Rate equation Puns

I tried to reverse engineer the drop rate formula based on today's newspost.

The approach used is almost identical to the one used to reverse engineer the Telos droprates, so for those interested please read that Reddit post: https://www.reddit.com/r/runescape/comments/7c9n5a/analysing_telos_data_and_the_solved_drop_rate/

The resulting formula is: 1/round(1M/(1000 + 10*enrage + 25*streak)).

I am currently unsure how LoTD impacts these drop rates.

Let's put this in a table and compare to published values:

Note: this table uses 1/drop_rate to better highlight how close the formula is.

I know Ryzen is the preferred CPU, but is there a way to do some math to get a round about on it? Which is more important, L3, cores, or frequencies and how much more important us it over the others?

Bay Street economists typically pull their punches, making the haymaker aimed at the Bank of Canada last week hard to ignore.

“Let us be blunt: Having achieved full employment, Canada no longer requires extraordinarily stimulative monetary policy,” Warren Lovely, National Bank’s chief debt strategist, and Stéfane Marion, the bank’s chief economist, wrote after Statistics Canada released its latest batch of hiring data on Dec. 3.

Employers added 154,000 jobs in November , far more than most forecasters were expecting, putting total employment back to where it would have been if the COVID-19 crisis hadn’t interrupted the trend early in 2020. Even more startling was the jobless rate, which plunged to six per cent from 6.7 per cent, and now sits at a level some economists associate with “full employment,” a statistical nirvana where it’s assumed that everyone who wants a job has one, and, therefore, any additional growth would stoke price pressures.

The jobs numbers have changed the weather ahead of the Bank of Canada’s final interest-rate decision of the year on Dec. 8. The Canadian dollar surged half a cent in a matter of seconds after the Labour Force Survey’s release, a signal that the odds over the timing of higher interest rates shifted in the aftermath of the latest Labour Force Survey, despite weaker oil prices and widespread trepidation about what the Omicron variant could mean for global trade.

Arlene Kish, director of Canadian economics at data firm IHS Markit, warned clients that her prediction the first post-pandemic rate increase would come in July is now probably wrong. With year-over-year increases in the consumer price index (CPI) approaching five per cent, a central bank whose sole job is keeping the CPI advancing at an annual pace of around two per cent will be hard pressed to coast into 2022, especially with the labour market flirting with full employment.

The United States Federal Reserve waved a white flag last week , as chair Jerome Powell conceded it was probably time to “retire” the characterization of inflationary pressures as transitory.

The benchmark interest rate was 1.75% when employment was last this high A jobless rate of six per cent is “consistent with the start of previous tightening cycles by the Bank of Canada,” said Charles St-Arnaud, a former Bank of Canada staffer who is now chief economist at Alberta Central, who advanced his prediction of when governor Tiff Macklem will raise the benchmark rate to April from an

There is a mathematical boundary that distinguishes a Wall Street Bet from an ordinary trade. This boundary may be described as the point at which the expected geometric growth rate of a trade becomes negative. The minimum fraction of ones available capital, w, needed to qualify a trade as a Wall Street Bet is found by solving the following equation for w:

(1+wb)^(p)(1-w)^(1-p)=1

Every trade can be described by the following variables:

r: an expected geometric growth rate, expressed as a fraction of capital. For example, if one’s expected geometric growth rate is positive 12%, then r=1.12. If the trade has a negative expected geometric growth rate of -15%, then r=0.85.

f: the fraction of capital invested. If one commits 20% of their capital to a trade, then f = 0.2. If one is all in, f=1.

b: the return earned on a winning trade, as a fraction of capital committed to the trade. For example, if the odds are 2:1, and your account is up $2,000 from $1,000 risked, then b = 2.

a: the loss from a losing trade, as a fraction of capital committed to the trade. For example, if one loses 50% of the money they spent on a trade, a = 0.5.

p: the probability of a winning trade. For example, if the probability of a winning trade is 69%, then p = 0.69.

The expected geometric growth rate is found by the formula: r =(1+fb)^(p)(1-fa)^(1-p)

The Wall Street gambler does not take partial losses however as they prefer to hold losing options until expiry. The loss from a losing trade, a, thus equals 1 as the Wall Street Bet’s losses are equal to the total portion f spent on the trade. The equation can thus be simplified:

r =(1+fb)^(p)(1-f)^(1-p)

The optimal amount f to commit to a trade is given by the Kelly Criterion. When a = 1, the Kelly Criterion is f = p+(p-1)/b. Plotting f on the x axis and r on the y axis, the Kelly Criterion gives us the maximum possible value of expected growth rate for a given probability p and odds b. Where the curve crosses the x axis, however, the expected growth rate of the trade equals zero. For values of f higher than this intercept, the trade is expected to lose money. It is thus a Wall Street Bet, and not a respectable trade. (https://i.imgur.com/39c5qH0.jpeg)

The trade that commits more to a single trade than Kelly and gives a growth rate of r < 1 is a Wall Street Bet, and the fraction of capital w above which the growth rate is negative

I'm trying to understand why area doesn't get taken into account for Bernoulli's equation. It kind of makes sense when I think about the fact that volume flow rate just assumes that the water has the right sort of pressure to keep the same amount of volume flowing constant, while Bernoulli's is a little more realistic. Still, it's kind of hard to convince myself that there would be no effect from area. So, does area affect pressure, or have a role in the Bernoulli's equation in some way, or do I really need to change how I think of it?

I once had an equation to find the hourly rate and OT rate from my over all day rate, but can't remember it off the top of my head.

It was something like 8xA(Bx4)= day rate to kind of give a general idea of how much an hour for 8 hours and if after 8 the time was considered OT. Hopefully this makes sense, and someone knows what I'm talking about.

Hello, is there a document where the interest rate models for each market are written down algebraically, with the parameter values? Or, where can I find the smart contracts that implement these models, presumably these will have the functional forms and parameters. Thank you!

Flying against the jetstream, a jet travels 4000 miles in 4 hours. Flying with the jetstream, the same jet travels 11,200 miles in 8 hours. What is the rate of the jet in still air and what is the rate of the jetstream?

Holding a sledge hammer closer to your person is easier than holding it with your arm extended (at the same height). What is this called? Thank you

So I understand that different reactions have different constants based on the different mechanisms of reactions but what role do the rate laws play in describing a reaction's rate?

After watching Chad Prep, he said that the equation for Flow Rate is Area x Velocity.

The formula for Flow Rate in the Kaplan book was

Q= (pi)(r^2)(change in Pressure)/ 8nL

How come these 2 formulas differ so much?

so I've seen earlier posts about Q402142 but I didn't really understand why increasing speed of blood flow wouldn't increase filtration of blood out of the caps. My understanding is: increasing v in Q = Av -> flow rate increases -> (from Bernoulli's) dynamic pressure increases so static pressure would decrease -> capillaries with lower pressures...get stuck here

Hello,

To start, I'll give a little background on my math knowledge so that people can know what I may and may not understand. I have general confidence that I am at least somewhat proficient with math concepts up to Calculus II. I am out of high school and have done Statistics, Calculus I and II, and all the disciplines preceding those, but I don't use them too often professionally or in my everyday life.

I had a personal curiosity while I was playing a game I like to play where I wanted to achieve a certain win rate. I was trying to come up with a way to calculate how many games it would take for me to achieve a certain win percentage given my total number of games, current win rate, and average win rate until I hit my goal. I'll give an example to further clarify:

I want to find a number of games left to go until I hit my goal, let's call it x.

I have 4 other known values that can be plugged in: my current win rate: r, my target win rate: t, my target average win rate until I hit my goal: a, and my total number of games played currently: g.

Let's say, just to plug some numbers in, my current win rate, r, is 48.7% (.487). I want to get a win rate, t, of 51% (.51). Lately, I've been playing with a win rate, a, around 54% (.54), and I have played 4601 games. I want to find x, how many games do I have to play at that 54% rate until I hit that 51% mark? (note these numbers are random, I don't want a numeric answer to this specific question, just help with the procedure to find the answer to different values)

I've been trying to think about how to make an equation for that, and I'm not even sure that there one equation that can find that for me. I'd love some help with this, even if it's just pointing out some concepts that might be helpful. Remember, this is a personal thing, it's not for homework or anything, so I'm in no real rush for answers. If you are sending your answer in the form of an equation, it'd be good for clarity's sake that you use the already assigned x, r, t, a, and g variables.

Thank you for the help!

Hey guys,

When I was trying to figure out the spice production rate for space stage, I have unintentionally created an equation as to how many seconds you make with one crate.

This equation how many seconds per spice.

1÷(x÷3600)

X= the amount of spiced produced on an hourly basis. (I can't really if it was just the city itself or a plant was a whole when you finalized your city building on a colony planet).

https://preview.redd.it/q3qd7umvrkx61.png?width=973&format=png&auto=webp&s=d720c6cd7bdfda274623af50105c762a39ac9957

Hello fellow physicists,

I'm in college studying physics, and I struggle with the following problem:

I have to solve this:

The rate at which a body in a colder environment cools is proportional to the 
difference between its temperature and that of the environment. If the 
temperature of a body located in a constant temperature environment equal to 20 
◦C, decreased by 120 ◦C to 70 ◦C in a period of one hour, calculate the required
 time so that the body temperature of 120 ◦C to reduced to 30 ◦C, after 
formulating the D.E. which describes the problem.

My professor starts solving the equation this way:

The D.E. describing the problem is:
- dθ/dt = h * (θ - θa)  (1)
where h is the ratio constant and θa is the ambient temperature. 
The negative sign left is set because it is a cooling problem.

>The negative sign left is set because it is a cooling problem.

I don't get that... What confuses me more is that he continues like this:

 Integral[θ1, θ2]( dθ / (θ - θα)) = Integral[t2, t1](h * dt)

https://prnt.sc/11ut5lg

Where did the minus sign go?

Why do I have to put a minus sign in the first place at (1)?

There is a mathematical boundary that distinguishes a Wall Street Bet from an ordinary trade. This boundary may be described as the point at which the expected geometric growth rate of a trade becomes negative. The minimum fraction of ones available capital, w, needed to qualify a trade as a Wall Street Bet is found by solving the following equation for w:

(1+wb)^(p)(1-w)^(1-p)=1

Every trade can be described by the following variables:

r: an expected geometric growth rate, expressed as a fraction of capital. For example, if one’s expected geometric growth rate is positive 12%, then r=1.12. If the trade has a negative expected geometric growth rate of -15%, then r=0.85.

f: the fraction of capital invested. If one commits 20% of their capital to a trade, then f = 0.2. If one is all in, f=1.

b: the return earned on a winning trade, as a fraction of capital committed to the trade. For example, if the odds are 2:1, and your account is up $2,000 from $1,000 risked, then b = 2.

a: the loss from a losing trade, as a fraction of capital committed to the trade. For example, if one loses 50% of the money they spent on a trade, a = 0.5.

p: the probability of a winning trade. For example, if the probability of a winning trade is 69%, then p = 0.69.

The expected geometric growth rate is found by the formula: r =(1+fb)^(p)(1-fa)^(1-p)

The Wall Street gambler does not take partial losses however as they prefer to hold losing options until expiry. The loss from a losing trade, a, thus equals 1 as the Wall Street Bet’s losses are equal to the total portion f spent on the trade. The equation can thus be simplified:

r =(1+fb)^(p)(1-f)^(1-p)

The optimal amount f to commit to a trade is given by the Kelly Criterion. When a = 1, the Kelly Criterion is f = p+(p-1)/b. Plotting f on the x axis and r on the y axis, the Kelly Criterion gives us the maximum possible value of expected growth rate for a given probability p and odds b. Where the curve crosses the x axis, however, the expected growth rate of the trade equals zero. For values of f higher than this intercept, the trade is expected to lose money. It is thus a Wall Street Bet, and not a respectable trade. (https://i.imgur.com/39c5qH0.jpeg)

The trade that commits more to a single trade than Kelly and gives a growth rate of r < 1 is a Wall Street Bet, and the fraction of capital w above which the growth rate is negative

The equation is: $13440 =

(1000*((1+R)^12))

+ (1000*((1+R)^11))

+ 1000*((1+R)^10)

+ 1000*((1+R)^9)

+ 1000*((1+R)^8)

+ 1000*((1+R)^7)

+ 1000*((1+R)^6)

+ 1000*((1+R)^5)

+ 1000*((1+R)^4)

+ 1000*((1+R)^3)

+ 1000*((1+R)^2)

+ (1000*((1+R)^1))

You can think of r as a monthly growth rate, and 12% as the annual growth rate (13440 = (1000*12) *12%), is there a way to calculate R in the equation?

I calculated R to be 1.7313356809958% using trial and error, but there must be some other faster way ( a formula maybe, or just excel is fine too). I'd really appreciate any help, I've been racking my brain on this for a while.

Feel free to ask me for any other info!

EDIT: also not really homework per se, more like personal work? something I wanted to figure out.