All Answers 356005 Answers

Turn 82.693 with the 9 and 3 repeating, into a mixed number.

Forget about the 82 for a second

.693  with the 9 and 3 repeating can be turned into a fraction thusly:

Writh the 693 without the decimal......from this, subtract the non-repeating part, 6.....[693 - 6] = 687 ...   this will be the numerator of our fraction.........for the denominator......writte the same number of 9's as the number of repeating digits  =  99 and append  the same munber of 0's as the non-repating part [ i.e, one "0" ]....this gives us 990

So we have :

[693 - 6] / 990   = 687/990    and we can reduce this by dividing the numerator and denominator by 3 →  229/330

And our mixed number is     82 + 229/330........check this for yourself .....https://www.wolframalpha.com/input/?i=82+%2B687%2F990

Simplify the following:
3 x^2-y^2-(4 x^2-y^2)

4 x^2-y^2 = (2 x)^2-y^2:
3 x^2-y^2-((2 x)^2-y^2)

Factor the difference of two squares. (2 x)^2-y^2 = (2 x-y) (2 x+y):
3 x^2-y^2-(2 x-y) (2 x+y)

(2 x+y) (2 x-y) = (2 x) (2 x) + (2 x) (-y) + (y) (2 x) + (y) (-y) = 4 x^2-2 x y+2 x y-y^2 = 4 x^2-y^2:
3 x^2-y^2-4 x^2-y^2

-(4 x^2-y^2) = y^2-4 x^2:
3 x^2-y^2+y^2-4 x^2

Grouping like terms, 3 x^2-y^2-4 x^2+y^2 = (y^2-y^2)+(3 x^2-4 x^2):
(y^2-y^2)+(3 x^2-4 x^2)

3 x^2-4 x^2 = -x^2:
-x^2+(y^2-y^2)

y^2-y^2 = 0:
Answer: |-x^2

Turn 82.693 with the 9 and 3 repeating, into a mixed number.

82.693939393..........=82  229/330

=~9.85sqrt(x)

a) It is essentially the same question as many in the same vein: Since they want the NUMBER of ways of obtaining a 9 with the roll of 3 dice, then the answer is the same as other examples of this sort: It is the coefficient of n^9 in the expansion of this series, which is 25!:

[n+n^2+n^3+n^4+n^5+n^6]^3.

b) Similarly here. It is the coefficient of n^20 in the expansion of above series to 10th power:

[n+n^2+n^3+n^4+n^5+n^6]^10. n^20 =85,228 different ways.

-3(2y+v)-5(-v+5y)   use  the distributive property

-6y - 3v + 5v - 25y     combine like terms

-31y + 2v

See my responses here : http://web2.0calc.com/questions/counting-and-probability-problem-urgent-please-help

(b) We have 10 standard 6-sided dice, all different colors. In how many ways can we roll them to get a sum of 20?

Like the last question , this just boils down to the number of ways to roll a "20"  with 10 dice.....

The probability =    21307 /   15116544   =   85228 / 6^10  =     85228 /  60466176

https://www.wolframalpha.com/input/?i=probability+of+rolling+a+20+with+10+dice

So.....the number  of ways of rolling a "20"  with 10  dice = 85228

a) We have three standard 6-sided dice, colored red, yellow, and green. In how many ways can we roll them to get a sum of 9? The dice are colored so that a red 2, yellow 3, and green 4 is a different roll from red 3, yellow 4, and green 2.

Notice

Roll Total         Frequency

 3                          1

 4                          3

 5                          6

 6                        10

 7                        15

 8                        21

 9                        25

10                       27        and the  rolls of  11-18   will be in the same descending frequency order from 27 back to 1

So....there are 25 ways to roll a "9"

1 2 6     2 1 6     2 6 1    3 5 1     5 1 3

1 3 5     2 2 5     3 1 5    4 1 4     5 2 2

1 4 4     2 3 4     3 2 4    4 2 3     5 3 1

1 5 3     2 4 3     3 3 3    4 3 2     6 1 2

1 6 2     2 5 2     3 4 2    4 4 1     6 2 1

And notice that, no matter that the dice have different colors, that every possibility has been accounted for.

For instance.....for a roll of 2-3-4....we have 6 different possibilities  as denoted in the table :

Red 2  Yellow 3 Grren  4

Red 2  Yellow 4 Green 3

Red 3  Yellow 2 Green 4

Red 3  Yellow 4 Green 3

Red 4  Yellow 2 Green 3

Red 4  Yellow 3 Green 2

So....there sre 25  distinguishable ways to roll a "9' with three different colored dice.

You do realize you can just input this into a calculator right?

I'm not sure why on earth you would need the answer to that.

Unless you're simply trolling. 

Ah I see 

Well, all you have to do is 25/4, which is 6.25.

Thus, the unit rate is 6.25 ppg (pounds per gallon). 

Very sorry,  wrongly worded question, how many Fittons does 1 decibel equal??

The answer is 1.4112 × 10-6 m^4.

(You can just use a calculator here :)

In your question you said 1 fitton equals 1 decibel (plus 7).

So then didn't you already answer your wuestion of how many decibels there are in a fitton? 

Solve for x:
4/3-(7 x)/6 = 5/3

Put each term in 4/3-(7 x)/6 over the common denominator 6: 4/3-(7 x)/6 = 8/6-(7 x)/6:
8/6-(7 x)/6 = 5/3

8/6-(7 x)/6 = (8-7 x)/6:
(8-7 x)/6 = 5/3

Multiply both sides of (8-7 x)/6 = 5/3 by 6:
(6 (8-7 x))/6 = 6×5/3

6×5/3 = (6×5)/3:
(6 (8-7 x))/6 = (6×5)/3

(6 (8-7 x))/6 = 6/6×(8-7 x) = 8-7 x:
8-7 x = (6×5)/3

6/3 = (3×2)/3 = 2:
8-7 x = 2×5

2×5 = 10:
8-7 x = 10

Subtract 8 from both sides:
(8-8)-7 x = 10-8

8-8 = 0:
-7 x = 10-8

10-8 = 2:
-7 x = 2

Divide both sides of -7 x = 2 by -7:
(-7 x)/(-7) = 2/(-7)

(-7)/(-7) = 1:
x = 2/(-7)

Multiply numerator and denominator of 2/(-7) by -1:
Answer: |x = (-2)/7

13 - 4x = 1 -x       add '4x' to both sides of the equation

13 = 1 + 3x          Subtract 1 from each side

12 = 3x                 Divide by 3

4 = x

Complimentary angles add to 90 degrees.

so   (3x+5) + 2x = 90    solve for 'x'

        3x + 5 + 2x = 90  

         5x + 5 = 90

          5x + 5    - 5   = 90   - 5

          5x = 85

           x = 17            LMN = (3x+5) = 3(17)+5 = 56    UVW = 2x = 2(17)= 34         34 + 56 = 90       Yea!

It would be the coefficient of the n^45 or the 34th term of the expansion of this generating series: [n+n^2+n^3+n^4+n^5+n^6]^13.Why? Because the process involved in calculating the coefficient in question is exactly the same as calculating the odds in this dice probability. Therefore the coefficient of n^45 is:833,196,442 / 6^13 =~0.06379 or ~6.38%.

P.S. It is exactly the same probability as in CPhill's answer. His has been reduced by a factor of 2.

Here you go :   https://www.wolframalpha.com/input/?i=probability+of+rolling+45+with+13+dice

416598221 / 6530347008     is the exact probability  ≈    1  out of 16

hay

 6^2 / 2(3) + 4   =

[36/ 2] * 3   + 4   =

18 * 3  + 4  =

54 + 4  =

58