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5005 digits / 55 min = 91 dig /min

Will covers some of the distance (5 minutes worth ) before Grace starts

    50 m/mim X 5 min = 250 meters

       there is 2350 - 250 = 2100 meters to cover before they meet

The are approaching each other at   (50 + 10) = 60 m/min

    the time to cover 2100 M      is        2100 m / (60 m/min) = 35 mintes

2:05 + 35 min == 2:40   when they meet

The greatest possible slope is 3/11.

The exact value is 1/sqrt(2).

The answer is C.

The distance to the hypothesis is 14.

hex  =  six   --->   so it has six faces plus a top and a bottom for faces = 8

It has 6 edges on the top, 6 on the bottom, and 6 on its sides:  edges = 18

It has 6 vertices on the top and 6 on the bottom, vertices = 12

Euler's formula:  V - E + F  =  2     --->     12 - 18 + 8  =  2

The wall is 12*80 = 960 m^2.  This converts to 960/0.3048 = 3150 square feet, so the number of gallons needed is 3150/200 = 15.74, which rounds up to 16.

How is that cheating with hw?

The prime factorization of 8! is 2^7 * 3^2 * 5* 7. The largest square that divides this is 2^6*3^2 = 576

When will the roots of  x² - 4x - log₂x  =  0  be real.

For the roots to be real, the discriminant of the quadratic formula must be  >=  0.

b² - 4·a·c  >= 0    --->     (-4)² - 4·1·log₂₍A)  >=  0 

                                              16 - 4·log₂₍A)  >=  0 

                                                   - 4·log₂₍A)  >=  16

                                                        log₂₍A)  >=  -4

                                                                 A  >=  2^-4

                                                                 A  >=  1/16

x/y  =  3/4     --->     4x  =  3y               (cross-multiplying)

y/z  =  2/3     --->     3y  =  2z

z/w  =  5/8    --->     8z  =  5w

What is  (x + y + w) / w?

Notice that there is no z is the question.

This means that we should rewrite each of the variables in the question in terms of z; then all the z-terms will cancel out.

Since  8z  =  5w     --->     w  =  (8/5)z

Since  3y  =  2z      --->     y  =  (2/3)z

Since  4x  =  3y  and  3y  =  2z,  4x  =  2z     --->     x  =  (1/2)z

(x + y + w) / w     --->    [ (1/2)z + (2/3)z + (8/5)z ]  /  [ (8/5)z ]

The z's will cancel     --->     [ 1/2 + 2/3 + 8/5 ] / [ 8/5 ]

                                  --->     83/30  /  8/5

                                  --->     83 / 48

There are 90 3-digit numbers ending in 6. 30 of those 90 are multiples of 6. Therefore, the probability is:

30 / 90 = 1 / 3

If the ball are distinguishable, let's say that they are red (R), yellow (Y), green (G), and blue (B).

The boxes are not distinguishable.

We could put all four balls in one box; this can be done in only one way [R,Y,G,B].

Since the boxes are not distinguishable, it doesn't make any difference in what box we place

the four balls.

We could put three balls in one box, and one ball in another box. This can be done 4 ways:

[R,Y,G] - [B]     [R,Y,B] - [G]     [R,Y,G] - [B]     [ Y,B,G] - [R]

We can put two balls in one box, and two balls in another box. This can be done 3 ways:

[R,Y] - [G,B]     [R,G] - [B,Y]     [R,B] - [G,Y]

We can put two balls in one box, and one ball in each of the other two boxes. This can be

done 6 ways:

[R,Y] - [G] - [B]        [R,G] - [B] - [Y]          [R,B] - [G] - [Y]

[Y,B] - [R] - [G]         [Y,G] - [R] - [B]          [G,B] - [R] - [Y]

What is "function AAA"?

1)  If you want to switch from radians to degrees, the relationship between the two is:

           2·pi (radians)  =  360 (degrees)     or     pi (radians)  =  180 (degrees)

    So, if you have  pi/6  radians and you want to switch it into degrees, replace the "pi" 

          with  "180^o     --->     this means that  pi / 6  becomes  180^o / 6  or  30^o

    To find  sin( pi / 6 ),  you can find  sin( 30^o  ).

2)  If triangle(ABC) has  AB = 25,  BC = 25,  and  AC = 40, then it must be an isosceles triangle.

     Draw the perpendicular from B down to side AC; call the point where they intersect X.

     To find  sin(ACB)  look at triangle(XCB):

     XC = 20  and  BC = 25.

     Using the Pythagorean Theorem to find BX:  BX² + XC²  =  BC².

          --->     BX² + 20²  =  25²     --->     BX² + 400  =  625     --->     BX²  =  225

          --->     BX  =  15

      sin(ACB)  =  opp / hyp  =  15/25

8 C 3   *   6 C 2 = ........... ways

or

8! / ( 5! 3!)  *  6! / (4! 2!) = ....... ways

I edited it.....make sure you have most recent answer ! 

thank you!

thank you!