2-4s. a 12-ft board is sawed into three smaller pieces. the longest piece is 2.5 ft longer than
the smallest one and 2 ft longer than the middle-sized one. find the length of the
middle-sized piece.

3.5 ft.

Step-by-step explanation:

Let the x ft be the length of the smallest piece then the longest piece will be x+2.5 ft and the middle piece is  x + 2.5 - 2 = x + 0.5 ft.

So we have:

x + x + 2.5 + x + 0.5 = 12

3x + 3 = 12

3x = 9

x = 3.

So the length of the middle-sized piece is 3 + 0.5

= 3.5 ft.

answer: the answer is 5/22

step-by-step explanation: if you subtract 17 from 22 the answer is 5 therefore the remainder of students are female

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