Simplify the expression (2y+1)-4y^2+2

-4y^2+2y+3

Step-by-step explanation:

(2y+1)-4y^2+2

2y+1-4y^2+2

-4y^2+2y+1+2

-4y^2+2y+3

(2 + 1 ) − 4 2 + 2

Step-by-step explanation:

1. Eliminate redundant parentheses

( 2 + 1 ) − 4 2 + 2 2 + 1 − 4 2 + 2

2 . Add the numbers  

2 + 1 − 4 2 + 2 2 + 3 − 4 2

3.  Rearrange terms

2 y +3 − 4 2 − 4 2 + 2 + 3

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0

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