CPhill

Probability that she walks  = 0.65

Probability that she cycles  = 0.35

Probability that  she is not late when she walks  = ( 1 - 0.4)  =  0.6

Probability  that she is not late when she cycles  = ( 1 - 0.1)  = 0.9

Probability that she is not late  =

(.65) (.6)  + (.35)(.9)   =   .705  =  70.5%

The diagonal of the square will be its greatest dimension....itf this is less than the diameter of the circle, it will fit

The sides of the square are the legs of a right triangle....so...by Pythagoras

Diagonal  = √ [ 5^2 + 5^2 ]  =  √50  ≈   7.07 units

So...it fits  !!!!

We can write this form, first

Since   x = 2  and x  = 4 are zeroes we know that it will factor as

y  =  a ( x - 2) (x - 4)     so.....when x  = 3  , y = 6    and we can solve for "a"

6 = a(3 - 2) ( 3 - 4)

6  = -1 a   ⇒     a = -6

So.....the fumction is

y  = -6 ( x - 2)(x - 4)

y  =  -6 (x^2 - 6x  + 8)

y = -6x^2 +36x - 48

Here's a graph to confirm this :

https://www.desmos.com/calculator/q6hbimtgh1

We need to find AC...it will be the hypotenuse of right triangle ABC

So we have

AC  =  √ [ AB^2 + BC^2  ] =  √ [ 5^2 + 9^2  ] =  √ [ 25 + 81  ] = √ 106

So....the area of the square is just the square of this  = 106 units^2

Good job, QS   !!!

I know this one...so.....I'll let someone else answer  !!!

f(x)  = 2x - 3        g(x)  = x^2  + 1

a)  f(g(x)  =    2 [ x^2 + 1] - 3    =   2x^2 + 2 - 3   =   2x^2   - 1

b)  g(f(x) )  =   [ 2x - 3 ] ^2 + 1  =  4x^2 - 12x + 9 + 1  =  4x^2 - 12x + 10

Thanks, lynx......!!!!

1)

Note, NSS....characteristics of inverse variation :

x will increase and y will decrease   or   x will decrease and y will increase

And   each  x, y association will multiply to the same thing

Note that the second choice is correct

x increases  and y decreases      ...and ....

each  x, y association multiplies to the same thing  ⇒  60

2)

y  = k / x

8 = k / 2   multiply both sides by 2

16  = k

So we have that

y  =  16  / x

3)   Just look  at the table, NSS

Multiplying each  n  by its associated c    gives  us   100

So 

 n * c  = 100