The Cold Be Gone Company conducted a study where 100 participants were assigned to either receive a cold
medicine or not receive a cold medicine. The Cold Be Gone Company then recorded whether the participant's
cold lasted 7 days or longer. The Venn diagram below shows their data.
Complete the following two-way frequency table.
Received cold medicine
Did not receive cold medicine
Cold lasted longer than 7 days
Cold did not last longer than 7 days
Cold medicine
Cold longer than 7 days
27
23
20
30

                     Received cold medicine  Did not receive cold medicine

Cold lasted longer than 7 days             23                                 20

Cold did not last longer than 7 days     27                                30

Step-by-step explanation:

i hope it helps

its 69.420

step-by-step explanation:

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