g Jack is polling New Yorkers to determine what proportion of them want to legalize recreational marijuana. How many New Yorkers should the sample to ens

1006

Step-by-step explanation:

Take proportion, p = 62%

n = (Z² * pq) / M.E²

Margin error = 0.03

p = 62% = 0.62

q = 1 - p = 1 - 0.62 = 0.38

Zcritical at 95% = 1.96

n = (1.96² * (0.62*0.38)) / 0.03²

n = 0.90508096 / 0.0009

n = 1005.6455

n = 1006

Sample size = 1006

pooopoopopoopop

step-by-step explanati∵∵∴∴on:

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