A school uniform shop has 3 red polos, 8 white polos, and 15 grey polos. Based on these results, how many red polos will be sold out of the next 182 polos?

Given:

A school uniform shop has 3 red polos, 8 white polos, and 15 grey polos.

To find:

The number of red polos that will be sold out of the next 182 polos.

Solution:

A school uniform shop has 3 red polos, 8 white polos, and 15 grey polos. It means red, which and grey polos are sold in the ratio 3:8:15 respectively.

Let the number of red, which and grey polos are 3x, 8x and 15x respectively.

Total number of polos = 182

Divide both sides by 26.

Now,

Therefore, 21 red polos will be sold out of the next 182 polos.

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