I know that in the long run you can never win at roulette. The casino will always win, even if you are using the Martingale technique (that doubles your bet with every loss).

But I am curious about how big the probability is that:

* when you play 60 times on black

* the roulette ball will fall on red or zero 11 times in a row

My quick calculation says is 2,44% ( = ( 2^(60 - 11) * (1 + (60 - 11)) - ( 60 - 1) - (((60 - 2) - (11 + 1))/2 * ((60 - 2) + (11 + 1))) )/ 2 ^ 60), but I am pretty sure it is not totally correct.

Who can correct me please? ]]>

It is given that there are four cases, 2 of which are identical, and that one of the cases is a domino on both A and B.

I'm not sure why there are only four cases or what they should be. ]]>

Am new to this forum, so Im not sure if this is the right place for these kind of question, but if someone is able to help it would mean very much to me.

I have a very important exam in a few days, and while I thought I got it, I got shocked when I was looking on previous graded exams to see what I could work on in the final days. And when I came to the part about resolutionmethod and counterexamples for predicate logic on one exam I realized that either there is something I dont understand, or they actually gave me a bad exam (Its soposed to be highest grade).

The picture look kinda bad since I changed a few words on my native language manually and had to refit it for the upload. So just ask if there is something I can clearify.

The question on the exam is as follows:

"Is the following true? If it is, then show that with the resolutionmethod, if it is not true then show that with a counterexample."

You can see the subquestions A and B and under that the answers to each subquestion in the picture.

One thing I dont get if this is actually correct is that when doing resolutionmethod you dont have to use all parts of the conclusion? In this case only \lnot q(a) is used and not \lnot s(a).

Other than that I get subquestion A. With B I first of all cant see why it wouldnt be possible to use only {a} to make a counterexample? And second it looks to me as q(b)=1 kind of negates the premise?

I would be extreamly greatful if someone could help me understand. I really want to get this and it is also hugely important for my studies.

With kind regards

Joonteee ]]>

Part (a) and part (b) is pretty easy but for part (c) I don't know how you would start the problem, I tried to look online for examples but all I found are general equations.

Any help would be appreciated.

Edit: The projected gradient descent is defined as [tex] x_{k+1} = \prod_X (x_k - \tau_k \nabla f(x_k)) [/tex] where [tex] \prod_X(x)[/tex] is orthogonal projection of [tex]x[/tex]on [tex]X[/tex] and [tex]\tau_k[/tex] is the step size. I have also attempted to run the first iteration but I am stuck to trying to do the projection. I don't know how to do [tex]\prod_X((1 -1)^T)[/tex]

Branch A: val = 10, x = 3, y = 4.5

Branch B: val = 26, x = 2, y = 0

Branch C: val = 26, x = 0.5, y = 3

Branch D: val = 20, x = 2, y = 3.4

Branch E: val = 30, x = 6, y = 3

Branch F: Infeasible

So I understand that I can prune branch E by optimality and branch E for infeasibility. However, I don't know if I am able to prune other branches (since the variable are non-integer) or will I be able to continue branching. ]]>

(*an ambiguous statement, I know, let me give you an example)

I'll pose this logic question to all of you experts out there:

In higher education healthcare, the terms "inversely proportional" and "directly proportional" are used many times over, usually to discus some physics law that is being applied to physiology.

Many look like this.

i.e.:

The statement is made that A is

therefore;

(as long as C is greater than or equal to 1) ***Correction: as long as C > 0 *****

However.....what if the equation looked like this:

A = B - C

?????????

It

is A still inversely proportional to C?

Why? or Why not?

Why? or Why not?

Thanks in advance for anyone willing to tackle this question that is probably much to simple for this category.

~Chris (ChaosCG) ]]>

Regards,

Fateme.

IMG_20181211_021446.jpg

Question is "Explain what it means for a set of vectors S={v1,v2,v3....vk} to be linearly independent."

My answer was, "The set of vectors must have trivial solutions (no non trivial solutions). This means the linear combination of the span a1v1+a2v2....+akvk=0 will give us all a1,a2...ak = 0 such that ov1+0v2+...0vk=0. Thus linearly independent."

I found that the answer I inputted about the linear combinations was correct, but my professor marked it wrong. Can anyone tell me where I went wrong? Or is my answer right and he accidentally marked it wrong? ]]>

Thanks ]]>

"Let n be a positive integer. Inside a convex polygon of perimeter 1 afinite number of line segments is drawn such that their total length is strictly greater than n. Showthat there exists a line that intersects at least 2n + 1 of the segments." ]]>

Consider a homogeneous linear ODE with constant coefficient: y''-9y=4+5sinh(3x), and the homogeneous solution is given by y

But I don't know how to find out the particular solution, and the answer is y

Sorry for my poor English and thanks for your help! ]]>

If for example, I have 20 specific 1/3 octave frequencies I am looking at, I can figure out a percentage of which of the 20 frequencies fall in tolerance fairly easily.

However, for the frequencies not in tolerance, I want to calculate how much they are in tolerance (how close was it to tolerance). Also, even if some frequencies are in and out of tolerance, what is the overall percentage in tolerance.

Each frequency is measured in dB, so I believe these are logarithmic...I am having difficulty wrapping my head around this so any help would be appreciated.

To have some sample numbers, lets say tolerance is 34.0 to 36.0 dB for each frequency band. lets look at four frequency values:

1. 35.0 - 100% in tolerance

2. 35.9 - 100% in tolerance

3. 36.1 - is out of tolerance, but actually very close to being in tolerance

4. 33.9 - is out of tolerance, but actually very close to being in tolerance

Two of the frequencies above (1&2) are 100% within tolerance, the other two are not. However, the two out of tolerance (3&4) are

Size of the largest component (when node 1 is deleted) = Number of nodes in the largest component, after node 1 is deleted/ Number of nodes in the largest component

Size of largest component, node 1 is deleted = 0.53

Size of largest component, node 2 is deleted = 0.85

Size of largest component, node 3 is deleted = 0.88

Size of largest component, node 4 is deleted = 0.94

Size of largest component, node 5 is deleted = 0.94

Size of largest component, node 6 is deleted = 0.94

Size of largest component, node 7 is deleted = 0.94

When I want to calculate robustness, do I have to average of all the above values?

Formula given to calculate robustness: Unique Robustness Measure(𝑅-index) , defined as𝑅 =1 /𝑁 ∑𝑆 (𝑄) (limit Q=1 to N)

where 𝑁 is the number of nodes in the network and 𝑆(𝑄)is the fraction of nodes in the largest connected componentafter removing 𝑄 = 𝑁𝑞 nodes using a given strategy. Thevariable 𝑞 is a current fraction of deleted nodes against thetotal initial number 𝑁 of network nodes. The 𝑅-index thusencompasses the whole attack process, not just one momentof damage at a current fraction q

Please let me know, if I am calculating robustness in the right way

Thank you ]]>