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1) Your $880 in Stock acct. over 25 years @ 10.8% will grow to =$1,339,663.24

2) Your $480 in Bond acct. over 25 years @ 6.8% will grow to    =$376,750.02

3) The total in your retirement account will be $1,339,663.24+$376,750.02=$1,716,413.26

4) From the amount in 3 above, you can withdraw a monthly payment of =$14,143.86 each and every month for 20 years, or 240 payments.

Agreed

-1

-4=3x-1

1-4=3x

-3=3x

3x/3=-3/3

x=-1

-4=3(-1)+2-3

-4=-3-1

-4=-4

TRUE

x=-1

Sorry!   I misread the question..... I was MAKING 100 gallons of 50% juice, not MIXING with 100 gallons of 45% juice!!

Let x  = the number of gallons of 55% juice to be mixed....and we have

.55(x )  + .45(100) = .50(x + 100)     simplify

.55x + 45  = .50x + 50     subtract .50x, 45 from both sides

.05x  =  5        divide both sides by .05

x  = 100 gallons of the 55% juice

{This makes sense when you think about it....equal amounts of 45% juice and 55% juice should produce a mixture with an "average" percentage of the two }

x = amount of 55%

100-x = amount of 45%

x(.55) + (100-x)(.45) = 100 (.5)

.55x + 45 - .45x = 50

.1 x = 5

 x= 50 gallons      (although you can mix INFINITE gallons of 'orange juice DRINK' and never make orange JUICE    haha)

[2.5+(4.3-1.1^2)]^2   =

[ 2.5 + (4.3 - 1.21) ] ^2  =

[2.5 + 3.09 ] ^2  =

[ 5.59] ^2  = 

31.2481

2.236067977

 500x³ + 108y¹⁸        take out the factor of 4

4 ( 125x³ + 27y¹⁸ )    now.........we can factor the terms in parentheses as a sum of cubes

4 (5x  +  3y⁶) ( 25^x2  - 15xy⁶ + 9y¹²)

Evie....only  B   is correct.....

Let x be the  number of Connecticut tiles and y be the number of Texas tiles manufactured

We have the following system of constraints 

17x + 51y   ≤ 255

68x + 17y  ≤ 272

And we wish to maximize the objective function

49x +  14y

As shown by the graph, here : https://www.desmos.com/calculator/h5pmmegzom, the corner point of the feasible region that maximizes the profit occurs at  (x,y)  = (3,4)

So....the maximum profit is 49(3) + 14(4)  = $203

Simplify the following:
(Y (1/X+1/Y))/(1/X)

Multiply the numerator of (1/X+1/Y)/(1/X) by the reciprocal of the denominator. (1/X+1/Y)/(1/X) = (1/X+1/Y) X:
X (1/X+1/Y) Y

Put each term in 1/X+1/Y over the common denominator X Y: 1/X+1/Y = Y/(X Y)+X/(X Y):
Y/(X Y)+X/(X Y) X Y

Y/(X Y)+X/(X Y) = (Y+X)/(X Y):
(Y+X)/(X Y) X Y

((X+Y) X Y)/(X Y) = (X Y)/(X Y)×(X+Y) = X+Y:
Answer: |X+Y

Using Algebra and emulating Alan(shame on me!), we have:

76d+19s =532, 16d + 24s=192, solve for d, s

d=dragons=6 and s=sharks=4

6 x $60=$360 and 4 x $12=$48 for a total of:

$360+$48 =$408 maximum earnings.

Mom's Monster Market manufactures plush dragons and sharks. A dragon requires 76 inches of fabric and 16 ounces of stuffing. A shark requires 19 inches of fabric and 24 ounces of stuffing. Mom has 532 inches of fabric and 192 ounces of stuffing. She can sell the dragons for $60 each and the sharks for $12 each. How many sharks must Mom manufacture to maximize her money?

Similar to the last question about tiles:

The best outcome that I can see is:

6 dragons which will require 456 inches of fabric and 96 ounces of stuffing.

That leaves: 76 inches of fabric and 96 ounces of stuffing out of which 4 sharks can be made:

So, 6 dragons X $60 =$360 and

      4 sharks X $12 =$48 for a total of:

$360+$48 =$408 maximum amount that she can earn by using all matrial at hand. She could make 7 dragons and make $420, but that will leave 80 ounces of stuffing!!.

OK guys. That is my take on it!!.

No,     cm^9  is what I meant          

cm x cm = cm^2   

cm^2 x cm = cm^3    

cm^3 x cm^3 x cm^3 = cm^9  (cm^9 is what I do not what )

(2.52 - 2.25) x 10^5  = .27 x 10^5  = 2.7 x 10^4        27,000  Miles difference

For an INFINITE series the sum S

S = a1/ (1-r)    where r is the common ratio (1/8)

60 = a1 / (1-1/8)

60 x (7/8) = a1 = 52.5

Do you mean cm squared? 

The exact value of WHAT?   The angle? (don't know)      The cosine? (-3/5) 

      3/4 15 300 6000 120000   2,400,000     48, 000, 000

n =  1     2   3    4          5              6                    7

48 million IS evenly divisible by 1,000,000    so n = 7