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We can use coordinates.  The equations of the lines are y = 1/3*(x + 2) and y = 1/3*(x - 2), and the distance between these lines is 2*sqrt(10)/5.

You can enter the numbers as follows:

1 4 7 10

2 5 8 11

3 6 9 12

Then there are 3! = 6 ways of arranging the numbers in each column, so the number of ways is 6^4 = 1296.

Ohhh, I'm so sorry! I thought you put an exclamation mark after the 3. Not 3 factorial. 

(a) There are 3^n ways of distributing the elements among A, B, and C, and there are 2^n ways of choosing each subset, so the probability is 3^n/(2^n*2^n*2^n) = 3^n/8^n.

(b) There are 2^n ways of choosing C, then 2^(n - 1) ways of choosing B, then 2^(n - 2) ways of choosing A, so the probability is 2^n*2^(n - 1)*2^(n - 2)/(2^n*2^n*2^n) = 1/8.

(a) Let P be the intersection of AD and MN, and let Q be the intersection of AL and MN.  Then by Menelaus's Theorem, Q is the midpoint of PK.  Since AD and LK are parallel, triangles ADL and LKQ are similar.  And since Q is the midpoint of PK, QK = PK/2 = DL/2.  Therefore, from the similar triangles, AD/LK = 2.

(b) Since QK = DL/2 and QG = LG/2, triangles GDL and GKQ are similar.  Then KG = DG/2, so by part (a), triangles ADG and LKG are similar.

(c) In part (b), we found that triangle GDL and GKQ were similar.  Then angle QKG = angle LDG, so D, G, and K are collinear.  And by the similarity in part (b), DG/GK = 2.  Easy!

ok...

u = (3, 3, -1).

By stars and bars, the number of ways is C(12,3)*C*(11,3) = 36300.

The probability is C(7,3)*3*C(11,2)/(10*1200) = 77/160.

#1) probability that the beads are different colors = 1(all probabilities) - (probability that the beads are the same colored)

#2) (probability that the beads are the same colored) = (probability that there will be 2 red beads) + (probability that there will be 2 pink beads) + (probability that there will be 2 blue beads)

#3) (probability that there will be 2 red beads) = (5/10) * (4/10) = 0.2

#4) (probability that there will be 2 pink beads) = (2/10) * (1/10) = 0.02

#5) (probability that there will be 2 blue beads) = (3/10) * (2/10) = 0.06

#6)  (probability that the beads are the same colored) = 0.2 + 0.02 + 0.06 = 0.28

#7) probability that the beads are different colors = 1 - 0.28 = 0.72

#8) Answer = 0.72

I don't quite understand your question! ALL multiples of 90 end in zero and ALL powers of 6 end up in 6 and are not divisible by 90. Example: 990 is a multiple of 90 but cannot be expressed as "perfect power of 6", in the sense that there such number n, where 6^n =990. If that is what you mean ! If you mean that the multiples of 90 that are also multiples of 6, then that is a different thing altogether.

The function is in the form: ax+b

2a+b=6

4a+b=14

2a=8

a=4 and  b=-2

(8)(4)-2=30.

I'm not sure what your cryptic response means.....

L2 =    2 y = 10x+3      simply divide through by 2

               y = 5x + 3/2        m = 5    the same as L1   so the lines are parallel

3 + 5 + 8  = 16 parts

3/16  is red     3/16  x 128 =        oz of red

5 /16  is blue  5/16  x 128 =         oz of blue

8/16 is white   8/16 x 128 =         oz of white  

29 y/o  is 2 standard deviation BELOW the mean of 33

37        is 2 standard deviations ABOVE the mean

so  look at standard bell curve (see below) :   2 standard dev above and below the mean covers 95 % of the graph

95%  x 400 = 380   

Use distance formula

sqrt (x1-x2)^2 + (y1-y2)^2  =  7

sqrt ((x- -2)^2 + (-1-5)^2 ) = 7        square both sides and expand

  x^2 +4x +4   + 36  = 49

x^2 +4x -9 = 0                                use quadratic formula   x = -2 +- sqrt 13          points  : (-2+sqrt13 , -1)  and  (-2-sqrt13 , -1)

You should not cheat on your homework.

Equation of line    y = mx + b    m = slope   b = y-axis intercept (value of y when x = 0)

find slope      (y1-y2)/(x1-x2)         it does not matter which point you assign as '1' or '2'

                        (-4-12)/(8-0) = - 2    = m = slope

y = -2x + b     now put in either one of the given points to calulate 'b'

12 = -2(0) + b     b = 12

y = -2x+12

Find the distance between these points....this will be the diameter

sqrt ((2-8)^2   + (-7-15)^2)   =  sqrt (36 + 484) = sqrt 520       1/2 of this is the RADIUS  =  sqrt 520  / 2

the CENTER (h,k) of the circle is the midpoint between the given points   h,k  =  5, 4 

Circle equation =   (x-h)^2   + (y-k)^2 = r^2

                               (x-5)^2  + ( y-4)^2 =  520/4 = 130

Number of eclairs      =  3

Number of humbugs  =  2x + 6

Number of mints        =  x

Total number             =  3 + 2x + 6 + x  =  3x + 9

Probability of being an eclair  =  3 / (3x + 9)

Probability of being an eclair  =  1/15

Setting these two equal to each other:  3/(3x + 9)  =  1/15

                     cross multiply:                               45  =  3x + 9

                     subtracting:                                   36  =  3x

                     dividing:                                         12  =  x

Number of humbugs  =  2(12) + 6  =  30

Number of mints        =  12

Total number              =  45

Probability of being a humbug  =  30 / 45

Please re-format your question so it is correct....  is that SUPPOSED to be   - 1/5

                                                                               is that SUPPOSED to be cos (2x)   or  cos (x/2) or cos^2 x ?

I think this is the trig identity you may need:

If angle x is in Q III...then x/2 will be in Q I    and will be + POSITIVE    in value   

.9564   from a z-score table  

9 l + 7 s = 171

3 l + 5 s = 75          Multiply this equation by -3

-9 l - 15 s = -225     Add to top equation

       - 8 s  = -54        solve for s, the kg wt of small pkgs      then use this value in one of the equations to compute l, the large pkg wt

In parallelogram ABCD,  AB = CD  and  AB || CD.

In parallelogram CDFE,  DC = FE  and  DC || FE.

Therefore,  AB = FE  and  AB || EF.

Since a pair of sides of quadrilater ABEF are both parallel and congruent, ABEF is a parallelogram.