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3/16 of the fruits at a stall are pears. 1/4 of the remaining fruits are oranges. The rest are apples. If there are 585 apples, how many fruits are at the stall??

f = fruits    p = pears   o = oranges   a = apples

(1) $$p=f\cdot \frac3{16}$$

(2) $$o=(f-p)\frac14 \quad \text { or }\quad o = (f-f\frac3{16})\cdot \frac14 = f \frac{13}{16}\cdot \frac 14 = f\cdot\frac{13}{64}$$

(3) $$f = o+p+a$$

$$\small{\text{$
\begin{array}{rcl}
a &=& 585 \\
f &=& o+p+585 \\
f &=& o+p+585 \qquad | \qquad o = f\cdot\frac{13}{64} \qquad p=f\cdot \frac3{16}\\\\
f &=& f\cdot\frac{13}{64}+f\cdot \frac3{16}+585 \\\\
f - f\cdot\frac{13}{64}-f\cdot \frac3{16} &=& 585\\\\
f (1- \frac{13}{64}- \frac3{16}) &=& 585\\\\
f (\frac{64-13-3\cdot 4}{64}) &=& 585\\\\
f \cdot \frac{39}{64} &=& 585\\\\
f &=& 585 \cdot \frac{64}{39} \\\\
\mathbf{f} &\mathbf{=}& \mathbf{960}\\\\
\end{array}
$}} \\\\$$

At the stall are 960 fruits.

pears = 960 * (3/16) = 180

oranges = (960-180)/4 = 195

apples = 960 - 180 - 195 = 585 ( okay )

Hello MaiaMitchell !

Here my answer !

all fruits together:   x                             =>  1040

pears                 :   3/16 * x                  =>    195

oranges              :   1/4 * x                   =>    260

apples                :  585                          =>   585

$${\frac{{\mathtt{3}}}{{\mathtt{16}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{4}}}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{585}} = {\mathtt{x}}$$             |  * 16

3x + 4x  + 9360 = 16x

9360 = 9x     =>     x = 1040      ( all fruits )

Gruß radix !

Cheryl is 3/5 as old as her mum. In 8 years time, the ratio of her age to her mom's age will be 2:3. How old is Cheryl now??

m = mum      c = cheryl

(1) $$c = \frac 35 m \qquad \text { or } \qquad m = \frac 53 c$$

(2) $$\frac{c+8}{m+8} = \frac 23 \qquad \text{ or } \qquad c = \frac 23 \cdot (m+8) - 8$$

$$\small{\text{$
\begin{array}{lcl}
c &=& \frac 23 \cdot (m+8) - 8 \qquad | \qquad m=\frac 53 c\\\\
c &=& \frac 23 \cdot (\frac 53 c+8) - 8 \\\\
c &=& \frac {10}{9} c + 8\cdot \frac 23 - 8 \\\\
c &=& \frac {10}{9} c + \frac {16}{3} - 8 \qquad | \qquad \cdot 9\\\\
9c &=& 10 c + 3\cdot 16 - 72\\\\
9c &=& 10 c -24\\\\
10c - 9 c &=& 24\\\\
\mathbf{c} & \mathbf{=} & \mathbf{24}\\
\end{array}
$}} \\\\$$

Cheryl is now 24 years old

There are 2 hotels, Hotel Duxton and Hotel Supreme. There were 219 more guests in Hotel Duxton than in Hotel Supreme. After 57 guests had left Hotel Supreme, the number of guests in Hotel Duxton became 4 times the number of guests in Hotel Supreme. How many guests are left at Hotel Supreme?

d = Hotel Duxton       s = Hotel Supreme

(1) $$d-s = 219$$

(2) $$s_1 = s - 57$$

(3)$$d - s_1 = 219 + 57 = 276$$

(4) $$d = 4\cdot s_1$$

put (4) into (3):

$$\begin{array}{rcl}
4\cdot s_1 -s_1 &=& 276\\
3\cdot s_1 &=& 276 \\
s_1 &=& 92
\end{array}$$

$$\text{\small{
\begin{array}{lrclr}
& Hotel Duxton & Hotel Supreme \\
bevor & 368 = 149 + 219 & 92 + 57 = 149 \\
after & 368 = 92\cdot 4 & 92\\
\end{array}
}}$$

January = 10|1|7 10 is the position of letter J in alphabetical order. 1 is the position of January in months. 7 is the number of letters used in the word January. Same goes for all the months, thus September = 19|9|9 (1999).

$$\small{\text{$\mathbf{n^{th}}$ derivative of $\mathbf{10^{-x}}$}}$$

$$\text{ \small{Formula} $
\boxed{
\begin{array}{lcl}
y &=& e^{k\cdot x} \\
y' &=& k \cdot e^{k\cdot x} \qquad y'' = k^2 \cdot e^{k\cdot x} \qquad y''' = k^3 \cdot e^{k\cdot x} \qquad \cdots \\
y^{(n)} & = & k^n \cdot e^{k\cdot x}
\end{array}
}
$} \\\\\\
\small{\text{$
\begin{array}{lcl}
y &=& 10^{-x} \qquad \Rightarrow \qquad
y = e^{-x\cdot \ln{(10)} } = e^{ \overbrace{\left[
-\ln{10} \right] }^{=\big{k}} \cdot x }\\
\end{array}
$}} \\\\
\small{\text{$
\underline{ y^{n} = k^n \cdot e^{k\cdot x} }
\qquad \underline{ k = -\ln{(10)} }
$}} \\\\
\small{\text{$
\begin{array}{lcl}
y^{(n)} &=& [-\ln{(10)} ]^n \cdot
\underbrace{ e^{ [-\ln{(10)} ]\cdot x} }_{=\big{10^{-x}}}\\\\
\mathbf{y^{(n)}} & \mathbf{=} & \mathbf{[-\ln{(10)} ]^n \cdot 10^{-x} }\\\\
\end{array}
$}} \\\\$$

More generally:

.

1.  Add 5 to both sides to get a/2 = -7+5 or a/2 = -2

2. Multiply both sides by 2 to get  a = -2*2  or a = -4

.

If you mean you have something like sin(x) = a, where a is known and you want to find x, then use x = asin(a). (asin is short for arcsin, which is the same thing as sin^-1).

Similarly, most calculators have acos and atan.  Some also have asec, acosec and acot.

.

Purpe wrote "I am wondering if this is correct, if not where did I make a mistake?"

Your last line doesn't follow from your next-to-last-line.  All lines but your last are correct; however, they don't lead towards a solution, so are not useful here.

. 

If x^2+(3a+1)x+2a^2-b^2 is a perfect square, what is a,b?

for example:

$$a=-\dfrac 13 \text{ and }
b = \dfrac {\sqrt{2}}{3} \quad
\Rightarrow x^2$$

 yes, when reducing fractions you divide the numerator and the denominator 

guys im back from the mission

17/52 is already reduced to its simplest form;

This means that there are no numbers that can be divided from both the numerator and the denominator.

7x-15+1x=5+2x

There's a start :)

Oh hey MathsGod

speaking of god, i pray to you that tomorrows math homework wont be difficult lol

Same reaction? XD haha 

i wonder how Zegroes will reply to what 7UP just said

I had the same reaction.

Oh yeah, hey Heather!

WHOA THERE!

i looked it up as well, k, and it scared me when i read the definition, not cuz it means it starts you know what, but also cuz my mom was about to come in my room the minute i looked it up (thank you pc for being super fast at switching tabs)

who does threesome relationships these days?

im sorry if im overreacting, i usually dont see that type of stuff lol

btw, its true that TR likes some other girl, and let me stop you right there, its not me

its actually someone TR will have to tell you

p.s. its true that Royality fell, but its not true that his alt ego did it

it was actually THE PRINCIPAL WHO SHUT ALL EMPIRES DOWN!!!

whoa, i did not know that Melody had a sister, i thought she already flew out of the nest lol

well, welcome Melody44?

btw, someone plz give me some Dr. Pepper.....

Start by multiplying the numbers in the parenthesis, in this case, (-2)2

7 * (-3) * -4

Take the -3 out of parenthesis, it's only there to check your understanding

7 * -3 * -4 = 84

225 - 225(10%) =  225  -  225 (.1)  =  225 - 22.5  =  202.5

We have.....

Pt = Pb^t-1     where P is the original population ....   Pt is the popoulation after "n" days  ... b is the growth rate... and t is the number of days ...[ t = 1 is the first day.....so, we're looking for the population 3 days after. the first day = the end of the 4th day ]....and we have

94 = 6b^{(4 - 1)}   =    6b⁽³⁾      divide both sides by 6

(94/6)  = b³        take the cube root of both sides

b ≈ 2.5022

So, our function is  :     Pn =   6(2.5022)^{(t - 1)}

Run wait a minute let me deal with 7up whose mind is somewhere else!

menage A trios? I didn't know 7up you were too much educated !Ooooh! Looks like 7up is tasking " tasting its human taste" somewhere else! Don't fly too much , you'll break my rose shield , or maybe I'll place you in one of the world wars as I mostly take trips in times! 

In general,  (d/dx) (a^x)  = (ln a)* a^x * (the derivative of the exponent on "a").....so......

(d/dx) 10^-x =  ln(10)* 10^-x * (-1)  = -(ln10)10^-x     .....and.....

(d/dx) [- ln(10)* 10^-x ] =  -(ln10) * (ln 10)* 10^-x (-1)  =  (ln10)^2* 10^-x

So.......the "nth" derivative would be

(-1)^n * (ln 10)^n * 10^-x

7UP....

Wow, I searched it up too, that's deep.

Hi Patsy

Lancelotlink do like to throw poo and mangos and drink banana daceries. He get in trouble for sneaking mangos across state lines. He went into the woods to eat his mangos in peace and no one see him here after that.

I like the chimp too.

Maybe he come around when he see his name.  :)