Jose is making a trail mix. the recipe calls 3 parts golden raisins to 2 parts cashews. jose would like to make 30 cups of trail mix. how many cups of golden raisins and cashews does jose need?

18 cups of golden raisins.

12 cups of cashews.

Step-by-step explanation:

The recipe calls 3 parts golden raisins to 2 parts cashews.

Jose would like to make 30 cups of trail mix.

We can define this as :

Dividing both sides by 5, we get

x = 6

Hence, Jose will need cups of golden raisins.

And cups of cashews.

So, answer is :

18 cups of golden raisins.

12 cups of cashews.

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