A) This problem involves 8-digit binary strings such as 10011011 or 00001010.

i How many such strings are there?

ii. How many such strings end in 0?

iii. How many such strings have l's for their second and fourth digits?

iv. How many such strings have l's for their second or fourth digits?

b) Find how many 9-digit numbers can be made from the digits 1, 2, 3, 4, 5, 6,

7, 8, 9 if repetition is not allowed and all the odd digits occur first (on the

left) followed by all the even digits.

c) How many permutations of the letters A, B, C, D, E, F, G are there in which

the three letters ABC appear consecutively, in alphabetical order?

dsfdsf

step-by-step explanation:

fddsf

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

angle addition postulate

2x=56

step-by-step explanation:

14

step-by-step explanation:

14 x 3 = 42