Katy bought 5 packages of stickers with 25 stickers in each packages. she also bought 3 boxes of markers with 12 markers in each box. if she receives 8 stickers from a friend how many stickers and markers does katy have now ?

Number of stickers Katy has = 133

Number of markers Katy has = 36

Step-by-step explanation:

Since we have given that

Number of packages of stickers =5

Number of stickers in each packet =25

Number of boxes of markers = 3

Number of markers in each box = 12

Number of stickers she receives from a friend = 8

Total number of stickers she will have now, is given by

Total number of markers she will have now, is given by

so,

Number of stickers Katy has = 133

Number of markers Katy has = 36

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

t hope this

: