All Answers 356415 Answers

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

thank you Cphill

Let's check

600  * .07  *  3  =

42  *  3  =

$126

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

Why, thank you so much, Foxy. It's so great to be here again. :D

I don't know, but I hope that all of us will be able to help you with all of the questions you have. :D

Hello, Guest. How are you on this fine evening? 

1)  Correct  !!!!

2)   Correct again  !!!

Good job  !!!

thanks Cphill

THANK YOU

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

The area formula of a trapezoid is given \(A=h\left(\frac{b_1+b_2}{2}\right)\)

The problem also tells you the following information:

A = unit of area (in a square unit like square feet)

b_1 = one base

b_2= other base

h = perpendicular height

The order in which you substitute the bases are immaterial in this case since addition abides by the commutative and associative properties.

If the questions asks for "how many square feet," this is the unknown. Square feet is indeed a unit of area, so this would be A in the formula above. We don't know what "A" is yet, but we will solve for it. The question directly states the other variables' meaning.

A = unknown area in square feet

b₁= 125ft

b₂ = 81ft

h = 75ft

All this information has been nicely synthesized, and we have established the meaning of every single variable in the original formula. Now, we must use the formula to figure out the unknown or the area in square feet:

thanks can you help me with a other one?

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

343 /   125   =   (scale factor)³

scale factor   =   [343 / 125]^1/3

height of larger cylinder   =   5 * scale factor

height of larger cylinder   =   5 * [343 / 125]^1/3

height of larger cylinder   =   5 * 7 / 5

height of larger cylinder   =   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

4.

\(\quad\,(7-\sqrt7)(-6+\sqrt7) \\~\\ =\,(7)(-6)+(7)(\sqrt7)+(-\sqrt7)(-6)+(-\sqrt7)(\sqrt7) \\~\\ =\,-42+7\sqrt7+6\sqrt7-7 \\~\\ =\,-49+13\sqrt7\)

thank you

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

35%  of what number is  21

35%  *  what number  =  21

35/100  *  what number  =  21       Multiply both sides of this equation by  100/35 .

what number   =   21 * 100/35

what number   =  60

35%  of  60  is  21

17 is what percent of  68 ?   In other words...

17 out of 68 is what out of 100  ?

17 / 68   =   what / 100

17 / 68 * 100   =   what

25   =   what

17  is  25  percent of  68 ,  as you found! 

what number is  16%  of  80

what number   =   16%  *  80

what number   =   16/100 * 80

what number   =   12.8

12.8  is  16%  of  80 ....You got it!!

Equi   =  "Equal"

Lateral  =  "Side"

so.....

"Equal- Side"  =  "Equil-Lateral "

4)If f(x)=2x^3 −5x^2 −7,find f(h−1).

So we have

2 (h - 1)^3  - 5(h - 1)^2  -  7   =

2( h^3  -  3h^2 +  3h - 1 )  -  5 (h^2 - 2h  + 1)  - 7   =

2h^3  - 6h^2  + 6h  -  2  -  5h^2  + 10h  -  5  -  7   =

2h^3  -  11h^2  +  16h  - 14

5)  Find the average rate of change of f (x) = 2x^2 − 5x −12 over the interval [–2,–2+h], whereh>0.

We have

[   (  2 ( -2 + h)^2  - 5 ( -2 + h) -  12)   -  ( 2(-2)^2 - 5(-2) - 12 )  ]  /  [ (- 2 + h)  - (-2) ]  =

[  (  2 (h^2 - 4h + 4)  + 10 - 5h - 12 )  -  ( 8  + 10 - 12 ) ]  /  h  =

[ 2h^2  -  8h  + 8  +  10  - 5h  - 12   - 8  - 10  + 12 ]  / h  =

[  2h^2   - 13h ] /  h   =

h ( 2h - 13)  /  h  =

2h - 13

6) The value of a boat is $800,000 in year 2006 and it depreciates $30,000 per year, after year 2006. Find a model to represent the boat’s value V(in $1000) as a function of t. Variable t represents the number of years t after year 2006. 

We have that

V(t)   =  800  -  30t

Where  V(t)  is the value in thousands, t years  after 2006

\(\quad\,\frac{\sqrt3-\sqrt6}{\sqrt3+\sqrt6} \\~\\ =\,\frac{\sqrt3-\sqrt6}{\sqrt3+\sqrt6} \,\cdot\,\frac{\sqrt3-\sqrt6}{\sqrt3-\sqrt6}\\~\\ =\,\frac{3\,-\,2\sqrt{18}\,+\,6}{3\,-\,6} \\~\\ =\,\frac{9-2\sqrt{18}}{-3} \\~\\ =\,\frac{9-6\sqrt{2}}{-3} \\~\\ =\,-3+2\sqrt2\)

180(s - 2)   =   2520         Divide both sides of this equation by  180 .

s - 2  =   14      Add  2  to both sides of the equation.

s   =   16

thanks Cphill

Note that

1/5  =  20/100   =  20%

0.4  =  4/10  =  40%

So....from  least to greatest, we have

15% , 1/5, 25% , 0.4