geno3141

You start with 9 balls, 5 white and 4 black.

To choose a black ball from the 9 balls, there are 4 possible choices:  4/9

Now, there are only 8 balls left, 5 white and 3 black.

To choose a black ball from the 8 balls, there are 3 possible choices:  3/8

The probability that both will occur is:  4/9 x 3/8  =  12/72

f(x)  =  3x + 2

g(x)  =  ax + b

f( g(x) )  =  3( ax + b ) + 2  =  3ax + 3b + 2

g( f(x) )  =  a( 3x + 2 ) + b  =  3ax + 2a + b

Since  f( g(x) )  =  g( f(x) )     --->     3ax + 3b + 2  =  3ax + 2a + b

                                                                  3b + 2  =  2a + b

                                                                  2b + 2  =  2a

                                                                    b + 1  =  a

Since  ab  =  90     --->     a  =  90 / b

Substituting:     b + 1  =  a     --->     b + 1  =  90/b

                                                        b² + b  =  90

                                                 b² + b - 90  =  0

                                            (b + 10)(b - 9)  =  0

If  b = -10,  a = -9.

If  b = 9,  a  =  10

First:  find the three values f(100), f(101), and f(102).

Then, go to https://www.calculatorsoup.com/calculators/math/factors.php 

This is a site that will find all the factors of these numbers.

Use this site to find your answer.

Placing the expression into graphing form:

                     y  =  3x² + 16x + 4  

                y - 4  =  3x² + 16x                            Place the  4 on the other side

                y - 4  =  3(x² + 16/3x       )                Factor out the 3

     y - 4 + 64/9  =  3(x² + 16/3x + 64/9)            Complete the square

           y + 28/9  =  3(x² + 16/3x + 64/9)            Simplify

          y  +  28/9  =  3(x + 8/3)²                             Factor

                       y  =  3(x + 8/3)² - 28/9                Rewrite

There is still a little left for you to do ...

This is a geometric series with first term = 1 and common ratio = -1/5.

Using the formula for an infinite geometric series with a common ration -1 < r < 1:

      Sum  =  1 / ( 1 - 1/5)  =  1 / (4/5)  =  5/4.  

If the average (mean) of 10 numbers is 85, then the sum of the numbers is 10 x 85  =  850.

Removing the numbers 70, 76, and 77, we get:  850 - 70 - 76 - 77  =  627.

There are now 7 numbers remaining, so the average of these 7 numbers is 627 / 7  =  89.57...

8x² - 32x + 32  =  8(x² - 4x + 4)  =  8(x - 2)(x - 2)  has double root = 2.

Let  z  =  log_y⁵(x³)     --->     (y⁵)^z  =  x³     --->     y^5z  =  x³

Then  z  =  k·log_y(x)     --->     z/k  =  log_y(x)     --->     y^z/k  =  x

Substituting:     y^5z  =  ( y^z/k )³     --->     y^5z  =  y^3z/k

                                                     --->      5z  =  3z/k

                                                     --->        5  =  3/k

                                                     --->        k  =  3/5

I will assume that you can use the Law of Cosines:  c²  =  a² + b² - 2·a·b·cos(C).

1)  Find the size of angle(B) in triangle(ABC):  b²  =  a² + c² - 2·a·c·cos(B).

                     5²  =  7² + 3² - 2·7·3·cos(B)

     You now know the size of angle(B)

2)  Find the length of side AD in triangle(ABD):

                    AD²  =  3² + 3.5² - 2·3·3.5·cos(B)

Change 1/2 in fourths:  1/2  =  2/4.

Subtract:  3/4 - 2/4  =  1/4.

Since the denominators (bottom numbers) are the same, just subtract the numerators (top numbers) and write that answer above the common denominator.