# Search results

1. ### Combinatorial Probmlem

Let's work on the 2 weeks without replacement. There are C(9,3) ways to take out 3 people from a group of 9. This is where I get stuck. How can I calculate the odds of an individual being picked as 1 of 3 for the 2nd week? I have difficulty with understanding combinatorics/permutations. So...
2. ### Statistics: Confidence Intervals

Hey LearnFrench, How do they determine the 0.93 statistic in the first place? Assuming I have no life, how could I derive a table on my own? Thanks, HF08
3. ### Combinatorial Probmlem

Hi, I was reading a models book and read about a study where 9 analysts were chosen at random. Out of this group, 3 were selected for 2 week training, 3 were selected for 3 week training, and 3 were selected for 5 week training. Now I believe this models course had the idea that the first...
4. ### I have variance of response. How can I find it's MSE?

To All, I did a study and my response is defined as y = b1x1 + b2x2 + e where e ~N(0,1). I have y~N(4,33). In my data results, I did an ordinary least squares regression model for y = b1x1+b2x2+ e. The ANOVA is telling me the mean of y is 4, but MSE is 1. So here is my question. If I...
5. ### Show multiplicative order is multiplicative (told this was easy but I can't see it)

One more question I was trying to show this part rigorously. Do you have any ideas on how I might do this? I agree it is true, but I am wondering if I should shore it up exactly.
6. ### Show multiplicative order is multiplicative (told this was easy but I can't see it)

Thanks Thank you very much for your help. I wonder if your interesting observation may give us an easier proof. lcm(x,y) = x*y/gcd(x,y) = x*y. I think this is the last proof of that. I guess we could call that a lemma or corollary? Seems to me something easier to prove after we...
7. ### Show multiplicative order is multiplicative (told this was easy but I can't see it)

Thanks. Got it. (Almost got it?) Yes, you are correct. The notation was getting to me. I believe I am more clear on your presentation and comments now. Thank you. We know gcd(x,y) = 1 and x|k and y|k implies xy|k. Since ab^xy = 1, then k|xy. Hence, k= xy. Note: (a^y)^x = 1...
8. ### Show multiplicative order is multiplicative (told this was easy but I can't see it)

So how can I justify just saying a^k=1 and b^k=1 for some k? I doubt I can just say, suppose there is some k>x and k>y such that.... Clearly, number 2 is just saying that the order of ab is k. I think I can show (ab)^k=a^k b^k=1 easily. So I get x|k and y|k. Since gcd(x,y) = 1, then xy|k...
9. ### Show multiplicative order is multiplicative (told this was easy but I can't see it)

gcd(x, k ) = x, since x is the smallest integer such that a^x = = 1 mod n Right? Am I getting warmer? I have been stating x | k ?
10. ### Show multiplicative order is multiplicative (told this was easy but I can't see it)

Thanks for the reply and some comments of my own... I found your post confusing. This is what I have been doing. Staying true to the notation in my original problem. Part I. Let x = ord_n(a). So a^x = = 1 mod n iff gcd(a,n) = 1 Now, let y = ord_n(b). (a^y)x = = 1 mod n. Hence...
11. ### Show multiplicative order is multiplicative (told this was easy but I can't see it)

Thanks for your quick reply. Well, the way the problem is written is written with gcd ( ord_n(a), ord_n(b) ) = 1. So, does this condition imply gcd (a, b) = 1? Please tell me how to solve this with just (a , b) = 1. Perhaps there is something analogously that may be done. Thanks, HF08
12. ### Show multiplicative order is multiplicative (told this was easy but I can't see it)

Please help me prove this. I worked hard to make my notation somewhat easy to follow: If gcd ( ord_n(a) , ord_n(b) ) = 1 , then ord_n(a*b) = ord_n(a) * ord_n(b) Attempted proof: I can't see how to use the gcd condition. Which is bad news. I do realize the following. Let k1 =...
13. ### Show integrable is uniformly continuous

H = [a,b]\times[c,d] . f:H\rightarrowR is continuous, and g:[a,b]\rightarrowR is integrable. Prove that F(y) = \intg(x)f(x,y)dx from a to b is uniformly continuous. I initially ripped g(x) and f(x,y) apart and tried to show each was continuous. This failed. In short, I am...
14. ### Help me evaluate this limit

Thanks Excellent post HallsofIvy. I have found both limits to be 0. This is more useful than the definition approach. If you agree with what the limit is, I will mark this solved. Thank You, HF08
15. ### Help me evaluate this limit

[SOLVED] Help me evaluate this limit Part a: Show that f(x,y) = \frac{x^{4}+y^{4}}{x^{2}+y^{2}} as (x,y) -> (0,0) Part b: Similarily, show that f(x,y) = \frac{\sqrt{\left|xy\right|}}{\sqrt{x^{2}+y^{2}}} as (x,y)->(0,0) Lets work with Part a, shall we? I seemed to be...
16. ### 4 by 4 Inverse Matrix

Thanks Can you please provide some links to the n = 2 and n = 3 cases please? After that, I'll do the rest on my own. Thanks. HFO8
17. ### 4 by 4 Inverse Matrix

Inquiry: Is there a standard equation for a 4 by 4 inverse? I know that one exists for 3 by 3, 2 by 2, but I cannot find one in my text nor in my searches online. I know I could find one by using the Jordan-Gaussian Method. But, I would be more comfortable with knowing a 4 by 4 general...
18. ### Can you help me evaluate this limit?

Thanks (Slaps forehead). Thanks Rocophyics. Can I modify this thread to show solved? I am still new to this forum.
19. ### Can you help me evaluate this limit?

Almost there... Right. Now, this gives us \lim_{k\rightarrow \infty}\left(\frac{-1}{1+\frac{\sqrt{k^2+k}}{k}}\right) So, the next question is how to show that \lim_{k\rightarrow \infty}\left(\frac{\sqrt{k^2+k}}{k}}\right) = 1 . I tried l'hopital, but I wonder if there is another way? I...
20. ### Can you help me evaluate this limit?

Hf08 \lim_{k\rightarrow \infty}(k-\sqrt{k^2+k}) This should be right...
21. ### Can you help me evaluate this limit?

[SOLVED] Can you help me evaluate this limit? lim k -\sqrt{k^{2}+k} as k\rightarrow\infty I have evaluated the limit using computer technology and I know it should be -1/2. I have tried using something like the squeeze theorem but failed. My other attempt is to mutiply the limit by...
22. ### Prove ||B(x,y)|| = ||(x,y)|| for all x,y in R^2 (Rotations in R^2)

Solved This was easy! Thanks for your kind replies. My problem was the notation, after that, it just follows very quickly. Regards, HF08
23. ### Prove ||B(x,y)|| = ||(x,y)|| for all x,y in R^2 (Rotations in R^2)

Ah... I know what a vector and ordered pair is. So what they are really saying is this: Bx=x, right? If so, that makes alot more since then the (x,y) notation to me.
24. ### Prove ||B(x,y)|| = ||(x,y)|| for all x,y in R^2 (Rotations in R^2)

B = [cos\theta -sin\theta] ......[sin\theta cos\theta] for some \theta in R^{2}. (a) Prove that || B(x,y) || = || (x,y) || for all (x,y)\inR^{2} Question: What does B(x,y) and (x,y) notation mean? I have a result that says Let B=[b_{ij}] be an mxn matrix whose entries...
25. ### Inquiry: Find two lines in R^3 that are not parallel but do not intersect

To Mr. Hurkyl, I agree sir. It was more of a whim and wishful thinking. I shall consider my Calculus 3 text for this problem. Perhaps it has more tools for consideration than is provided in my current text. I will keep your comment in mind. Perhaps I should consult a linear algebra text...
26. ### Inquiry: Find two lines in R^3 that are not parallel but do not intersect

In other words, could I claim that there is some t such that l_{1}=l_{2}? This seems more direct. Sigh...I keep editing this. The latex should be saying l1=l2, but it's not working out right. I can't explain myself right if I can get this latex quick paste not to work right. I am going to...
27. ### Inquiry: Find two lines in R^3 that are not parallel but do not intersect

Let me ask this question in a new way I have obtained the following two lines. The brackets with numbers are vectors. Unfortunately, I was not able to put them in vertical notation. That is, pretend that the they are given in the correct notation. l_{1}=[4,0,4]+t[-4,0,4]...
28. ### Inquiry: Find two lines in R^3 that are not parallel but do not intersect

Gentlemen, I apologise if I seemed too sharp. Thank you for your posts. I agree with your points. First, I need to develope better communication skills. I would appreciate suggestions on being more clear. Second, I feel we are making progress. I do have a result about lines (actually it...
29. ### Inquiry: Find two lines in R^3 that are not parallel but do not intersect

I shall refer to another text than the one I am currently using. I feel as your comment as suggested, there is a more simple method than what I am doing, which is being needlessly complicated and stupid. HF08 PS - It is because the question in the section of my text is in love with cross...
30. ### Inquiry: Find two lines in R^3 that are not parallel but do not intersect

Okay, your point is taken sir, and I accept your criticism. However, I do feel your being a little cute in saying all I have to show is that they do not intersect and are not parallel. That is merely repeating what the problem implies. I may be learning, but that doesn't mean I am stupid...