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(7, - 1)   =  (x, y)

sin θ   = y / r

We need to   find  r   =  √ [x^2 + y^2 ]  = √ [ (7)^2 + (-1)^2 ]  = √ 50

So....

sin θ   =  -  1  / √ 50  =    - √ 50 / 50

When did you ask a question like this? This is master level statistics.  

It will be at least a year or two before you study anything like this. 

Because we can't use the "dots answered" mark......

I know why the guest knew what they meant.  The guest is Mr. BB, the same one who posted the question. Mr. BB often uses unconventional math terminology and symbols.   

I have to say Mr. BB, that’s an optimal method for improving your answering speed, not forgetting your accuracy.  You are much less likely to fuck up the answers when you cherry pick and post your own questions. Of course, you’d know what your own chicken scratch (and crap) means.

 Even with your cherry-picking,   you still manage to bugger the answers.  

The minimum slope occurs when the y intercept is (0,9)

And the slope is

[ 365 - 9 ]           356

________  =     ____  =      89

 [ 4 - 0 ]                4

It was an attempt to help. When I asked a question like this, you said you had to ask something with numbers. 

so whats your answer? 

why is the question have the "question answered" mark?

Let the y-intercept be the point  (0, a)  where  1 ≤ a ≤ 9

So the slope   =   \(\frac{\text{rise}}{\text{run}}\ =\ \frac{365-a}{4-0}\ =\ \frac{365-a}{4}\)

To make the slope as small as possible, we want to make the fraction  \(\frac{365-a}{4}\)  as small as possible.

To make the fraction as small as possible, we want to make the numerator as small as possible (we can't change the denominator).

And to make the numerator as small as possible, we want to subtract as much as we can from  365 .

To make  365 - a  as small as possible, we want to make  a  as large as possible.

The largest possible value of  a  is  9 ,  so the smallest possible value of the numerator is  365 - 9

And the smallest possible slope  =  \(\frac{365-9}{4}\ =\ \frac{356}{4}\ =\ 89\)

It's kind of hard to see the difference but here is a graph where you can see what changing the value of  a  does to the slope:

Thanks, Guest....I was unsure as to what the "dots" were supposed to represent....!!!

CPhill: Why did you sum up the group of "5 integers" instead of multiplying them together as follows:
5!/(5-5)! + 6!/(6-5)! + 7!/(7-5)! + 8!/(8-5)! + 9!(9-5)! + 10!/(10-5)! =5!/0! + 6!/1! + 7!/2! + 8!/3! + 9!/4! + 10!/5! +........+1000!/995!. Which works out as:
∑ [ (n + 4)! / (n - 1)!, n, 1, 996] = 165,170,830,829,004,000

(1, 7)  and (-2, -3)

The slope of this line is     [  -3 - 7 ]            -10             10

                                         ________  =    ____  =       ____

                                          [ -2 - 1 ]             -3                3

So....using (1, 7)  the equation of the line is

y = (10/3) ( x - 1)  + 7       multiply through by 3

3y  = 10 (x - 1) + 21        simplify

3y  = 10x - 10 + 21

-10x + 3y  =  11         mutiply through by  -1

10x - 3y  = -11

Using the information that the line passes through the points  (0, 0)  and  (-4, 3) ,  we can find the slope.

slope  =  \(\frac{\text{rise}}{\text{run}}\ =\ \frac{y_2-y_1}{x_2-x_1}\ =\ \frac{3-0}{-4-0}\ =\ -\frac34\)

Using the point  (0, 0)  and the slope  -\(\frac34\) ,  the equation of the line in point-slope form is

y - 0  =  -\(\frac34\)(x - 0)

Simplify both sides of the equation to get

y  =  -\(\frac34\)x

This is also a terrible question.  

how do you compute the model with a minimum residual after fitting probability distributions on a dataset

I can tell by the question that either you are in a master’s level statistic class, or a master’s level science class that requires these skills to complete assignments. My guess is the latter, because in a statistics class, you could ask and receive reasonable answers from your classmates or professor.  

I can also tell by your posted question that you probably should not be in that class. Your posted question indicates a lack of communication skills, short-sighted thinking skills, and just plain laziness.  If you posted this on stack exchange, it would be deleted, but not before you were mocked for being brain-dead. 

The answer to your question is not difficult, but the actual process can be difficult. Start by using known data models that process the type of data you have. If it’s climate data then use climate models; if it’s biomedical data then use biomedical models.  There are plenty of boxed models available for either of these types of data sets.

 After computing the data using several boxed models, select the top (N) models that have the best fit based on Least squares and Chi squared statistics. To minimize the residual, you will need to analyze the residual.  This “residue” is often referred to as “noise” in statistics and it’s composed of measurement errors, rounding errors, or random errors, and it can be false noise because the data falls outside the models measurement process. 

To correct for noise and false noise, use inverse modeling.  This is accomplished by setting one or more data elements for each multidimensional data point to an average, then rerunning the altered data using the same models that generated it. The outputs of this will start indicating from which dimensional parameters the noise is originating or where valid data is not utilized.  After identifying the parameters of interests adjustments are made to accommodate or restrict the processing of the data in the original set. 

Note the complexity of inverse modeling increases well beyond the exponential if your data points (P_x) have large numbers of dimensional parameters in its composite form; if some of the parameters have high dependency on other parameters, then it will increase more. 

Some boxed model programs have Big O notations approximating the time needed for various inverse modeling procedures. It’s not unusual for the time to exceed thousands of hours on fast, highly optimized computers. 

I think you should do it manually. This will give you an appreciation for what the computer is doing.    

GA

Yes Tomm, it is a terrible answer. Why did you post it? 

P(5 or 6)  =  2/6  = 1/3

P ( rolling 5 or 6  five times )  =  C(6, 5) (1/3)^5 (2/3)

P( roling 5 or 6 six times)  =  (1/3)^6

So....the combined probability is

C(6,5) (1/3)^5 (2/3) + (1/3)^6   =  13 / 729  ≈ .02

1+ 2 + 3 + 4 + 5  =   15    =   3(5)

2 + 3 + 4 + 5 + 6 =   20   =    4 (5)

3 + 4 +5 + 6 + 7  =   25   =    5(5)

4 + 5 + 6 + 7 + 8  =  30   =    6(5)

.

.

996 + 997 + 998 + 999 + 1000 = 998(5)

So...we have

3(5)  + 4(5) + 5(5) + 6(5) + ..... + 998(5)  =

5 ( 3 + 4 + 5 + 6 +  ..... + 998)  =

5  [998 + 3]  [  998 - 3 + 1]  / 2 = 

5 [ 1001] [ 996] / 2  =

5005 * 498  =

2,492,490

sorry i was making changes because i was trying to solve this my self but thats the final change hint: half the number and half more the other

No point solving your riddle since you change it so much. 

Your original riddle was:

I'm a number thats odd

But I'm a number of two

I'm more than 22

I'm less that 27

What am I 

Now you changed the 22 to a 20. There is no point in solving your riddle if you're going to change it

Not quit again the number is a three digit

You forgot the edit, when making a riddle at least make sure the riddle is written correctly.

A number of two that is odd is 23. It ends with 3 and it is a number of two (two digits).

So 23

My twin lives at the reverse of my house number. The difference between our house numbers ends in two. What are the lowest possible numbers of our houses?

Here's my guess......

One person's house number is  91

The other's is 19

The difference is

91  - 19   =    72