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Ummm... 1 day 4 hours and 15 mins?

in minutes, its 1705 mins

There are a total of 110 men and women in a hall. If 3/7 of the men leave the hall and another 40 women enter the hall,the ratio of the number of men to the number of women becomes 8:11. Find the number of women in the hall at first

$$\small{\text{ We set m = man, and w = women. In the hall are
}}\\$$

$$\small{\text{$
\begin{array}{rrclr}
& 110 &=& m + w \\
or &\mathbf{ m }& \mathbf{=} & \mathbf{110 - w} & (1)\\\\
\dfrac{3}{7} \text{ of the men leave the hall}: & m_{now} &=& m-\dfrac{3}{7}m\\
& m_{now} &=& \left( 1 - \dfrac{3}{7} \right)m \\
& m_{now} &=& \left(\dfrac{4}{7} \right)m \\\\
40 \text{ women enter the hall}: & w_{now} &=& w+40 \\\\
\text{ The Ratio of the number of men to the number of women becomes }: & \dfrac{8}{11} &=& \dfrac{m_{now}}{w_{now}} \\\\
& \dfrac{8}{11} &=& \dfrac{ \left(\dfrac{4}{7} \right)m }{ w+40 }
\qquad | \qquad m = 110-w \\\\
& \dfrac{8}{11} &=& \dfrac{ \left(\dfrac{4}{7} \right)(110-w) }{ w+40 } \\\\
& \dfrac{56}{44} &=& \dfrac{110-w}{ w+40 } \\\\
& 56\cdot(w+40) &=& 44\cdot (110-w) \\\\
& 56w+56\cdot 40 &=& 44\cdot 110 - 44w\\
& 100w &=& 44\cdot 110 - 56\cdot 40 \qquad | \qquad : 10\\\\
& 10w &=& 44\cdot 11 - 56\cdot 4\\
& 10w &=& 484- 224\\
& 10w &=& 260\\
& \mathbf{w} & \mathbf{=} & \mathbf{26}
\end{array}
$}}$$

The number of women in the hall at first is 26

what is x cubed in exponential form

$$\small{\text{$
\begin{array}{rcl}
x^3 &=& e^z \qquad | \qquad \ln{()}\\
\ln{(x^3)} &=& \ln{(e^z)}\\
3\ln{(x)} &=& z\ln{(e)}\qquad | \qquad \ln{(e)}=1\\
3\ln{(x)} &=& z\\\\
\mathbf{x^3} & \mathbf{=} & \mathbf{e^{3\ln{(x)}}}\\
\\
\hline
\\
\end{array}
$}}$$

We have....

M + W   = 110     →  M = 110 - W  .... and we know that

[(110 -W) - (3/7)(110 -W)]/ [W +40] = 8/11    simplify

[(4/7)(110 - W)] /[W + 40]  = 8/11      multiply both sides by [W + 40]

[(4/7)(110 - W)]  = (8/11)(W + 40]     multiply both sides by  (7/4)

110  - W   = (56/44) (W + 40)  simplify

110 - W  = (14/11)(W + 40)     multiply both sides by 11

1210 - 11W  = 14(W + 40) 

1210 -11W = 14W + 560

1210 - 560 = 25W

650  = 25W     didived both sides by 25

W = 26 women in the hall originally

Check......

[(4/7)(110 - 26)] / [ 26 + 40]  =    

(4/7)(84) / 66  =

48/66  =  8/11

The graph of x = 2 is  a vertical line that goes through the x axis at the point (2, 0)  ....the slope is undefined.....to see why......take two points on this line, say, (2, 0) and (2,  1)..............note that the slope is: [1 - 0]/[2 - 2]   = 1/0    but, since we can't divide by 0, the slope is, by definition, undefined.  Also, this line never intersects the y axis, so there is no y intercept.

The line y = 3 is a horizontal line that interesects the y axis at (0, 3). Since a horizontal line neither rises nor falls, its slope is 0.  Three ordered pairs on this line are (0, 3) (1 ,3) and (2.3)....note that the y values are all the same.....only the x values change !!!

Subtract the change from $20.

$20-0.80=$19.20.

Divide $19.20 by the amount of pens Yolan bought. 

$${\frac{{\mathtt{1\,920}}}{{\mathtt{8}}}} = {\mathtt{240}}$$ 

Move the decimal one point, resulting in 2.40

Each pen cost Yolan $2.40 

wow what an interesting imagination Judith Guest has

really deep and dark plot

$${\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{5}} = {\mathtt{20}}$$

$${\frac{{\mathtt{25.8}}}{{\mathtt{4.3}}}} = {\mathtt{6}}$$

the quotient of 25.8 and 4.3 is 6

alright, looks like were dealing with a PEMDAS Operation the evil orginization is planning

so, this is how you setted it up, and by using PEMDAS everything should lead you to this:

$${\mathtt{2.34}}{\mathtt{\,\times\,}}{\mathtt{0.2}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{10}}}^{{\mathtt{1}}}$$

$${\mathtt{2.34}}{\mathtt{\,\times\,}}{\mathtt{0.2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{10}}$$

$${\mathtt{0.468}}{\mathtt{\,\small\textbf+\,}}{\mathtt{10}}$$

$${\mathtt{10.468}}$$

overall,

$${\mathtt{2.34}}{\mathtt{\,\times\,}}{\mathtt{0.2}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{10}}}^{{\mathtt{1}}} = {\mathtt{10.468}}$$

3/4=.75=75%

$${\mathtt{0.75}}{\mathtt{\,\times\,}}{\mathtt{6\,770\,696}} = {\mathtt{5\,078\,022}}$$

3/4, or 75%, of 6,770,696=5078022

is it 5078022

|x| splits at 0: 

   for x ≥ 0: |x| = x

   for x < 0: |x| = -x

So:

   for x ≥ 0: |x| + x² - 5x + 8 becomes x + x² - 5x + 8 --->   x² - 4x + 8

   for x  0: |x| + x² - 5x + 8 becomes -x + x² - 5x + 8 --->   x² - 6x + 8

Both of these are (partial) parabolas.

The vertex of y = x² - 4x + 8  occurs at (2,4) so the minimum value is 4.

The maximum value of x² - 4x + 8 on [0,4] occurs at x = 4 --->  y = 8.

The maximum value of x² - 6x + 8 on [-1,0] occurs at x = -1  --->   y = 15.

Thus, the maximum value is 15.

in the interval [-1,0] the function is equal to

-x + x^2-5x+8 = x^2-6x+8

On this interval, this function has a minimum at x=0 (with y=8) and a max at x= -1 (with y=15)

On the interval [0,4] the function is equal to

x + x^2-5x+8 = x^2-4x+8

On this interval, this function has a minimum at x= -b/2a = 4/2 = 2 (with y=4) and a max at x=4 (with y=8)

over the entire interval from -1 to 4, the smallest value occurs when x=2 giving y=4, and the largest value occurs at x= -1 with y=15

alright, this time I have to agree with my now Alt Ego

my new alt ego and a bunch of other math masters gave some great responses to an earlier situation, where someone failed their end of the year important math exam

this is what some people said:

Come on Denzel it is not the end of the world :)

If you want to improve your maths why don't you post more questions. 

They can be general questions if you like.  We can send you off to look at video clips or we can help you directly.  :)

Anyway, like I said, it is not the end of the world.  So cheer up :)

-Melody

Hallo Denzel,

i have seen that picture here in the forum.

If you have trouble with your maths teacher, please write to me ! (Message Center)

Gruß radix !  -Radix

Eh, its alright. If you dont fail, youre not human.

however, not many realize that

well, you failed. What can you do?

-ask your allies (friends, parents, the members here, maybe your teacher if you feel cool talking with him)

-upgrade your troops (hit the books or youtube math videos to function your brain with the minature stuff)

-upgrade your spells (hit the books or youtube math videos to function your brain with the main turning point stuff)

And when you feel youre ready for next years math:

you fight with all the might (try your best) and get that math test mothership base (defeat the math test)         -TitaniumRome aka 2nd Ego

aww dont worry denzel. its not like you failed the test to enter Paradise.

ok, you failed this year. it doesnt mean youll fail the next. you can still do this with skill, and a lucky feather as well. :) -HeatherF

c = 0, a = 1 and b = 6.  

the zeroes are at x = 0 and x = -6. you can see this by factoring:

x^2 + 6x = x(x + 6)

this is equal to zero when either

x = 0 or

(x + 6) = 0 which happens when x = -6

Add the expense percentages. 

20%+23%+42%= 85%

Subtract the percentage you found from 100%.

100%-85%=15%

This percentage is the amount of money the family saves monthly, in this case, $360.

To find how much money the family makes monthly, divide 100 by 15 and multiply that by $360.

$${\frac{{\mathtt{100}}}{{\mathtt{15}}}}{\mathtt{\,\times\,}}{\mathtt{360}} = {\mathtt{2\,400}}$$

The amount of money the family earns in a month is $2400. 

cant edit point 3 above so seperate post -> pi*pi = pi^2 which cant be expressed as a fraction so this is irrational

1) sometimes -> 1 - 6.?????...... = 3.???????......

  so two irrational numbers 6.??? + 3.?????? = 1 (A rational number)

2) yep always

3) Sometimes -> Sqrt(2) * Sqrt(2) = 2

This probably isnt rigorous enough but here's what I think:

A rational number can always be expressed in the form p / q for integers p and q

then (using m/n for the other rational number):

p/q + m/n = (np+mq)/qn.

two integers multiplied together will always be integers so in the end the numerator/denominator will still be integers so it will always be a rational number

I assume you want to know this:

[155,517.27 / 140,342.43] = about 1.1081  = about 110.81%

@@ End of Day Wrap  Wed 5/8/15     Sydney, Australia Time   12:18am  (Yes it is Thursday) ♪ ♫

Hi all,

There have been fabulous answers from Heureka, CPhill, Dragonlance, Royal Titanium aka TR, Geno3141, Biotomic121 and Dritil.  Thanks you.  

It's 19

10+9=19(addition )