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w / l = 7/2        l = 2/7 w

also l+ w = 450       so     2/7 w + w = 450       shows w = 350      l = 100 gallons

now add water     

(350 + x )   /  ( 100 )   =  8/1

350 + x = 800 

x = 450   gallons of water to add     

List the numbers in ascending order....    the median is the number in the middle

    If the list has an even number of elements, the median is the average of the middle TWO numbers.

The mean is the same thing as the average....  add all of the numbers together then divide by eight ( the number of elements in the list)

You asked me to clarify my last answer.

I did that at length.

I am still waiting on a response from you.

You description is not clear.  You say the triangle ABC is right anged but you have not said where the right angle is.

Which letter is at the vertex? 

It is very confusing.  People cannot answer you if they do not understand your question.

Thank you guys!!

Yes, subsets of just 1 term are possible. !!

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the fourth digit is at most  twice the second digit    ....   I think you may need to recalculate .....

second digit = 0    fourth = 0

                       2    fourth    0 1 2 3 4

                       4    fourth     0 - 8

                       6    fourth   0-9

                       8    fourth   0-9         Right?

Question BB :    Can a subset have just one element ?       If so, there is one more possibility

Total subsets possible =   2⁵  = 32

     I believe 1/2 of these would contain the symbol     = 16 subsets

6 months is 1/ 2   of a year

20 000 * .0625 * 1/2 = $ _________ interest

I didn't understand the question either.

I think it is \(11 \choose 7\). There are 7 ways to choose the boys with orange caps, and the rest have yellow caps. 

Thus, there is \(\color{brown}\boxed{330}\) ways. (Note, \({11 \choose 7} = {11 \choose 4}\), so the answer would be the same either way. 

Here's a better way to get the same answer. 

For groups of 2 including  ₯, there is \(4 \choose 1 \) choices, because 1 of them is already taken. 

For groups of 3 including  ₯, there is \(4 \choose 2 \) choices, because 1 of them is already taken. 

For groups of 4 including  ₯, there is \(4 \choose 3\) choices, because 1 of them is already taken. 

For groups of 5 including  \(₯\), there is \(4 \choose 4\) choices, because 1 of them is already taken. 

Adding everything up, there is \(\color{brown}\boxed{15}\) subsets that contain ₯.

I will number these from right to left, starting with 1, going up to 5. The rightmost one is 1, the leftmost is 5. 

2 1

2 3

2 4

2 5 

2 1 3 

2 1 4 

2 1 5 

2 3 4 

2 3 5 

2 4 5

2 1 3 4 

2 1 3 5 

2 1 4 5 

2 3 4 5 

2 1 3 4 5 

Thus, there is a total of \(\color{brown}\boxed{15}\) subsets with the ₯ symbol. 

I think this is a permutation problem. 

If you order the Yellow and Orange caps in the following order:

Y, Y, Y, Y, O, O, O, O, O, O, O

It is different from:

Y, O, Y, O, Y, O, Y, O, O, O, O

So to me this is a permutation problem. 

Apply formula. 

11P11 = 39 916 800 ways

I'm not confident in my answer. 

It has to be in the form ABCBA. There are 5 choices for A, 5 for B, and 5 for C, making a total of \(\color{brown}\boxed{125}\) choices.

\( If \ 12^2 \cdot 18^3 = 2^x \cdot 3^y, find\ x+y. \)

Hello Guest!

\(12^2 \cdot 18^3 = 2^x \cdot 3^y\\ (2^2\cdot 3)^2\cdot (2\cdot 3^2)^3=2^x\cdot 3^y\\ 2^4\cdot 3^2\cdot 2^3\cdot 3^6=2^x\cdot 3^y\\ 2^7\cdot 3^8=2^x\cdot 3^y \)

\(x=7\\ y=8\\ x+y=15\)

  !

Why wont anyone answer?

p+j = 48      p = 48- j

(j + 2/5 p) 8/9 = 24

(j + 2/5 ( 48-j) ) 8/9  = 24

j = 13

There are 2 cases: The second digit is a 2 or it is a 4

If the second digit is a 2: \(9 \times 1 \times 10 \times 5 = 450\)

If the second digit is a 4: \(9 \times 1 \times 10 \times 9 = 810\)

Add these together for a total of \(\color{brown}\boxed{1,260}\) ways

The force of gravity is given by the equation   F = G m₁m₂ / r²

    where G = gravitational constant

at 4000 miles      600 = G m1m2/ (4000)²

                        or simply            600 = k / (4000)²             Then   k = 600(4000)²

   at 240 000 miles      F =   G m1m2 / (240000)²           ( we are ignoring the gravity of the moon for this problem)

                   F  = k / ( 240 000)^2 

                        = 600(4000)^2 / 240000² = .1666 N      <==== ( basically weightless !)

HAPPY ANIVERSARY CPHILL!!!

You made it so easy to learn new math skills and topics!!!

Because it's a right triangle, and the remaining angles are equal, this is a 45-45-90 triangle, with a width and heigth of 6, making the area \(6 \times 6 \div 2 = \color{brown}\boxed{18}\)

As follows:

HAPPY ANNIVERSARYYYYY :)))

Thank you for being such an amazing person on web2.0calc.

=^._.^=

I'm not sure I understand this question properly. 

If n = 4, then z = 3. 

So there must exist an interger a such at 4 = a^6. 

I don't think an integer a exists.

Am I interpreting the problem wrong?

=^._.^=