A philosophy professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below the top 12% and above the bottom 59% C: Scores below the top 41% and above the bottom 23% D: Scores below the top 77% and above the bottom 10% F: Bottom 10% of scores Scores on the test are normally distributed with a mean of 71.7 and a standard deviation of 7.2. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

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

yes   because as the functions are graphed they eventually will intersect unless otherwise

step-by-step explanation:

the equation is not included but the answer is (1.50, 2.00, 2.75)

step-by-step explanation:

what is the your question?