Applied Mathematics

I entered a local newspaper contest where you have to predict the Oscar winners and whoever gets the most correct answers wins. So, my question is this: The categories were: Best Actor Best Actress Supporting Actor Supporting Actress Animated Film Director Best Picture Best Adapted Screenplay Best Original Screenplay so theres 9 categories with 5 nominees in each category. What are the chances of someone getting all 9 correct, stastistically speaking? I got 8/9 correct. There were 700 people who entered the contest. What are the odds that I would get this many right? The winner gets free movie tix for a year!

Can someone show me in a step-by-step way how the following partial differentiations were obtained?

hi every1~ I am doing a research project and someone has told me that a basic knowledge of stats would be required during the research. I am not certain how the knowledge of stats would help me and how it has anything to do with my sci. reserach project. FYI, my research project is based on the study of Nuclear Magnetic Resonance, and Lithium Ion Batteries. So far the previous research papers I've read have nothing to do with stats. But is there anything that I may encounter in the future? Thx.

Circle A is fixed at center (1,0) with a radius 1. Circle B, also with radius 1, rotates at one revolution per (2*PI) seconds. Circle B is always connected to circle A at a single point. If at t=0, circle B is centered at (3,0) and point P (point p is on the edge of circle B) is at (4,0), what is the equation for P's path? (It should be a heart). X=_________ Y=_________

[math]m_{t+h}-m_{t}=hm_t[/math], so [math]\frac{dm_t}{dt}=m_t[/math] I am told that you use differential equations to the get the differentiation above, but I don't see how. Can anybody see?

hi, I am having a little problem with conterminal angles. I know what they are as defined by my textbook as "...sum of there degree measure is 360 or a multiple of 360". But I am not certain about the "multipe of 360" part. According to what I've read, the rotation has to be multiple of 360. And that's pretty striaght-forward. But in the book following example contradicts the statement, as far as I am concerend: 870 - 360 = 510 510 - 360 = 150 It's stated that 870 and 150 are coterminal angles. But 870+150 =1020 / 3 =340; not 360.

How do you guys create a random number? ..and ensure that a number is truly random. By that I mean for example: a set of dice should be predictable if all the physical variables are calculated. So that would make dice not truly random.

On the contrary of what the title suggests, this is an actual serious question born of curiosity that came to mind while spending a miserably dreary morning outside in the pouring rain waiting for the bus. Is there a greater chance of a mass getting hit by a raindrop if said mass is moving or stationary? I can't work out the answer. Is there some advanced math formula for stuff like this?

How can I solve the equations above using matrixes to get [math](u_1, u_2, ... , u_8)=\left(\frac{9}{34},\frac{3}{34},\frac{1}{17},\frac{3}{34},\frac{3}{34},\frac{1}{17},\frac{3}{34}, \frac{9}{34} \right)[/math]? I tried substitution but it soon became confusing trying to figure out which I had to substitute with which. Is there a systematic process I can use?

found some interesting stuff about 4d cube and its visualization, please comment and reply if you have any suggestions more to visualise it http://lordofnet.blogspot.com/2006/01/experience-4d-cube.html

The answer for the (i) is 0.049, which I got by evaluating Poisson pdf [math]\frac{e^{-3}3^{0}}{0!} = e^{-3} \approx 0.049[/math], but I'm not sure what to do for (ii) and (iii). The answers are (ii) 0.0446; 0.9826 and (iii) 0.2798. I just don't know how the answers were obtained.

I have made a correlation between group A and B and the pearsson coefficient constant, r, is at 0.97. The values are expression levels and hence they are non-parametric. I wonder how can i calculate the p-value of this correlation between group A and B? I know how to calculate the p-value for the difference between group A and B, but not for the correlation between group A and B. Thanks for any inputs!

hi there, have just completed an exam, but got a little question, i was given two sets of data displayed in a table, the first were rankings for the acessibility to a tourist site and the other were figures for how many visitors visited the site, now i obviously ranked the second column accordingly, but was i suppose to re-rank the first column, given the fact we have been taught to rank both columns to carry out the test effectively????

When u flip a coin . there are three possible events E1= Head E2=Tails E3=landing on its side now P(E3) must be really small. but even if its small, imagine the number of times coins have been flipped!!!. there must have been a coin landing on its side. Just wanna know if there is any record of that ever happening.

[math]\frac{1-sinx}{1+sinx} = (secx - tanx)^2[/math] The solution by solving the right side: [math]=(\frac{1}{cosx} - \frac{sinx}{cosx})^2[/math] [math]=\frac{1}{cos^{2}x} - 2\frac{sinx}{cosx} + \frac{sin^2{x}}{cos^{2}x}[/math] This is the question: How did I get to join all the [math]cos^{2}x[/math]? Because the middle one is only [math]cosx[/math]? Can anyone help me here? [math]=\frac{1-2sinx+sin^{2}x}{cos^{2}x}[/math] [math]=\frac{1-2sinx+sin^{2}x}{1-sin^{2}x}[/math] [math]=\frac{(sinx-1)(sinx-1)}{(1-sinx)(1+sinx)}[/math] [math]= \frac{1-sinx}{1+sinx}[/math]

Hello guys. I was doing my math review in preparation for my Advanced Trigonometry exam, and I encountered this question with a difficulty. When there were 1000 hares ([math]N_h = 1000e^{kt}[/math]), the number of foxes was increasing so that [math]N_f = 74e^{0.08t}[/math]. How many years will it take for the number of foxes to reach 10% of the number of hares? I know I have to use the Natural logarithms to solve this question, but I'm not sure what I should do? If you guys can give me hints, that would be great, or I'll have to ask my teacher when I go back to school.

I came up with a cheap formula to solve the surfice of any triangle. Though I'm not sure if it is correct. I wonder if you 1337 guys could check it.*points to sig*

A problem I come to in electronics is I can't design certain circutes (I make simple ones) because I can't use capacitors or inductors while accurately predicting their effects. (I'm self-taught in these things) The reason is this: Calculus. I am familiar with most concepts below calculus, but the "function" and "derivitive" things are still somewhat vague to me. Formulas containing these things are used in capacitors, transformers, etc. It seems to me, if I have looked at it right, that a calculus problem is like a little machine that keeps repeating and running through a changing variable causing a gradual curve, graphing the effect being studied. …

Is there an alternative to using pi in calculating area/circumference? I'm curious if a method has ever been explored that can measure the area of a circle as perfectly as a square, even if it is complicated.

While we are told that g = 9.81 m/s/s, this is only an approximation and isn't necessarily always true when we do precise calculations. Since, by the Universal Gravitation Laws, acceleration is determined by the mass of each object and the distance between the objects, we can't necessarily use a "fixed" gravitational acceleration of 9.81, since as we are free-falling gravity's acceleration changes as a function of distance. In fact, even mass changes as we accelerate. I've always wondered how we could compute the true free-fall for an object of mass m as it falls. Any ideas?

Just to see if my notion of randomness is relatively correct, i ask, what is randomness? Is it possible to have perfectly random relations in a finite set. If that sounds uncomfortable, i iterate with modifications,... Is it possible to have a perfect random number generator. The question arised when in the middle of a conversation about the random generators in programming languages like c, i learnt that these generators generate the so called random numbers by carrying out a finite number of mathematical operations on some time varying variable like say the least significant Integer of the second indicator(For example, take the integer which indicates the sec…

Dear all, I have two independent and non normalized samples where one sample has n=30 and the other has n= 1. Due to both samples don't have a normality distribution so i have to use non-parametric methods. I plan using Mann-Whitney Test, but then it needs that both samples have to be larger than n=5 or both are lesser than n=5. In my case then i have n=30 and the other is n=1. What kind of statistical methods should i use to get a reliable answer? I thank you alot! Hope for a quick answer!

Hi. Unable to rescue by books at the moment, and several decades after the university years, cannot remember enough to calculate this : A paddle wheel with 1m² paddles (1m x 1m) is turned by a river flowing at 0.5 m/sec. What is the horsepower generated? -The paddle wheel is attached to a pier, the paddles submerge fully when at the low point.- Or, if someone can lend me the formulas, thanks! Miguel

Hey, it help me alot if you could give me an equation solved for a complex [math]z[/math] in the complex plane union with infinity (sorry I don't know the latex for that). I'm looking for an equation of the form z = an expression made of the 3 complex numbers that determine it. I've been trying to find something like this for a few days, any help is appreciated. Edit: By the way this is in Mobius geometry. The name aludes me of the plane, but basically the plane is the union of the complex plane and the point at infinity. Again, thanks for any help.

A parabola is defined at the locus of points equally distant from a point (called a focus) and a line (called the directrix). I would like to generalize on this idea. My questions are: 1) In 3-space, what is the locus of points equally distant from a point and a plane? (My guess is a paraboloid.) 2) In 3-space, what is the locus of points equally distant from a line and a plane? 3) In 3-space, what is the locus of points equally distant from two lines? Can any of you give me help in either computing or visualizing these loci?