How do I make the number to perfectly center to the circle in Google Slides?

I am using Google Slides to create some prototype designs.

If the circle is a bit small, the number would not be fit to the center.

What should I do?

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co.combinatorics – Why is the number of permutations of n adjacent transposition where the outputs are different equals $2^{n-2}$?

Maybe im wrong, but i just noticed that the different permutations of (1,2)(2,3)(3,4),…,(n-1,n) seems to be $2^{n-2}$ and i dont know why this is true. Can someone help if im right about this and explain a little bit?

e.g.: $n=4$, $(1,2)(3,4)(2,3) = (3,4)(1,2)(2,3)$ and $(2,3)(1,2)(3,4) = (2,3)(3,4)(1,2)$ but $(1,2)(2,3)(3,4)$ and $(3,4)(2,3)(1,2)$ gives unique outputs. So the number of different permutations is $2^{4-2}=4$, I checked it for 5, 6, 7 and gives the same pattern.

Can we create events for “n” number of office 365 accounts using one zap? (Zapier – Office365)

I need help regarding zap creation in zapier. I have been working on a meeting system and created a zapier app that will fetch all meetings from my system into office 365 calendar.

My problem is, if my client has 500 employees then all those 500 employees will have to create their own zap to sync my application with office 365 calendar.

For example, if I create a zap and add office 365 in to do list, then I have to provide the credentials of single office 365 account where I can send the meeting details but I want to send the meeting details to n number of office 365 accounts using same zap.

Please let me know about this solution that how can I solve this. Any help will be appreciated. Thank You

How to make infinit gmail accounts with a same number? | NewProxyLists

You do realize that a single Gmail address can be MANY Gmail addresses? Let’s say, for example, you have [email protected]. Well, that is ALSO [email protected], [email protected], etc., etc. this is because Gmail ignores the period.

In addition, you can ADD additional words to a GMail address by simply using a +. So, [email protected] can become [email protected], and it will go to the same inbox. Now, there are email address validations that will prevent this one from working in some cases, but not all.

probability – Find the number of ways of arranging the letters in the word ARTICHOKES

Find the number of ways of arranging the letters in the word ARTICHOKES if it must end in CH?

Find the number of ways of arranging the letters in the word ARTICHOKES if you make a five letter arrangement that must contain a T

Find the number of ways of arranging the letters in the word ARTICHOKES if the even-numbered positions must remain unchanged.

oracle – ORA-00932: inconsistent datatypes: expected CHAR got NUMBER

I am trying to SUBSTR the first 3 character in use this query -> CASE WHEN (RMSTMP_PNG.ota_activity_lotinfo.KEY = ‘TestProgram’) THEN TO_CHAR(SUBSTR(RMSTMP_PNG.ota_activity_lotinfo.VALUE,1,3)) ELSE 0 END AS Test1
But it return me this ORA-00932: inconsistent datatypes: expected CHAR got NUMBER
00932. 00000 – “inconsistent datatypes: expected %s got %s”. May i know what wrong in my query? I tried to use To_NUMBER or To CHAR, it also return me same error. Appreciate if someone could help on this issue.
Below is my query:

SELECT RMSTMP_PNG.ota_activity.EQP_ID,
SUM(CASE WHEN (RMSTMP_PNG.ota_activity.MESSAGE='Load lot success.' AND RMSTMP_PNG.ota_activity_lotinfo.KEY = 'Quantity') THEN 1 ELSE 0 END) AS LOT_ID,
SUM(CASE WHEN (RMSTMP_PNG.ota_activity.MESSAGE='Load lot success.' AND RMSTMP_PNG.ota_activity_lotinfo.KEY = 'Quantity') THEN TO_NUMBER(RMSTMP_PNG.ota_activity_lotinfo.VALUE) ELSE 0 END) AS QUANTITY,
CASE WHEN (RMSTMP_PNG.ota_activity_lotinfo.KEY = 'TestProgram') THEN TO_CHAR(SUBSTR(RMSTMP_PNG.ota_activity_lotinfo.VALUE,1,3)) ELSE 0 END AS Test1
FROM RMSTMP_PNG.ota_activity 
FULL OUTER JOIN RMSTMP_PNG.ota_activity_lotinfo ON RMSTMP_PNG.ota_activity.ID = RMSTMP_PNG.ota_activity_lotinfo.ID 
WHERE RMSTMP_PNG.ota_activity.MODIFIED_DATE >= to_date('27-Sep-2020')
AND RMSTMP_PNG.ota_activity.MODIFIED_DATE < to_date('27-Sep-2020') + 1 
group by RMSTMP_PNG.ota_activity.EQP_ID,RMSTMP_PNG.ota_activity_lotinfo.VALUE, RMSTMP_PNG.ota_activity_lotinfo.KEY
order by RMSTMP_PNG.ota_activity.EQP_ID

gr.group theory – Bound the number of the minimal generating set of group G by its abelianization

This is probably already well-known or too big to answer. Let $G$ be a finite group and $G^{ab}$ be the abelianization of the group G. Is there any bound on $d(G)=min{#Smid G=<S>}$ by using $d(G^{ab})$ without considering the order of $G$?

Thanks for any answer and comments.

algorithms – Is there a way to uniquely map every natural number x

Imagine you have a number x, when x ∈ (0, N). Is there any algorithm that can map x to y, so that y is also y ∈ (0, N) with the mapping being unique, and the distribution of all y is distributed pseudorandomly across the whole range? I know it’s possible by just generating a set from 0 to N, shuffling it, and using x as an index. I want to know if there is some smarter way to do this that doesn’t involve a memory footprint that is linear to x.

The Pigeonhole principle shows that this is impossible when y > x, and it is trivially possible when x = y (well… y := x), but is this possible in a manner when y is randomly distributed?

My first (bad) attempt in C# was to use a golden ratio and travel around a circle, since mathematically this is guaranteed to give a unique angle every time. In theory (phi * n) mod 360 is sort of random looking and unique. Sadly this only works if you have infinite precision and not at all when you have discrete buckets for the output, so this idea didn’t really work out, even when N = 255:

Code

Result

So out of pure curiosity I’m wondering – is there some beautiful algorithm to map this so that it doesn’t involve either a predefined list of candidate numbers or a list of already used numbers, or so on?

Trying to create a list that counts the number primes for each remainder class

Considier the remainder of the first $2500$ prime numbers by the numbers from $3$ to $30$, included.

  1. Calculate how many primes are in each remainder class. That is, create a list that for each number between $3$ and $30$, gives for each remainder class the number of primes in it.
    Example. the first $5$ primes are: $2,3,5,7,11$. If we consider the remainders by $3$, we have: $2,0,2,1,2$.
    That is: $1$ with remainder $0$; $1$ with remainder $1$ and $3$ with remainder $2$.

I am having trouble condensing my program because I need to create a list for each number between 3 to 30. How could I add the remainders $3$ to $30$ to my program before it counts how many primes are in each remainder class.

I shortened just to see what is happening (ie. I shortened $2500$ to $5$)

list = Sort(Flatten(Table(n, {n, 1, 5})));
PrimeQ(list);
primelist = 
Length(Select(list, PrimeQ)) ;
divide = Mod(Total /@ list, 3); 
remainder2 = Count(divide, 2)
remainder1 = Count(divide, 1)
remainder0 = Count(divide, 0)

results were:

    {2, 3, 5, 7, 11}
    {True, True, True, True, True}
    3
    1
    1