geno3141

The probability that the first marble is green:  5/20

The probability that after drawing the first green marble, the second marble will also be green:  4/19

The total probability:  5/20 x 4/19  =  20/380  =  0.0526      (you can round this answer)

If you mix 0.1 quart of oil for every 3.5 quarts of gasoline, you total mixture will be 3.6 quarts.

The percentage of oil is           0.1 / 3.6  =  0.0277777...

The percentage of gasoline is 3.5 / 3.6  =  0.9722222 ...

If there are 3 quarts of the mixture,

the amount of oil is            3 x 0.277777  =  0.0833333 quarts

the amount of gasoline is  3 x 0.972222  =  2.9166667 quarts.

Let us say that each week, the company decreases the cost by $2.00 and the number sold will increase by 40.

Let  x  =  number of weeks

Then the number sold  =  800 + 40x

and the cost per phone  =  $80.00 - $2.00x

Revenue  =  (800 + 40x)(80 - 2x)

To graph this, rewrite as:  y  =  (800 + 40x)(80 - 2x)

 Multiply out:                     y  =  64000 + 1600x - 80x²                    (This is a parabola)

Find the vertex:                y - 64000  =  -80x² + 1600x

                                         y - 64000  =  -80(x² - 20x)

Complete the square:      y - 64000 - 8000  =  -80(x² - 20x + 100)

                                        y - 72000  =  -80(x - 10)²

So, after 10 weeks, the number sold will be 800 + 40(10)  =  1200

                                and the cost per phone will be  $80.00 - $2.00(10)  =  $60.00.

-½x + 3  =  4 - ¼x

Add ¼x to both sides:

-¼x + 3  =  4

Subtract 3 from both sides:

-¼x  =  1

cos(angle)  =  adjacent / hypotenuse

cos(angle)  =  6/18  

angle  =  cos^-1(6/18)  =  71°

One of doing this is to work backwards.

   if the roots of an equation are p and q, then the equation is (z - p)(z - q)  =  0.

So, if the roots are  2 - 3i  and  2 + 3i,  then the equation is  [z - (2 - 3i)]·[z - (2 + 3i)]  =  0

If you multiply out the left-hand side of that equation and combine like terms, you get  z² + 13  =  0

Since there is no z-term, the value of a is 0.

The value of b is 13.

1)     If  x + y  =  7/12  and  x - y  =  1/12  then  x² - y²  =  (x + y)(x - y)  =  (7/12) x (1/12)  =  7/144

2)     24x² - 19x - 35  can be factored as (3x - 5)(8x + 7)

                      so  A = 3     2B = 8  --->   B = 4     C = 7

                     and  AB - 3C  =  (3)(4) - 3(7)  =  your answer. 

Let x be the number of miles:  12.00  =  1.75 + 0.45x

                                                 10.25  =  0.45x

                                                        x  =  10.25 / 0.45

                                                        x  =  22 miles (discard the fraction)

Since there is a 75% chance that Santa will be at the mall and there is a 40% chance that both Santa and your best friend will be at the mall, there is a 75% - 40% = 35% chance that Santa will be at the mall but your best friend won't be.

Since there is a 55% chance that your best friend will be at the mall  and there is a 40% chance that both Santa and your best friend will be at the mall, there is a 55% - 40% = 15% chance that your best friend will be at the mall but Santa won't be.

Add these three mutually exclusive events together:

    (only Santa is at the mall) + (both Santa and your best friend is at the mall) + (only your best friend is at the mall)

           =  35% + 40% + 15%  =  90%

To find the x-intercepts:         y  =  x² + 4x - 12

                                              0  =  x² + 4x - 12

                                              0  =  (x + 6)(x - 2)

x-intercepts:                                   x = -6  and  x = 2

To find the vertex:                 y  =  x² + 4x - 12

                                      y + 12  =  x² + 4x

                                y + 12 + 4  =  x² + 4x + 4

                                       y + 16  =  (x + 2)²

vertex:                                   (-2, -16)

The endpoints of the base of the isosceles triangle are (-6, 0) and (2, 0)     --->     so its base is 8

The height of the triangle reaches from the midpoint of the base (-2, 0) and the vertex (-2, -16)     --->     so its height is 16

The area is  ½ · base · height  =  ½ · 8 · 16  =   64