BRAINLIEST AND 100 POINTS FAST PLEASE A student is assessing the correlation between the number of workers in a factory and the number of units produced daily. The table shows the data: Number of workers (x) 0 10 20 30 40 50 60 70 80 90 Number of units (y) 2 52 102 152 202 252 302 352 402 452 Part A: Is there any correlation between the number of workers in a factory and the number of units produced daily? Justify your answer. (4 points) Part B: Write a function that best fits the data. (3 points) Part C: What does the slope and y-intercept of the plot indicate? (3 points)

see below

Step-by-step explanation:

Number of workers (x) 0 10    20 30   40    50   60   70   80  90

     Number of units (y) 2 52 102 152 202 252 302 352 402 452

Part A

There is a correlation

For each increase of 10 in x, there is an increase of 50 in y

                                      10   10    10   10   10     10   10     10   10

Number of workers (x) 0 10    20 30   40    50   60   70   80  90

     Number of units (y) 2 52 102 152 202 252 302 352 402 452

                                        50  50 50  50   50   50    50   50   50

Part B

m = (y2-y1)/(x2-x1)

   = (452-402) /( 90-80) = 50/10 = 5

The y intercept is the value of y when x =0

The y intercept is 2

The slope intercept form of the the line is

y = mx+b

y = 5x+2

PartC

The y intercept is that we start with 2 of the units and for each worker gained, they will make 5 units per day

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

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).