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Patty has an icing recipe that makes 24 cupcakes and the ratio of cups of sugar to sticks of butter is 3:1. If she has to make 60 cupcakes, how much of each ingredient will she need?

 \(\dfrac {60}{24}=\dfrac 5 2 \\ \dfrac 5 2 \times 3 = \dfrac {15}{2} \mbox{ cups of sugar.} \\ \dfrac 5 2 \times 1 = \dfrac 5 2 \mbox{ sticks of butter.}\)

a₁₂ = 7(12) + 4 =  88

Write the rational expression in lowest terms.

 

3n^2-3n/4n-4

\(\mbox{Assuming } n\neq 1 \\ \dfrac{3n^2-3n}{4n-4} = \dfrac{3n(n-1)}{4(n-1)}=\dfrac {3n}{4}\) 

2.6 * 10^-5 * 0.0000052  =  1.352 x 10^-10

 25=10(log(i)+16)

\(25=10\left(\log(i)+16\right) \\ \dfrac 5 2 = \log(i)+16 \\ -\dfrac {27}{2}=\log(i) \\ \mbox{Assuming we are using logs base 10 we have } \\ i = 10^{-\frac {27}{2}}\) 

y-4.7=-12.52                             

y-4.7+ 4.7=-12.52+4.7            add 4.7 to both sides 

y=-7.82

Thank you so much

That is ok mathkid, it is all good practice for you and I am glad that you are showing an interest. :)

4(x-5)-8/3=12            distrubte  4 to X and -5

4x-20-8/3=12    

-20-8/3 or -20-2.67 = -22.67                       subtract -8/3 from -20

4x-22.67=12

4x-22.67+22.67=12+22.67                  add 22.67 to both sides 

4x=34.67

4/4= 34.67/4                                   divide by 4 by both sides 

X=8.67

25  = 10 *( log i + 16)   divide both sides by 10

25/10   =  log  i + 16    subtract 16 from both sides

2.5 - 16  = log i

-13.5 = log i   in exponential form, we have

10^(-13.5)  = i   = about  0.00000000000003162  W/cm^2

4 bars / 3 people  =     1 + 1/3  bars per person

umm d

2^8   = 256

2^2 = 4

So.....

256 / 4  =   64

 9+3x=-15

9-9+3x=-15-9

3x=-24

3/3x=-24/3

x=-8

1 foot = 12 inches....so 5 of them = 5 x 12 = 60 inches....and 6 more inches = 66 inches.......

???

thanks guys but im 11 so its 4th grade stuff 

what is 3200(1/2)^11/14 I don't understand how to enter this into the calculator. Help?

First you enter the number inside the bracket. You have to enter it as .50, which is easier. Then press the key "x^y". Next you open a bracket "(" then enter 11/14, then close bracket")". Next press X sign followed by 3200. Finally, you press = sign, which should give you your answer.

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Just like this :

3200*(1/2)^(11/14)    =   1856.20701785626048

The idea here is just to end up with "x"  on one side....so.....

4x-9=39      add 9 to both sides

4x = 48     divide both sides by 4

x = 12

Just divide the population of the US by the population.

(3 X 10^8) / (6 X 10^5)=500x the population of US is greater than the population of Vermont in 2000.

[ 3 x 10^8] / [6 x 10^5]  =

3/6   x  10^8 / 10^5  =

0.5 X 10^3  =

500 times as large

use a calculator      

(3^(5/7))^n = 3    take the log of both sides

log (3^(5/7))^n  = log (3 )     and we can write

n *   log (3^(5/7))  =  log (3)        divide both sides by  log (3^(5/7))

n =   log(3) / log (3^(5/7)) =  7/5