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For this, we can use a tree diagram for each coin flip.

For every H, add one to the total floor level. For every T, subtract one floor.

Count all the numbers in total. Then count all the numbers 6 or above.

39/62 Chance (or 62.9%) that she is above or at the 7th floor at any time during her game

4. The measure of two complementary angles are in the ratio 1 : 5. What are the degree measures of the two angles?

1 : 5  means there are 6 equal parts....

So...one  of them  is  (1/6) of these

So     (1/6) * 90   =   15°

And   (5/6) * 90   =  5 * 15   =  75°

5. The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 56 feet, what is the length of the rectangle?

P  =  2 (L + W)      but  L  =  3W.....so we have...

56   =  2 ( 3W + W)     divide by 2

28  =  3W + W

28  =  4W     divide by 4

7 = W

So  L  =  3W  =  3(7)   =  21 ft

How bout we do a riddle competition? Heres my first riddle. (These are old riddles i found in older posts) 

i touch the earth, i touch the sky, but if i touch you, you just might die.

        x^2 - 6x + 8            x  - 2

x

0            8                        -2

1            3                        -1 

2            0                         0     

3            -1                        1

4             0                        2

5             3                        3  

The solutions  are  in red  ⇒  x  =  2   and x  =  5

5 : 2    means that there are  5 + 2  =  7 equal parts

And  the red bricks  are   5/7  of the total....so.....

(5/7) 210  =

5 (210 / 7)  =

5 (30)  =

150   red bricks

And

The grey bricks  are 2/7  of the total  =

(2/7) (210)  =

2 ( 210 / 7)  =

2 (30)  =

60  grey bricks

As Julius found

y  =  8 / x

This is  a  hyperbola

There's an equal chance of each letter being chosen.

There are 6 letters with no repeats in letters.

1/6 probability of each letter being chosen

L / W  = 

( 7 + 1/2)  / ( 2 + 3/4)  =

(15/2)  / ( 11/4 )  =

 { Invert the second fraction and multiply } 

(15/2)  * ( 4/11)   =

60 / 22    =  30 / 11  =    30 : 11

No big deal....everyone makes mistakes.....

x^4   + x^2 - 20  =  0      factor

(x^2 + 5) (x^2 - 4)  = 0

(x^2 + 5)  ( x - 2) ( x + 2)  = 0

Set each factor to 0...and solve for x

x  - 2  = 0       x +  2  = 0       x^2 + 5  = 0

x  =  2             x  =  -2           x^2  =  -5         take both roots

                                              x = ±√-5

                                              x  = ±√5 i

So....the solutions are

x  =   { -2, 2, √5 i ,  - √5 i    }

Oh, my! How could I make such a mistake 

Thanks, CPhill! 

Ratio  =

Height of Model  / Actual Height   =

Note, RP....we must compare similar units....so...  24 inches  =  2 ft 

2 / 1450  =     1  / 725

You have the correct idea....but a lttle mistake on the math

Derivative   =   6x  + 1

Set  =   to the slope of the line

6x + 1   =  4      

6x  = 3

x  =  3/6  = 1/2

And   y  =   3(1/2)^2  + 1/2   =  5/4

So.....the point  is   ( 1/2, 5/4)    and the equation of the line is

y  = 4(x - 1/2)  + 5/4

y = 4x - 2 + 5/4

y  = 4x - 3/4

Here's the graph, Julius : https://www.desmos.com/calculator/48aijjgr6d

1.   (-4, 0)    and   ( 6, 8 ]

2. Relative minimum  ⇒  (1, - 5)

3. Intervals of increase⇒  (-inf, 0)  and  (1, 2)

4. Constant   ⇒  (-6, 0)

5.   Not even because f(x)  is not equal to f(-x)

      If odd......  f(-x)   must be equal to  -f(x)

f(-x)  =   -x^3  - x^2

-f(x)  =   -x^3 + x^2

So.....neither

But i think the answer is this:

-2,2,i√5,-i√5

is this correct?

thank you!!

5.

First let's find what time the rockets are at the same height.

height of Brynn's rocket  =  f(x)

height of Denise's rocket  =  g(x)

height of Brynn's rocket  =  height of Denise's rocket

f(x)  =  g(x)

-4.9x² + 75x   =   -4.9x² + 50x + 38     Solve this equation for  x . Add  4.9x²  to both sides.

75x  =  50x + 38                                   Subtract  50x  from both sides.

25x  =  38                                             Divide both sides by  25.

x   =   1.52

Now we know that after 1.52 seconds, the rockets are at the same height.

To find what this height is, plug in  1.52  for  x  into either function.

f(1.52)  =  -4.9(1.52)² + 75(1.52)   ≈   102.7     meters

5 + 4x   =  9y

9y = 4x + 5      divide both sides by 9

y  =  (4/9)x + 5/9

This should loolk familiar....it's the equation of a line

4.

When  x = 0 ,  f(x)  =  -4   and   g(x)  =  -4    so

When  x = 0 ,  f(x)  =  g(x)

so  x = 0  is a solution to  f(x) = g(x)

There is one more solution to  f(x) = g(x)  .  Can you find it?

Ok. Im very bored right now. What do u want to talk about?

3.

When  x = 4 ,  f(x)  =  1   and   g(x)  =  1 ..so

When  x = 4 ,  f(x)  =  g(x)

so  x = 4  is the solution to  f(x) = g(x)

2.

When  x = -1 ,  f(x)  =  -3   and   g(x)  =  -3     so

When  x = -1 ,  f(x)  =  g(x)

so  x = -1  is a solution to  f(x) = g(x)

When  x = 1 ,  f(x)  =  -1   and   g(x)  =  -1     so

When  x = 1 ,  f(x)  =  g(x)

so  x = 1  is a solution to  f(x) = g(x)

Those are the only two solutions.

1.

When  x = 3 ,  f(x)  =  -9   and   g(x)  =  -9 ..so

When  x = 3 ,  f(x)  =  g(x)

so  x = 3  is a solution to  f(x) = g(x)

When  x = 7 ,  f(x)  =  2   and   g(x)  =  2 ..so

When  x = 7 ,  f(x)  =  g(x)

so  x = 7  is a solution to  f(x) = g(x)

Those are the only two known solutions.

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