4The Monarch Butterfly is essential to the pollination process of many native and farmed North American plants. These butterflies migrate thousands of miles over several months. A Florida Department of Forestry outpost in Hawthorne, Florida has been tracking their population since the 2005 migration cycle.

-Part B: Of the following choices, which equation is the best fit line for the data?Immersive Reader
(1 Point)

We have been given a graph that represents the data of population of butterflies since the 2005 migration cycle.  We are asked to find the line of best fit for the given data.

Upon looking at our given data, we can see that the data has a negative correlation, so slope of line of best fit will be negative.

We can see that 2nd and 4th option has a negative slope. So our choice will be from these two options.

We can also see that the data shows only positive y-axis and x-axis.

We know that initial value is the point, where line intersects y-axis. Out line will intersect y-axis above 300, so y-intercept will be positive 320.

So our required equation would be .

Therefore, 4th option is the correct choice.

nope

step-by-step explanation:

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