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The probability is $\boxed{\frac{4}{15}}$.

HAPPPY BIRTHDAY ROSALA!

Heyyyy it's been so long. I'm in contact with Rosala still through Instagram I'll let her know to come back and check out the website. This is an insane coincidence that I decided to check out the website around her birthday, it's almost like fate. I just saw TitaniumRome online and wanted to check. Ahh, it feels so good and nostalgic to be back here. I hope everyone's doing well :))

Thanks very much Alan.

I understand perfectly now :)

What about $\sqrt[12]{4096}=2$ as well?

As follows:

n=28

D = 176            G = 101

(176 - x) / (101 - x) = 6 / 1 ()

x = 86     This is the number of books each friend gave away.

Thank you,  I am pleased that it helped.   

It was also answered here

Let total straw be $x$
 

Alisson's share = ${x\over 2}{}{}+8$
Remaining = $x -$$( {x \over 2} + 8) = {x \over 2} -8$
Jennifer's share = $({x \over 4} - 4) + 8 = {x \over 4} + 4$
Remaining = $( {x \over 2} + 8) - ({x \over 4} + 4) = {x \over 4} - 12$
Laura's share = $({x \over 8} - 6) +$Remaining

Remaining = $({120 \over 8}- 6) + 9 = 18$
x% of 120 = 18 ⇒ $x = 15$
Laura's share = 15%

x_f = x_o + v_o t + 1/2 at²               (I used x as a matter of convention.....but you can switch them to 'y' )

xf = final height= the ground =  0

xo = intitial position (what we are looking for)

vo = original velocity = 0

a = accelaration of gravity    choose either  -32.2 ft/s²   your answer will be in feet

                                                  or choose  -9.81 m/s²    your answer will be in meters

t = time = 1.1   (given)           Plug in the numbers and calculate.....

The number of boys 8. Hence, the number of girls is 20 – 8 = 12.

The number of boys, who have a speaking part in the play is 5. Hence, the number of boys, who do not have a speaking part in the play is 8 – 5 = 3.

The number of girls, who do not have a speaking part in the play is 7. Hence, the number of girls, who have a speaking part in the play is 12 – 7 = 5.

Hence, consider the below contingency table:

Gender  Speaking part in play  No speaking part in play  Row Total 
Boy          5                                 3                                     8

Girl          5                                 7                                     12

Column Total 10                       10                                     20 

The total number of children, who have a speaking part is 10.

Thus, if a child from the cast of the play is chosen at random, the probability that the child has a speaking part is 10/20 = 1/2 = 0.5.

What is the final speed?

Hello Guest!

$v=v_0+at=\frac{15m}{s}+\frac{2m}{s^2}\cdot10s\color{blue}=35m/s$

  !

Thank you so much Melody! Your solution was really clear and easy to understand! :D 

Let Anne, Bernard and Catherine had A, B and C

amount of money (in dollars), separately 

at first

Catherine gave 1/4 of C to Anne now

Anne have A + 1/4C

Catherine have C - 1/4C = 3/4C

given Anne had thrice as much as before

         =>            A + 1/4C = 3A => 2A + 1/4C = 0

Now Anne gave 1/2 of (A + 1/4C) to Bernard now

Bernard have B + 1/2A + 1/8C

Anne have 1/2A + 1/8C

given Bernard had 1 1/2 times as much as before

                      => B + 1/2A + 1/8C = 3/2B

               =>    1/2A - 1/2B + 1/8C = D

               =>       4A - 4B + C = D

also Anne still had $129 left then

=> 1/2A + 1/8C = 129

We have -2A + 1/4C = D

               4A - 4B + C = D

               1/2A + 1/8C = 129

-2A - A = -2 * 129

-3A = 2 * 129

   A = -2 * 43

So A = 86 now 2A + 1/4C = D

    => 1/4C = 2A = 2 * 86 => C = 8 * 85

 =>   C = 688 

     4 * 86 - 4B + 688 = D

                  =>  4B = 688 + 4 * 85

                  =>    B = 172 + 86 = 258

        B = 258

Anne had $85, Bernard had $258 and Catherine had $688 at first.

Simplify sqrt(72)/sqrt(28).

Hello Guest!

$\frac{\sqrt{72}}{\sqrt{28}}=\sqrt{\frac{72}{28}}=\sqrt{\frac{2^3\cdot3^2}{2^2\cdot 7}\cdot \frac{7}{7}} \color{blue}=\frac{ 3\cdot \sqrt{2\cdot 7}}{ 7}$

  !

1/3 of the apples = n + 29

        After removing 1/3 of the apples remaining apples

                            = (n + 29) - (n + 29)/3 = 2 (x + 29)/3

=> After removing 1/3 of the apples the remaining apples

                                = ${2n + 58 \over 3}$

 Given after removing 1/3 of the apples from the crate

   there were 5 more apples than pears.

  So, 2n+58/3 = n + 5

    => 2n + 58 = 3n + 15

    => 3n - 2n = 58 - 15

    =>  n = 43

     n + 29 = 43 + 29 = 72

72 apples and 43 pears at first.

Find the area of triangle ACE.

Hello Guest!

This is how it works easier:

$\Delta_{ACE}= ◻ _{ABFG+CDEF}-\Delta_{ABC}-\Delta_{CDE}-\Delta_{AEG}$

${\color{blue}\Delta _{ACE}}=17^2+13^2-\frac{17(17-13)}{2}-\frac{13^2}{2}-\frac{17(17+13)}{2}\color{blue}=84.5$

The area of triangle ACE is 84.5
  !

First 10-digit number divisible by 9 =1,000,000,008

Last 10-digit number divisible by 9   =9,999,999,999

Subtract Last from First, divide by 9 and add 1

[9,999,999,999 - 1,000,000,008] / 9 + 1 =1,000,000,000 ten-digit numbers divisible by 9.

Let pens with Robert be 3x and pens with Steven be 2x

After Steven gave 8 pens to Robert, pens with Robert = 3x+8 and pens with Steven= 2x-8 and the ratio =13:2

3x+8/2x-8=13/2

cross multiplication

2(3x+8)=13(2x-8)

6x+16=26x-104

26x-6x=16+104

20x=120

x=120/20=6

Number of pens with Robert at first=3*6=18

There isn't one ....

There are only four integers: $\sqrt{4096}$, $\sqrt[3]{4096}$, $\sqrt[4]{4096}$, and $\sqrt[6]{4096}$.

four

if b = 0      degree will be 4

  if b cannot be zero, degree will be 5