014 A company has made some changes to the way its employees work The manager wants to know if these changes have made any difference to the number
of days employees take off work because of illness
She can't just compare the total days as there are fewer people working in each
department after the changes.
She gives you this information about the employees in one department.
Number of days
each employee took off sick
in the year BEFORE the changes
14
12
11
0
15
6
11
3
10
7
0
5
8
10
15
16
14
3
Number of days
each employee took off sick
in the year AFTER the charges
12
0
2
11
3
7
14
10
10
3
8
9
8
4
4
12
Did the changes make any difference to the average number of days that employees took off
sick?
Explain your findings to the manager Show calculations to support your explanation
Decision (yes/no)
Explanation and supporting calculations

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

9 sandwiches per hour

step-by-step explanation:

when we have a rate, we want a 1 in the denominator

27/3 = 9

27 sandwiches/ 3 hours = 9 sandwiches/hour

2.2°  

step-by-step explanation:

let θ = the angle of elevation.

tanθ =77/2020

tanθ = 0.038 12

      θ = tan⁻¹0.038 12

      θ = 2.2°