(grade 9 academic math) last night your sister made cake for dessert. she cut the cake into 15 equal slices but only 13 slices were eaten. the next day, you ate 1/5 of the remaining cake for a snack. what fraction of the cake was left?

Step-by-step explanation:

If the cake was initially cut into 15 equal slices and 13 of those were eaten:

slices would be left

Since you only had 2/15 left and ate 2/75, we can subtract these amounts to find the remaining amount of cake.  However, fractions can only be subtracted if they have the same denominator:

4.6875 pounds

step-by-step explanation:

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