CPhill

1.    Range  =  [ -10, 0 )  U  [6, 13 ]

2.    (−5, 33) and (2, 5)

Slope  =   (33 - 5)  / ( -5 - 2)  =   28/ -7  =  - 4

Equation

y  = -4 ( x - -5) + 33

y  =  -4x - 20 + 33

y  =  -4x  + 13

4.   g(x)  is f(x)  shifted 3 units to the left and 6 units up  ...so...

g(x)    =   f(x + 3)  +  6

The diameter will be the longest side of the triangle......If we let this   = 2r, the height of the triangle is r

So.... the area of the triangle  is  

(1/2)(2r) (r)   =  r^2

And the area of the circle is pi * r^2

So.....the ratio of the area is  

r^2  / [ pi * r^2 ]  =

1 / pi    ≈   31.8%

We are looking for the values that make  f(x)  =   8

So we have

x^2 - 7x + 18  =  8       subtract 8 from both sides

x^2 - 7x  +  10  =  0      factor

(x - 5) ( x - 2)  = 0

Setting each factor to 0 and solving for x we have that  

x  = 5  or   x  =  2

So.....g(8)  =  either     2(5) + 3   =  13    or

                                    2(2)  + 3   =  7

And the sum of these  =   20

We have 

(2/5) * (Prob 2nd draw red   )   =  1/7       multiply both sides by  5/2

(Prob second draw red   )   =   1/7  * 5/2  

(Prob second draw red    )   =   5 / 14

Hypotenuse  = 

√  [ ( leg 1)^2  + (leg 2)^2  ]  =

√ [  12^2  +  9^2  ] =

√  [ 144 + 81 ]  =

√225  =

15

5.

a.  Minimum height  =  .5        Max height  =  4

b.  It will reach a minimum after 1 second

c.  Height after  2.5 seconds  =  

Note : cos (2.5 pi)  =  same as cos (pi/2)  =  0

1.75cos (2.5 pi ) + 2.25  =  1.75 (0) + 2.25  =   2.25

Here's a graph : https://www.desmos.com/calculator/lcxviz3ffb 

Let x  =  0.....then  y  = 5(0)  = 0

So  (0,0) is on the graph

Now......let x  = 1.....then y  = 5(1)  = 5 

So   (1, 5)  is on the graph

Plot   (0,0)   and  (1, 5)....then draw a line through them.....this will be the graph 

It should look like this  :  https://www.desmos.com/calculator/ettknmo0vy

P ( A I B )  =  P ( A ) ???

P( A I B )  =   P (A and B ) / P (B)  =  .24 / .90  =  4/15   ≈  .267  

And P(A)  = .3

So....not independent because P(A|B) ≠ P(A)   [ the first answer ]

I know the first two....unsure about the third

Not Independent   ..."Without replacement" usually always signals this

Independent  ...  the outcome of one cube does not affect the outcome any other  

Outcomes of tossing three coins

T  T   T

T  T   H

T  H  H

T  H  T

H  H  T

H  T  H

H  T  T

H  H  H

Prob  of  one head and two tails   =  3 / 8