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The probability is 65%.

The probability is 71%.

Do you do that on purpose? I wont tell anyone, I promise, I just want to know.

I do not understand your answer CU.

How many different integers represent the sum of two or more members of the set {-4, -3, -2, -1 , 0, 1, 2, 3, 4}?

What is the biggest sum?

What is the smallest sum?

So there is at the most how many totals?

I'd write all thes out in a row and then cross them off when I find a sum that adds to that number. 

Ultimately all the crossed numbers are possible sums. So count them.

Thank you, CPhill !

Each number is a multiple of 3, or 1 more than a multiple of 3, or one less than a multiple of 3.  These number we will call x's, y's, and z's.

If we add x + y + z, then we get x, because y and z will even each other out, since y is 1 more than multiple of 3 and z is one less.

Because of this, we can conclude that we have to arrange the numbers in a repeating pattern, like x, y, z, x, y, z, ... or z, y, x, z, y, x, ...

In this set 1, 2, 3, ..., 9, there are 3 x's, 3 y's, and 3 z's.

To fill up a pattern, there are 3 choices for the first x, y, z, 2 choices for second, then 1 choice.

3^3 * 2^3 * 1^3 = 27*8*1 = 216

This is equal for both patterns, so there are 216 * 2 = 432 ways to arrange the numbers.

xxJenny,

I have helped you with your question in more than a totally trivial way and you have implied that you used my help  to get an answer for yourself. (maybe that is not what you meant to imply)

You have not thanked me or asked me for any clarification, you have  only lodged a formal complaint because I have not given you the exact answer to your question.

You have been registered for all of three days and already you think you have the right to DEMAND to be treated like royalty.

None of us here are your private subjects who are obliged to do you homework for you!  If you get free help then be grateful!

HINT:

Find the angle between the minute hand and 12 o clock.

Find the angle between the hour hand and 12 o clock.

Find the absolute difference between them.

wow, welcome back Eight MersennePrime!

After 2 years (checked your profile) you are back!

oopsies doopsies

The only way to get the answer is to read the explanation ENTIRELY

List this out, trust me, it won't take long.

We see that there are 3 * 5 = 15 total possible values of x^y.

We find all the number of values that are NEGATIVE, then subtract that number from 15.

Looking at the y sets, we see that anything value of y that is -2, 0, 2, will create positive values no matter what.

So the y values can be -1 or 1.

There is only one x-value that has potential to be negative, and that is -1.

We see that -1^-1 and -1¹ both create negative values.

Since there are 2 negative values.

15 - 2 = THE ANSWER?

We check with a table

BUT WAIT! They said distinct.

So count the distinct values in the table, and you should get the answer.

Guest made a teeny tiny mistake.

The answer is actually

 \(2

EDIT: What happened to the LaTeX???????

Response to you   asking if the German stole the fish.

This is the same as asking for the multiple choice answer. Please do not do that.

If you have understood and answered with care then you can trust your own answer.

The solutoin so x^2 - 5x - 6 < 0 is -1 < x < 6, so the set of all possible values of x^2 + 5x + 6 is (2,72).

CU: While the "1" of 10 is the tenth digit, the "2" of 20 is actually the 30th digit. You are counting the actual numbers ( or the integers) not the INDIVIDUAL digits from 1 and up. For example: there are 189 individual digits between 1 and 99 inclusive.

To add on to guest's answer.

Notice the pattern

123456789101112131415161718192021222324

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

the first digit is 1, the tenth digit is 10, the twentieth digit is 20. etc.

lel never mind the above statement my brain is wired wrong

or you can go tryhard and download Autodesk Inventor for some 3d Printing.

Find the greatest sum and the smallest sum.

smallest sum: -4 + (-3) = -7

greatest sum: 4 + 3 = 7

We can assume that \(-7\leq{x}\leq7\) would work.

BUT WAIT.

We check if the sums -6 or 6 are possible, but they aren't. We check if the sums -5 or 5 are possible, and they ARE.

We can assume that all ODD numbers between the interval \(-7\leq{x}\leq7\) work.

Now its up to you to find the answer.

EDIT: Sorry Fixed it was kind of confusing.

Suppose that \(\sec x+\tan x=\frac{22}7. \)   Find \(\csc x+\cot x. \)

Hello Guest!

\(\color{BrickRed}\sec x+\tan x=\frac{22}7\\ \pm\sqrt{1+tan^2x}+\tan x=\frac{22}7\\ \pm\sqrt{1+tan^2x}=\frac{22}7-tan\ x\\ 1+tan^2x=\frac{484}{49}-\frac{44}{7}tan\ x+tan^2x\\ \frac{44}{7}tan\ x=\frac{484}{49}-1\)

\(\frac{44}{7}tan\ x=\frac{435}{49}\\ tan\ x=\frac{3\cdot 5\cdot 29\cdot 7}{7\cdot 7\cdot 4\cdot 11}=\frac{3\cdot 5\cdot 29}{4\cdot 7\cdot 11}\)

\(tan\ x=\frac{435}{308}\)

\(x=0.954690764748\)

\(csc\ x=\frac{533}{435}\)

\(cot\ x =\frac{308}{435}\)

\(csc\ x+ cot\ x=\frac{841}{435}\)

\(\large csc\ x+ cot\ x=\frac{29}{15}\)

           Thank you heureka!

  !    Not logged in, asinus.

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