A population of honey bees lives in a rectangle shaped area of the wood that is 30 meters long by 20 meters wide. What is the population density of the honey bees

i.e. In every 10 honey bees live !

Step-by-step explanation:

We have , A population of 6,000 honey(Correction as this isn't given in question ) bees lives in a rectangle-shaped area of the woods that is 30 meter long by 20 meters wide. We need to find What is the population density of the honey bees. Let's find out:

We know that ,

Population density = (Population) / (Land Area)

Now , Area of rectangle =

⇒

⇒

⇒

Hence ,

⇒

⇒

Therefore , i.e. In every 10 honey bees live !

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.