The frequency distribution representing the number of frequent flier miles accumulated by employees at brumley statistical consulting company is given below. frequent flier miles (000) frequency 0 up to 3 5 3 up to 6 12 6 up to 9 23 9 up to 12 8 12 up to 15 2 total 50 a. how many employees accumulated less than 3,000 miles? employees
b. convert the frequency distribution to a cumulative frequency distribution. miles f cf 0 up to 3 5 3 up to 6 12 6 up to 9 23 9 up to 12 8 12 up to 15 2
c. based on the cumulative frequency polygon, about 75% of the employees accumulated how many miles or less? employees

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

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