If there is no seasonal effect on human births we would expect equal numbers of children to be born in each season (winter, spring, summer, and fall). a student takes a census of her statistics class and finds that of the 120 students in the class, 21 were born in winter, 38 in spring, 35 in summer, and 26 in fall. she wonders if the excess in the spring is an indication that births are not uniform throughout the year. what is the expected number of births in each season if there is no "seasonal effect" on births? compute the x^2 statistic. how many degrees of freedom does the x^2 statistic have?

right

step-by-step explanation:

center= (-2,0)

radius= sqrt2/2

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

i got 10.28 but that rounds up to 10.3