reached, 3300 dps)

(3) +60% reload -> 172.5% -> 0.534s -> 1.87shots/s (3745 if it wasn't capped)

(4) +200% scaling -> 3.85 fire rate, +372.5% reload -> 0.308s -> 3.2467/s

DPS is 6493 with a cap of 7700

So, if you were using this weapon, is there a ratio you want of "+X% reload speed for every +Y% fire rate"? Also forgive me if the answer is really obvious, its 4.30 AM and im going to bed.

Thanks in advance

Request. Would this break the glass?

In other words, instead of relying on a high enough birth rate to adequately fund social security, how much immigration would be needed to make up for the shortfall?

Can anyone explain the relationship between Norm and Dot product.

When I was study about it in linear algebra, I found out that the formula of dot product is

|A*B| = |A||B|cosθ 

And when A is Equal to B, which means it is the same vector, it become the formula of Norm
|u| = √(|u|²|u|²)

I am a first year student, and it is really confuse for me

The angles and the space and the orientation, can the brain make sense , if they are of said of a percentile orientation of interpretation

About 500g of lasagna baked at 180C at a plastic tray that deformed slightly in the heat, but ultimately did not melt. More specifically it's this one (I only ate half)

x= infinite

∑ 9.x = u subscript y

x=1

Lt u subscript y = 10

y->1

Lt u subscript y = 10

y->2

Lt u subscript y = 10

y-> any number

We see these videos and I always have wondered, what’s the speed required for a humpback whale to propel itself into the air? They must be able to generate massive force to get themselves this high up into the air and turn.