geno3141

Since there are 6 b***s and they are each equally likely to be chosen, the probability that any one is randomly chosen is 1/6. It doesn't matter what number is on the ball.

There are a total of 12 persons. You will pick 2 of them; since it is a committee, order is not important. This is a combination of 12 persons, taken 2 at a time:  12nCr2 = 66.

By hand:  12nCr2  =  12! / [2! ·10!]

A' is the complement of A; which means that if A is true, A' is false, and if A is false, A' is true.

A and A' cover all possibilities, with no overlap.

Thus P(A) + P(A') = 1.00.

So if P(A) = 0.72, P(A') = 1.00 - P(A) = 1.00 - 0.72 = 0.28.

neative times negative is poiitive.

3 times 3 is 9.

y times y is y².

Answer:  9y²

Since  y  =  -3x     and     y  =  -x - 2     are both solved for y:

you can set them equal to each other:     -3x  =  -x - 2

To get all the x-terms to one side, add x to both sides:

                                                        -3x + x  =  -x + x - 2

                  Simplify:                                -2x  =  -2

                                                                  x  =  1

If x = 1:  y  =  -3x  -->  y  =  -3(1)  =  -3

if x = 1:  y  =  -x - 2  -->  y  =  -(1) - 2  =  -3    

Since you get the same answer in both equation, the point (1, -3) checks.     x  =  1        y  =  -3

If you factor  x² + 3x + 2  =  0

you get:       (x + 2)(x+ 1)  =  0

This means that either     x + 2  =  0     or     x + 1  =  0

                                           x  =  -2                  x  =  -1

Thee are the two values that solve the equation.

Check:  (-2)² + 3(-2) + 2  =  4 - 6 + 2  =  0   It checks!

            (-1)² + 3(-1) + 2  =  1 - 3 + 2  =  0   It checks!

Using h  =  3w + 2:

Table:

  w = 0:  h  =  3(0) + 2  -->  h  =  2   --->   (0, 2)

  w = 1:  h  =  3(1) + 2  -->  h  =  5   --->   (1, 5)

  w = 2:  h  =  3(2) + 2  -->  h  =  8   --->   (2, 8)

  w = 3:  h  =  3(3) + 2  -->  h  =  11   --->   (3, 11)

  w = 4:  h  =  3(4) + 2  -->  h  =  14   --->   (4, 14)

  w = 5:  h  =  3(5) + 2  -->  h  =  17   --->   (5, 17)

Graph these points, connecting the points with a straight line. Continue the line out until you get the point (8, something); the 'something' is the answer to the second question.

Label the horizontal axis as 'w'; label the vertical axis as 'h'.

6  =  4.8sin[ (π/6)(t + 3.5) ] + 9

-3  =  4.8sin[ (π/6)(t + 3.5) ]                     subtract 9

-0.625  =  sin[ (π/6)(t + 3.5) ]                    divide by 4.8

-.675  =  (π/6)(t + 3.5)                               invserse sin

-.675 radians will be equivalent to 5.608 radians     2π - .675

For sin, -.675 radians is also equaivalent to 3.817 radians               π +.675

Using 3.817  =   (π/6)(t + 3.5)     

22.902  =  π(t + 3.5)                             multiply by 6                       

7.29  =  t + 3.5                                     divide by π

3.79  =  t                                              subtract 3.5

.79 x 60  =  47   --->  3:47 a.m.

cos(2θ) / sin²(θ)  =  0

cos(2θ)  =  cos²(θ) - sin²(θ)

[cos²(θ) - sin²(θ)] / sin²(θ)  =  0                   Use the substitution.

cos²(θ) / sin²(θ) - sin²(θ) / sin²(θ)  =  0         Divide the numerator into two parts.

cos²(θ) / sin²(θ) - 1  =  0

cos²(θ) / sin²(θ)  =  1

sin²(θ) / cos²(θ)  =  1                                 Multiply both sides by sin²(θ) / cos²(θ) and exchange sides.

tan²(θ)  =  1

tan(θ)  =  1   --->  θ  = 45°  or 225°

tan(θ)  =  -1   --->  θ  = 135°  or 315°

2.44 x 10^3  =  2440.

1.9 x 10^5  =  190000.

When you add them, you do not get 1.9.