Carlos F

So there problem states:

Suppose that a school has 20 classes:

16 with 25 students in each

3 with 100 students in each

1 with 300 students, for a total of 1000 students.

a)

What is the average class size?

b)

Select a student randomly out of the 1000 students. Let the random variable X equal the size of the class to which this student belongs, and define the p.m.f. of X.

c)

Find E (X), the expected value of X.

So for a), the average class size is 50 because there's 1000 students/20 classes, or it can be viewed as a weighted average: [16(25)+3(100)+1(300)]/1000. So this makes sense to me because if you were to take a student at random, they would belong to a class of 50 students on average.

For b), if X is the size of the class to which a student belongs, then X = is the set of random variables, which are the class sizes: {25, 100, 300}. So the p.m.f. is the probability of someone being in a class of 25, 100, and 300, respectively. There are 25*16 = 400, 100*3 = 300, and 300*1 = 300 students in each of the class sizes, so out of 1000 students, the respective probabilities are 0.4, 0.3, and 0.3, when x (the class size ) = 25, 100, and 300, respectively.

So f(x) = {0.4, 0.3, 0.3} for x = {25,100,300}

Thus, for c) the expected value E[X] = x1(f(x1))+...x3(f(x3)) = 25*0.4+100*0.3+300*0.3 = 130.

So this is saying that the expected outcome of choosing a student out of 1000 is that they belong to a class size of 130, right?

Clearly, 50 and 130 are not equivalent. So if 50 is the average class size, then wouldn't each student, on average, belong to a class of 50 students? Or is this saying that each class category, on average, has 130 students?

This is the part that isn't clear to me. Is there a very simple way of explaining this?

I dream to maybe become a college professor in math one day. Whether or not I do become one, though, I would be interested in what would be the best way to teach a child who is just starting from the ground up. I feel like our current way of being taught maths (as well as the order) is flawed here in the USA. Here is what I think. Let me know if you disagree or what you would change:

1.

Reading, writing

Numbers

2.

Logic and reasoning

Mainly sets, truth values, and arguments

3.

Addition, subtraction

Multiplication, division, fractions

Powers, roots

Factorials

Logarithms

4.

Plotting points on graph paper (2D) and a computer (3D)

5.

Basic algebra (just PEMDAS)

Word problems

6.

Geometry

Trigonometry

7.

Graphing different kinds of graph for discrete data

Graphing continuous functions (polynomials, then other ones)

8.

Probability

Statistics

9.

Precalculus

10.

Calculus I (differentiation and integration in 1 var)

11.

Linear algebra

Programming

12.

Calculus II (differentiation and integration in 2 vars, series, sequences, errors, etc.)

Calculus III (Same as the above, but in vector functions)

13. Differential equations

From here on, one could expand to whatever. Don't get me wrong. I want my children to have a childhood. If I realized I'm hurting them, then I'd probably stop. But I think it'd be fine as long as I allow them to have a social life. Moreover, I'm more interested in the idea of there possibly being a tree (or trees) of knowledge, starting from a very binary and Boolean set of rules to higher maths.

Does it vary due to Earth's ellipticity and tilt?

How can you mathematically determine how much of Earth is covered by sunlight rays ?

My precise definition of "covered" is how much of the area would be hit by the light vectors coming from the sun.

I know for a fact that at least more than half of Earth is covered by light. I just need to know what is/if there is a quantifiable way of showing how Earth is covered by sunrays in terms of vectors.

I also know that this ultimately depends on how big Earth is compared to the Sun and how far Earth and Sun are.

Thanks a lot.

So I smoked with my friend on Friday (about 4 days ago) and yesterday I found out I'm getting a drug test for a job today. I don't regularly smoke. I hadn't smoked in about a week or so and I've seldom smoked in the past few months because I don't have much time to. But when I found out yesterday I drank a whole thing of cranberry juice and took 1000mg of niacin last night before going to sleep. And I'm still drinking water right now and my test is in 2 hours. I'm thinking of taking a lot of vitamins soon. What will happen?

I e-mailed a potential employer today about becoming a teller and I asked her which time slots were available. She said "Tuesdays closing and MWF day shift." I'm not sure what that means. Also, I think it's a local bank so I don't know if their times are the same as your typical big national bank.

No estoy muy entrado en la politica mexicana porque naci y vivo en los EEUU. Sin embargo, ahora que hay elecciones en los dos paises, quiero estar al tanto de los dos lados. Vi dos entrevistas, una de Pena Nieto y la otra de Vazquez Mota, donde les pregutan, "Quieres ser presidente/a de Mexico?" y hacen todo lo possible para no responder eso. Por que es eso? Nunca habia visto eso en mi vida y no es algo que se ve aca en los EEUU.

We're all natural-born American citizens.

I think it's not permissible for underage people to ride a bus alone, especially if you're crossing the border into the USA. Both my sister and cousin are underage, which is why my parents want to send me there (I'm 20 years old).

They both have documentation so that if they ask me how my sister and I are related, it'd be easy cos I can show them my passport and whatnot, and I've even got pictures of both of us when we were little to further prove that we are, indeed, related.

However, for my younger cousin, who I'm also related to, it is harder for me to prove that we're related cos he's my mom's brother's son. My last names are Fernandez Felix, and his is Felix Piñon. I don't know if it would suffice to show that in the documentation. We don't want to risk it because it's a very long and expensive trip to Mexico. Thus, I want to know how easy/possible it is for me to get back to the USA with my cousin (and sister), given that we're still related and I'm legally an adult.

Also, is it OK to bring my laptop? I've heard of people getting their electronics taken away, either going or returning, and I don't want to risk that because I have a lot documents from college that I need, and I'm taking the laptop to do a little bit of studying while I'm over there. Also, I just don't want to lose my laptop.

Thanks

I used to use Ubuntu because I always found Windows to be really shitty. I moved out of my parent's, though, and they're more comfortable with Windows. So, I reinstalled Windows XP Professional for them, but now neither the sound or the USB ports work.

I went to this webisite:

http://en.kioskea.net/forum/affich-7670-no-sound-a...

and followed the directions carefully, but the computer is still exactly the same. I don't know what to do anymore. I just want to throw it out the window, but that's obviously not an option.

Hablo de los gritos que se oyen en los géneros como mariachi, banda, o norteña. ¿Se pueden encontrar fuentes academicas en el internet sobre este fenómeno? Gracias.

I'm in a bit of a pickle. My adviser mistakenly told me that I could minor in math and major in engineering by simply taking the upper math classes required for the minor. However, there is a prerequisite that I must take and, ultimately, my graduation would be held back about a semester. I've tried finding many ways of expediting my graduation if I were to do research and get a minor in math, like taking summer courses, but there doesn't seem to be a way around that.

I've been doing so well these past two semesters (about a 3.6 cumulative. gpa), especially in math (I haven't had anything lower than an A in any of my math classes) that I was accepted into a research program where they're going to let me do research in math. I've yet to decide, still, but it'd be either a pre-harmonics analysis research or research in fractals (I'd go to grad school afterwards and hopefully be able to find applications of either research topics to engineering).

However, if I can't graduate on time, will that affect me when applying to grad school, even though I was minoring in math and doing research? I'm currently majoring in mechanical engineering and I don't want a late graduation to affect me for grad school or a job if I decide later on I don't want grad school.

I guess what I'm essentially asking is if graduating with a minor in math and with some research done would outweigh graduating a semester or two late in terms of either going to grad school or getting a job.

The only reason I wouldn't consider going to grad school is because it would mean more time in school and not beginning a career soon. Originally, all I wanted to do was go to school to get a good job and make money. But I've become more interested in research and I know it's something I would enjoy and something that would ultimately pay off more, job-wise, in the future.

This is what my book says:

F=ma = -mgj where F and a are vectors and j is the vector component.

g= |a|, which is about 9.8m/s^2. Thus a=-gj

since v'(t) = a, we have v(t) = -gtj+C (t is the time variable and C is the position vector)

Where C=v(0)=v0 (v0, here, is a vector).

Therefore r'(t) = v(t) = -gtj + v0.

Integrating again, we obtain r(t) = -1/2gt^2j + tv0

If we write |v0| = u0 (the initial speed of the projectile, then

v0=u0cos(α)i+u0sin(α)j

and equation 3 becomes

r(t) = (u0cos(α))ti + [(u0sin(α)t-1/2gt^2)]j.

I can't see where they derived this from. Most of the book skips a lot of steps you you kind of just have to go over it over and over until you see why. I just can't see what I'm overlooking/not getting. Thanks in advance.

Oh, and just to clarify, α is the angle at which a particle is being thrown.

What is the typical amount needed or the typical range for a bank to provide a business loan in the midwest/Kansas?

I'm thinking of opening up a cafe-like business in my college town. Instead, though, it would be mostly frozen goods like shakes, fruit smoothies, etc.Oh, and this kind of business already exists, so it would actually be a franchise.

I think the total cost for opening such a store in a building that's already been used would be about $70,000 and about $200,000 if you're making the whole store from scratch (the building, mainly).

I can't see why

"If 0 ≤ an ≤ bn for n ≥ 1 and {bn} converges, then {an} converges." is false.

I'm in college, now, and fall semester I'll be living in apartments. I was considering many jobs, but due to the fact that I'm an introvert, I feel like any job involving me and many people would mean failure.

I considered housekeeping, since it would fit me perfectly - I have no problem cleaning (especially if I'm blasting music on my iPod), there are many big houses/mansions near my university, and usually there aren't people I have to interact with, and if there are, it's not constant.

The only drawbacks are that the classes at the university do not run past 6pm and those who do usually start at 4pm because they're labs that run for hours. I am aware that the best time to clean houses is in the morning, which I can't do since I have classes. Also, due to the fact that I'm a male, I'm sure there's a lower probability of me getting hired to do housekeeping.

My mom, who also needs a job, also considered being part of the business. I was thinking, thus, that I could run the business by getting a hold of houses, getting materials needed, and so forth. When I do have time, I would like to clean houses as well. My mom was thinking of being in charge of the cleaning, along with my sister, to help me pay for college and living, and to help herself as well.

So, what I think I'm asking are the following points:

1. What capital would I need to start something like this? What tools will I need?

2. What kind of housekeeping etiquette should I keep in mind?

3. What are some good cleaning methods I can learn, or where can I learn those methods?

4. What are the best ways to market/solicit to houses and how can I know which kinds of places would have people who are willing to pay for these services?

These really cute sorority girls are inviting me over tomorrow night that they usually "watch jersery shore and drink a bit."

I know the obvious answer is to go, but I need a little help on this sort of etiquette: Do I bring my own drink or do I go without one and take whatever they offer me? Thanks a lot.

I haven't figured out what's wrong. I wasn't here when this first started happening because I'm in college and I come back occasionally to visit my parents. Now, the letters get distorted. For example, the lower-case "n" looks like a short fat "T." Also, sometimes when I load a page I see tons of colors on the screen. It looks weird, sort of like this: http://i35.tinypic.com/34xz4.jpg

I'm using the latest version of Ubuntu (10.04) and I also have Kubuntu, which I've had on here since almost the very beginning.

I can't figure this out. The denominator of the function sort of makes sense as maybe the speed may not be more than 75mph for legal reasons, but here it goes:

Numerical and Graphical Analysis

A driver averaged 50 miles per hour on the round trip between Baltimore, Maryland and Philadelphia, Pennsylvania, 100 miles away. The average speeds for going and returning were x and y miles per hour, respectively.

(a) Show that y = 25x/(x-25)

(b) and (c) are easy to do, it was just a that no one I know has been able to answer correctly. I came up with a formula that was y = 100-x, which is different from this.

I don't have the manual with me, but is the code in there. Isn't it supposed to be on a sticker? I have a 1994 BMW 540i.

I need the code because my car's battery died out.

Thanks.

If I'm not mistaken,

Solid-state = slow write, fast read

Hard Drive = fast write, slow read

?