Melody

Thanks Heureka,

I had not thought to do it as a GP  :))

If john had 36 marbles and sally had 64 marbles and thomas has 5/8 of the total marbles,how many marbles does thomas have? 

Well if John, Sally and Thomas have all the marbles then 

36+64=100

3/8 of the marbles is 100

\(\frac{3}{8}x=100\\ x=\frac{100*8}{3}\\ \frac{5}{8}x=\frac{5*100*8}{3*8}\\ \frac{5}{8}x=\frac{500}{3}\\ \frac{5}{8}x=166\frac{2}{3}\\\)

Thomas has 166 whole marbles plus 2/3 of a marble.  I guess some of the marbles are broken!     

6 5/9 - 3 1/4

=(6+5/9)-(3+1/4)

put into the web2 calc

(6+5/9)-(3+1/4) = 3.3055555555555556 = 119/36 = 3 and 11/36

(-2x+11y)2

\((-2x+11y)^2\\ =(-2x)^2\;+\;2*(-2x)*(11y)\:+\;(11y)^2\\ =4x^2\;-\;44xy\:+\;121y^2\)

Compute. i+i^2+i^3+\cdots+i^{258}+i^{259}.

\(Compute. i+i^2+i^3+\cdots+i^{258}+i^{259}\\ i^1=i\\ i^2=-1\\ i^3=-i\\ i^4=1\\ i^5=i\\ \mbox{and so the pattern continues, so}\\ i^2+i^4+\dots +i^{256}=0\\ i^1+i^3+\dots +i^{255}=0\\ \mbox{so this leaves}\\ =0+i^{257}+i^{258}+i^{259}\\ =i^{4*64+1}+i^{4*64+2}+i^{4*64+3}\\ =i-1-i\\ =-1 \)

Thanks Omar,

You are right, I copied the question incorrectly but i think the steps are all good though :)

What a nice thank you       I am really pleased that my answer was helpful. :)

The following deposits were made into a balanced mutual fund in 2015. The number of days is the length of time each deposit earned interest:
$30,000 on deposit for 300 days.
$10,000 on deposit for 257 days.
$25,000 on deposit for 179 days.
$15,000 on deposit for 143 days
$20,000 on deposit for 107 days
These deposits totaling $100,000 were worth $112,500 on Dec,31, 2015. What was the overall yield on this mutual fund for 2015?. Thank you for any help.

I have assumed that the interested is calculated and added daily.

I have let R = 1+ the daily interest rate.

\(112,500=30000R^{300}+10000R^{257}+25000R^{179}+15000R^{143}+20000R^{107}\\ 11.25=3R^{300}+1R^{257}+2.5R^{179}+1.5R^{143}+2R^{107}\\ \)

Now I have no idea how to do this so I entered it into Wolfram|Alpha

How do i calculate 200 x 25 + 5x 800
                               5 x 20 + 25 x 4 

\(\frac {200\times 2\; + \;5\times 800}{ 5 \times 20 \;+\; 25 \times 4 }\\ =\frac {200\times 2\; + \;5\times 800}{ 5 \times 20 \;+\; 25 \times 4 }\\ \qquad 200*2=2*2\;and\; add\; the\; two\; zeros = 400\\ \qquad 5*800=5*8\;and\; add\; the\; two\; zeros = 4000\\ \qquad 5*20=100\\ \qquad 25*4=100\\ \qquad \mbox{Put it all together and you get...}\\~\\ =\frac {400\; + \;4000}{ 100 \;+\; 100 }\\ =\frac {4400}{ 200 }\\ =\frac {4400\div 100}{ 200\div 100 }\\ =\frac {44}{ 2 }\\ =\frac {44\div 2}{ 2 \div 2}\\ =\frac {22}{ 1 }\\ =22 \)

If there is a step that you do not understand then just ask :)

2x+3y*4x-2y

2x+12xy-2y

That is all the simplifying that you can do.