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Ahh, I see. Well reasoned and good logic :D

Simple interest   will result in   the following amount after 'x' years

400 000  + 50 000 x

If you invest in the fund you will have

400 000 (1 + .0425)^2x                             interest is .0425 for each 1/2 year  ( 1/2 of .085 )and there are 2 periods for each x years)

When does your accumulated total earn more money compounded  than 50 000 year?

 50 000 < (400 000 + 50 000 x)  (1.045)²  - (400 000 + 50 000x)

                  436 810 + 54601.25x  - 400 000 - 50 000 x

                    36810 + 4601.25x

13190 < 4601.25x

2.8667 < x                              ~~ at 3 years the fund account would make more money that 50 000 a year

at end of  3 years you would have   550 000     

        at end of 4 years 600 000                              if you put that money into the fund, at the end of 4 years you would have

                                                                       550 000 (1.045)^2 = 600 613.75

All of this says    At the end of 3 years , put your money in the fund.

1)  There are 15 rolls that result in A larger than B:  

     (6,5)    (6,4)    (6,3)    (6,2)    (6,1)    (5,4)    (5,3)    (5,2)    (5,1)    (4,3)    (4,2)    (4,1)    (3,2)    (3,1)    (2,1)

     Probability  =  15/36.

2)  There are 10 rolls that result in a sum of 5 or less:   

      (4,1)    (3,2)    (2,3)    (1,4)    (3,1)    (1,3)    (2,2)    (2,1)    (1,2)    (1.,1)

     Two of these have dice that are equal.

      Probability  =  2/10.

3)  There are only 6 results that have both dice landing on the same number: 

      (1,1)    (2,2)    (3,3)    (4,4)    (5,5)    (6,6)

      Therefore, there are 30 results that have different numbers.

      There are 8 results that have a difference of 2:  (6,4)    (4,6)    (5,3)    (3,5)    (4,2)    (2,4)    (3,1)    (1,3)

      Probability  =  8/30.

To find the distance from one vertex to the opposite vertex, use the three-dimensional distance formula:

     distance  =  sqrt( height² + width² + length² )

Any question about how to use this formula?

The possibilities that contain at least one blue ball are:

blue - blue - blue     (3/7) x (2/6) x (1/5)  =  1/35

blue - blue - red      (3/7) x (2/6) x (4/5)  =  4/35

blue - red - blue      (3/7) x (4/6) x (2/5)  =  4/35

red - blue - blue      (4/7) x (3/6) x (2/5)  =  4/35

blue - red - red       (3/7) x (4/6) x (3/5)  =  6/35 

red - blue - red       (4/7) x (3/6) x (3/5)  =  6/35

red - red - blue       (4/7) x (3/6) x (3/5)  =  6/35

1)  The sum of all the probabilities that have exactely two blue balls is:  12/35.

2)  The sum of all the probabilities that have at least one blue ball is:     31/35.

Dividing the result of 1) by the result of 2) gives:  (12/35) / (31/35)  =  12/31.

Melody:  I have put my response in the middle of your answers.  

First Question

(please include the question so I don't have to go look for it)

Response to first answer.

y = 4-3 sin (x/4)

The first lowest point should be (2pi, 1) and the first highest point should be (6pi, 7) At least, I think this is correct. 

YES, that is perfect, I hope you worked it out with a rough sketch BEFORE you used Desmos.

Just to expand upon EP's answer

Let x represent the number of liter of water to be added.:

The percentage of bleach solution in pure water is 0.00.

The final percent must be between the percentages of the parts.

The final amount is found by adding the amounts of the parts together.

(percent · amount)  +  (percent · amount)  =  (final percent · final amount)

               0.00 · x     +     0.14 · 18              =  0.10 · (x + 18)

Then finish, as EP states.

what is 9+10

9 + 10 =  sqrt(3249) / 3   

After 2 yrs @ 10% simple interest you would have

 2500 + 2500(.1)(2) = $ 3000

@ 10 % simple interest, after 5 more years you will have   3000  + 2500(.1)(5) = $ 4250.

Now take your 3000 that you have after 2 years

7% effective and compounded 5 years    3000 (1.07)^5 = $4207.66        Not quite as much as simple interest.....leave it at 10%

In TEN more years:

In ten years @ 10% you will have   3000 + 2500(.1)(10) = $5000

   @ 7% compounded you will have    3000(1.07)^10 = 5901.45         It would be best to move it to the 7% account  

The degree of the dividing polynomial is 5; the remainder can have any degree smaller than that:  4, 3, 2, 1, 0.

[The remainder can be an x⁴, x³, x², x, polynomial, or a constant (degree = 0).]

sin 60  = opp/hyp   =  15/hyp

sin 60 = 15/hyp     solve for hyp

You know there is a calculator on this site, right?   Use it !  

Bleach content of constituents  = bleach content of final solution

.14(18) =   .1 (18 + x).    Solve for x, the amount a

of water required

The answer is even in the reading of the number.....read it out loud " THREE hundred".     Haha 

Use tan  77            tan 77 = opp/adj        in the is example   opp = height of building (but you must add Leon's 6 ft height to the result)   and adj is the distanc from the building  (given as 25 feet)

Really? I thought it was 4

Let the number of small cups =C

The number of large cups        =70 - C

10C  +  20(70 - C) =1000, solve for C

C = 40 small cups sold

70 - 40 = 30 Large cups sold

Thank you so so much!

Here, I just plotted your equation onto the link that Melody gave you:

https://www.desmos.com/calculator/qbk061i3n3

(1/5) / (3/1) = 1/15

(1/5) / (3/1),

When you divide fractions, you take the reciprocal (flip fraction) of the second fraction (a.k.a, the one closest to the equal sign and change the division to multiplication.

(1/5) * (1/3) = 1/15

Hope this helped!

Well, let's make the area  "a".

And to calculate an area is a^2. 

So if we want to find just one side, we can square root it:

sqrt"a".

In this case, it's sqrt81 = 9.

Which means that one side is 9.

To find the perimeter of a square, we multiply by 4, or we can add up one side 4 times:

9*4 OR 9+9+9+9 = 36.

Perimeter = 36

It's 4... unless you're playing a joke.

Well, 30 tens are 30 * 10.

30 * 10 = 300.

Unless I messed up somewhere, you can count up to 300 by hundreds.

So one hundred, two hundred, and three hundred. That means that 30 tens = 3 hundreds.

So 887000/56133000 is the answer? that's a long one

Area of square = \(s^2\) where, \(s\) is the side length of the square.

\(81=s^2\)

\(9=s\) 

s must be positive since it is a side length, so the negative root of 81 is rejected.

Perimeter= \(4s\) 

Perimeter=\(4(9)=36\) \(inches\)