Your student email account requires you to choose a password of 4 letters followed by one of the digits 0-9. The password can consist of upper case letters (26) or lower case letters (26). How many different five-character passwords can be created?

520

Step-by-step explanation:

Total choices for letters = upper case letters (26) + lower case letters (26).

= 26+26 = 52

Choices for digits = 10

By Fundamental counting principle,

The different five character passwords can be created = (Choices for letters) x (Choices for digits)

= 52 x  10

= 520

Hence, the number of different five character passwords can be created = 520

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

it is 570

step-by-step explanation: