Christine makes 6 cakes per hour, while Kelly makes 4 cakes per hour. If Christine gets paid $11 less than Kelly for each cake, how much in dollars should Kelly be paid for each cake for Christine and Kelly to earn the same amount each hour?

$33

Step-by-step explanation:

Let Kelly's pay per cake be 'x',, then Christine's pay will be 'x-11'

Kelly makes 4 cakes per hour, her hourly income is 4x

Christine makes 6 cakes per hour, her hourly income is 6(x-11)

For the two to be equal,

4x = 6(x-11)

4x = 6x - 66

6x - 4x = 66

2x = 66

x = 33

Kelly should be paid $33 per cake

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

i wish i could u

step-by-step explanation:

i wish i could u