Find the area of the hexagen whose Vertices taken in order

Mathematics

1 answer:

lakkis [162]3 years ago

4 0

Answer:

Step-by-step explanation:

A(5,0),B(4,2), C(1,3),D(-2,2),E(-3,-1),F(0-4)

we divide the hexagon in triangles and trapeziums

area Δ BCD (with coordinates B(4,2),C(1,3),D(-2,2)) =1/2(2+4)×2=6

area Δ DEG (with coordinates D(-2,2),E(-3,-1),G(-2.-2))=1/2(2+2)×2=4

area ΔAOF(with coordinates A(5,0),O(0,0),F(0,-4))=1/2×5×4=10

area trapezium ABDH (with coordinates A(5,0),B(4,2),D(-2,2),H(-2,0))=1/2[(2+5)+(2+4)]×2=13

area trapezium OHGF (with coordinates O(0,0),H(-2,0),G(-2,-2),F(0,-4))=1/2[4+2]×2=6

Total area=6+4+10+13+6=39 sq units.

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A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial off

Zolol [24]

Answer:

(a) There are 32,760 different ways to appoint the officers.

(b) 3003 different ways can the committee be appointed.

(c) Probability of getting the five youngest of the qualified candidates is 0.00033.

Step-by-step explanation:

We are given that a corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a planning committee with five different members.

There are 15 qualified candidates, and officers can also serve on the committee.

(a) The number of officers are 4, i.e; A president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO).

There are 15 qualified candidates.

To find the number of ways to appoint the officers, we will use permutation because here the order of selecting the officer's matters.

So, the number of ways to appoint the officers = $^{15}\text{P}_4$

= $\frac{15!}{(15-4)!}$ { $\because ^{n}\text{P}_r = \frac{n!}{(n-r)!}$ }

= $\frac{15!}{11!}$ = 32,760 ways

(b) The number of committee numbers to appoint include five members.

There are 15 qualified candidates.

To find the number of ways in which the committee can be appointed, we will use combination because here the order of selecting the members doesn't matter.

So, the number of ways to appoint the committee = $^{15}\text{C}_5$