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Thanks, guest.....!!!

Here's a way to analyze this

We have 9   one-digit numbers  =  9

And [ 99 - 10 + 1 ]  =  90 two-digit numbers  =  180 digits

And  [ 999 - 100 + 1]  =  900 three-digit numbers  = 2700 digits

So.....the total number of digits  is   9 + 180 + 2700   = 2889

The digit "7"  will appear 10 times in each hundred in the units place  = 10 * 10  = 100

And it will appear  10 times in each hundred n the tens place = 10 * 10  = 100

And it will appear 100 times from 700 - 799  in the hundreds place

So......the probability is

[ 100 + 100 + 100 ] / 2889    =     300 / 2889

Here are the distributions of ALL numbers from 1 to 999:
(0=189, 1=300, 2=300, 3=300, 4=300, 5=300, 6=300, 7=300, 8=300, 9=300)
Total = 2889. So, the probability that it is a 7 is:
300/2,889=100/963 =~10.38%

thankyouu bothh

Let's see how CS  might have determined the x intercepts  (roots)

3x^3 + 10x^2 -13x - 20

By the Rational Roots Theorem ......one possible root is  -1

So

3(-1)^3 + 10(-1)^2 - 13(-1) - 20 =  -3 + 10 + 13 - 20  =  0

Using synthetic division, we can find the remaining polynomial

-1  [  3   10    - 13     -20 ]

              -3     - 7       20

      __________________

       3     7    -20         0

So....the remaining polynomial is   3x^2  + 7x - 20

Factoring, we have

(3x - 5) ( x + 4)

Setting each factor to 0  and solving for x we have that the other two roots are

x= 5/3     and x = -4

Then the x intercepts are  x = -4, -1   and 5/3

The rest of the answer is as CS has shown....!!!

!!! :)

9 is correct!

12 are waddling   if    3   6  and nine are different.....

It could be that 3 are waddling....then six start walking and end up waddling then the answer is 9

sqrt2/2 is the sin value for 45 degrees which is   pi/4 radians

sqrt3 / 2 is the cosine value for 30 degrees which is equal to  pi/6 in radians

this website solves this question: https://socratic.org/questions/how-do-you-evaluate-arcsin-sqrt-2-2

Penguins Rule!

We don't know the numerical value of "a"......it would depend upon the value of "d"

x * x^2   = x^(2+1) = x^3

this is NOT  (x^m)^n      this  is   x^m  *  x^n  = x^(m+n)    

     so  x^1 * x^2 = x^(2+1) = x^3

much appreciated!

Yes    0 * 6 + 2 * 3 = 6

thank you wold the 1st row 1st column element be "6"?

 0  2    x   6  -6  =        6     0

-2  -5       3   0            -27 12

this is a     2 x 1   *   1 x 2    so result should be  2 x 2  (the red numbers)    we can see this is an allowable multiplication because the green numbers are the same.

6     *    -5  4    =   -30   24

-3                           15   -12

Make sure you are using the Quadratic Formula like this:

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

and not as you wrote it in your question.......if you still get wrong answers , respond to this post....

for the first one   a =1  b = 20  c = 51       (make sure your quadratic is in the form  a x^2  + b x +c = 0   )

Yes, that is what I meant to do......but I typed in the incorrect number for the rust units ....it should be 10^27   not 10^23, so the answer is 100000 times bigger.....sorry.    And thanx!

  9.21 x 10^27 molecules / 6.02214 x 10 ^23 molecules/mole = 15290 moles of rust formula units

You will have much greater chances of having your question answered if you provide a picture of your problem.

There are actually several formulae for these "Birthday problems" depending on the number of people sharing the birthdays as follows:
Let d=365 =Number of days in a year.
Let n=Total number of people involved.
Let k =Number of people sharing same birthday

1 - Birthday probability for 2 people:
  p = 1 - ((d nPr n) / (d^n))

2 - Birthday probability for 3 people:
 p = 1 - ∑d!n! / {i! (n-2i)! (d-n +i )! 2^i d^n}, i=0 to n/2

3 - Birthday probability for 4 or MORE people.
 p = 1 - exp(-(d^(1 - k)* (exp(-n/(d* k))* n)^k)/((1 - n/(d* (1 + k)))* k!)).
So, for this last one, the problem becomes:
d =365, n=1,000, k=10 people (at least)
If you plug in these numbers into the formula above you should get: 0.186277 =~18.63%.
However, this last formula is supposed to give accurate results to within 0.5 of 1% up or down.

I do not want to confuse anyone more, but there are very specific circumstances where using a semicolon to separate items in a list is correct. This occurs when the items in the list contain commas already. This is not the case in OwenT154 question, though. Let's look at an example.

Look at the following list:

• New York
• California
• Nevada
• Florida

A sample sentence using these items is "I have been to New York, California, Nevada, and Florida."

Look at this modified list:

• New York, New York
• San Francisco, California
• Las Vegas, Nevada
• Miami, Florida

Notice how the items in the list already have commas. Therefore, semicolons are necessary to separate these items. A sample sentence using these items is "I have been to New York, New York; San Francisco, California; Las Vegas, Nevada; and Miami, Florida. For clarity purposes, commas are "promoted" to semicolons in order to show clear separation between each item.