Min has dozen blueberry muffins and 1 dozen pumpkin muffins. How many more blueberry muffins than pumpkin muffins does Min have? Enter your answer as a fraction in simplest form by filling in the boxes,

7/12

Step-by-step explanation

We have both of the values of the dozen of doughnuts 5/6 of a dozen blueberry and 1/4 dozen pumpkin. In order to determine how many more blueberry muffins Min has, we have to set the denominators to be the same number. To do this we need a common denominator. The least common denominator between 6 and 4 is 12. We multiply the top and bottom of the fraction 5/6 by 2 to get 10/12. We then multiply 1/4 by 3 to get 3/12. 10-3 = 7, therefore Min has 7/12 more blueberry muffins

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

step-by-step explanation: