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

HAPPPY BIRTHDAY ROSALA!

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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