CPhill

1. Sales Tax  =  Just multiply   98  by  .06

2.  Pct Change   =    

[  (  New Price  -  Old Price )  / Old Price  x 100 ]  %  =

[  (35 - 28) / 28   x  100 ] %  =

[ 7 / 28  x 100 ] %  =

[ 1/4 x 100 ] %   =

25%

3.    We want to find this

1000  = 500 * .05 * t      simplify

1000   =  25 * t            divide both sides by 25

40  = t  =   40 years  

BTW..... surprising fact....the time to double any amount at 5% would be the same  !!

Not an expert on this....but...I think we can use this formula to find the result :

Magnitude  =  log 5  + 8.2  =

.699  + 8.2   ≈

8.9

Here's a website that goes into more detail :

http://www.sosmath.com/algebra/logs/log5/log56/log56.html

Excellent  !!!!!

For both questions....

First....find the interest earned  [ I know you can do this.....]

Second....add the interest you calculated back to the original amount

This will give you the balance.....let me know if you get stuck

Let's check

600  * .07  *  3  =

42  *  3  =

$126

Hey....you're getting pretty good with this stuff....!!

1)  Correct  !!!!

2)   Correct again  !!!

Good job  !!!

Note that  the scale factor of B to A  is  (4 / 8)  =  1/2

So....the volume of B  =

Volume of A  *  (scale factor)^3  =

2720  *  (1/2)^3  =

2720 * 1/8  =

340 cm^3

To find the linear ratio  of both things we can use this :

³√343  /  ³√125     =     7 / 5

So.... the height of the larger cylinder is  7/5 ths  that of the smaller one...so we have

(7 / 5)  *  5   =     7 feet

Well....by the use of the word "increase" or "decrease" in the questions themselves, we should be able to  answer the first  part

Here's 1

Note something important   we can write an  "x"  percent increase  as

(1  +  the decimal representation of the percent increase )

So......this becomes

84  ( 1 + 12%)  =  84 ( 1 + .12)  =  84 ( 1.12)  =  94.08

Here's 2

Likewise.....we can write an "x" percent decrease  as

(1 -  the decimal representation of that decrease )

So we have

820 ( 1 - 25% )  =  820 ( 1 - .25)  =  820 (.75)  = 615

³√750 + ³√2058  +  ³√48

The trick here, NSS...is to simplify the radicands as much as we can...let's factor these, first

750  =  250 * 3   =   25 * 10 * 3   =  5^2 * 5 * 2 * 3  =  5^3 * 6

2058  =   1029 * 2   =  343 * 3 * 2  =  7^3 * 6

48  =  8 * 6  =  2^3 * 6

So  we have

³√ [ 5^3 * 6 ] + ³√ [ 7^3 * 6 ]  + ³√ [ 2^3 * 6 ]  =

5³√6  + 7³√6  + 2³√6

Now just add the coefficients in front of each radical and let the radical go along for the ride..so we have

[ 5 + 7 + 2 ] ³√6  =

14³√6