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You must have been in a rush, because your code was not bug-free!!

The smallest 5-digit integer with 9 divisors is:

11236 = (1, 2, 4, 53, 106, 212, 2809, 5618, 11236) = 9 (divisors)

The diagonals of a rhombus are perpendicular to each other.

If we draw the rhombus and its two diagonals, we get four congruent right triangles.

Looking at one of these right triangles, we can see that the hypotenuse is 169 (the side of the rhombus) and one of its sides is 65 (one-half of the one diagonal0.

I'm going to use the Pythagorean Theorem to find the other half-diagonal:

  c²  =  a² + b²   --->   169²  =  65² + b²   --->   b  =  156   --->  so the other diagonal is  312.

Now that I know the length of both diagonals, I can find the area of the rhombus:

  A  =  ½·diagonal₁·diagonal₂   --->   A  =  ½·130·312  =  20280

Since all four triangles are congruent, each triangle has an area of  20280 / 4  =  5070.

I'm going to use this area to find the radius of the inscribed circle.

The center of the circle is the center of the rhombus. 

The radius of the circle is the height of each of the triangles (the base will be a side of the rhombus).

  A  =  ½·base·height   --->   5070  =  ½·169·height  --->   height  =  60

The radius of the circle is 60.

Find the area of the circle and subtract from the area of the rhombus.

I got 3/16 but it said it was wrong...

You can win in any of four ways:

1) Getting two of the three winning white balls and the red SuperBall.

    Two of the three wining white balls and one out of seven losing white balls:  

           ₃C₂·₇C₁ / ₁₀C₃  =  3·7/120  =  7/40

    Combine this with getting the red SuperBall  =  1/10     --->     7/400

2) Getting two of the three white balls and not getting the red SuperBall:

    The  7/40  from above combined with not getting the red SuperBall  =  9/10   --->   63/400

3) Getting all three of the white balls and the red SuperBall:

    Three of three winning white balls and none of the seven losing white balls:

          ₃C₃·₇C₀ / ₁₀C₃  =  1·1/120  =  1/120

    Combine this with getting the red SuperBall  =  1/10     --->     1/200

4)  Getting all three of the white balls and not getting the SuperBall:

      The  1/120  from above combined with not getting the red SuperBall = 9/10   --->   3/400

To get the final answer, you must add the individual answers from above.

hi guest!

∏[1 - 1/n^2], n, 2, 100 =101 / 200

If f(-4) = -22, f(-1)=2, and f(2)=-1, what is the function if f(x) is a quadratic polynomial?

thanks guest! :)

Two steel poles have diameters of 12 inches and 36 inches.  A wire bundles both of them together.  What is the shortest possible length of the wire?

The shortest length of the wire is  129.534 inches.   

( The diagram, I hope, explains everything. )  

Oh okay, thank you!

Solve |x + 2| - |x - 5| = 1.

The probability is 1/C(20,4) = 1/4845.

it is 4/3

I think i know...

Tan repeats itself every 180 degrees

(3000 - 300 )/180 = 15      so these two are equal

(30000-300)/180 = 165        equal 

so   300 3000 30000   tan's are equal      (as guest found)

Jan is thinking of a positive integer.  Her integer has exactly 16 positive factors, two of which are 12 and 15.  What is Jan's number?

Factoring 12:  1 x 2² x 3

Factoring 15:  1 x 3 x 5

So, the number must have these factors:  2², 3, and 5.

2² x 3 x 5  =  60

60 has these factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60   --  12 factors, not 16.

So, let's try putting in another factor of 2:  60 x 2  =  120.

120 has these factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120   --  16 factors!

Hour hand starts at 270   and adds 1/2 degree per minute

Minute hand starts at 0   and adds 6 degrees per minute

270 + 1/2x   -  6x   = 28

242 = 5.5 x

x = 44 minutes  

9 :44             270 + 44(1/2)  -   44(6) = 28  degrees

x = original number of candies

ate 1/3     means    2/3 x remains

gave away 1/4    means    3/4 * 2/3 x  reamins

ate 30        3/4 * 2/3 x - 30

Brat Brother took 1 to 5      so     3/4 * 2/3 x -30   -  (1 to 5) = 3

                                                     6/12 x  -  30     - 1to5 = 3     

                                                     6/12x - 1to5 = 33

        6/12 x = 33    means x = 66        since BratBro took 1- 5 

6/12 (68) -1 =33

6/12 (70) - 2

6/12 (72) - 3     This is the only one that results in whole candies after 1/3 removed and 1/4 removed        72

6/12(74) -4

6/12(76) - 5

Since there are 4 kinds of bread, 6 kinds of meat, and 5 kinds of cheese,

there are a total of  4 x 6 x 5  =  120  different sandwiches.

However, we need to exclude a ham/cheddar cheese combination.  Since we can have this

with any kind of bread there are 4 sandwiches excluded.

We also need to exclude a white bread/chicken combination. We can have this with any

kind of cheese, so we have to exclude these 5 sandwiches.

There are  120 - 4 - 5  =  111  sandwiches remaining.

I THINK:

he has a 5/6 chance of NOT winning a soda each time

(5/6)⁶ = .335   chance of NOT winning a soda with six purchases

1- .335 = .665 chance of WINNING with a six-pak purchase     66.5%

My guess is 31  --  31 works, but I haven't checked to see if it's the smallest ...

What is x and y in the system of equations 3x + 2y = 170 and 4x + 6y = 360?

One way to solve this is by "linear combinations" --  getting either the x-term or the y-term in

both equations to be the same and then either add or subtract.

I'm going to make the y-term (2y) of the first equation to be the same as the y-term of the second

equation (6y) by multiplying the first equation by 3:

3x + 2y  =  170   --->   multiply by 3   --->   9x + 6y  =  510

4x + 6y  =  360                                            4x + 6y  =  360

subtract down the columns:                        5x          =  150

divide by 5:                                                            x  =  30

Now, substitute that value back into the first equation:

     3x + 2y  =  170   --->   3(30) + 2y  =  170   --->   90 + 2y  =  170

                                                                                         2y  =    80

                                                                                           y  =  40

Factor (2x + 1)(x - 3) + (2x + 1)(7x - 2).

Notice that you have a common factor of (2x + 1):    (2x + 1)(x - 3) + (2x + 1)(7x - 2)

Factor it out  -- put it in front:      (2x + 1)[ (x - 3) + (7x -2) ]

Simplify: (2x + 1)(8x - 5)

I'm assuming that you mean that the largest int. n,n^2  divides 2000 into a integer, so n^2 is a factor of 2000.

Factors of 2000:

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000

So 2000 isn't a perfect square, nor 1000,

500, isn't.

400 = 20^2!

n = 20.

If you don't understand anything feel free to ask.