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Morgarella [4.7K]
3 years ago
11

At a concert, the number of security guards needed is based on the average density of people in an area of 25'x25' called a bloc

k. The concert space measures 350' by 200'. The number of security guards is based on the number of blocks necessary and each security guard can only be responsible for one block. 12,000 people are expected to attend the concert.
a) how many security guards will be needed?
b) how many people, rounded to the nearest 10, will be in each block?
Mathematics
1 answer:
ira [324]3 years ago
3 0

find total area  by multiplying  350' x 200' = 70,00 sq ft

area of one block, multiply 25' x 25' = 625 sq ft  = area for one Security guard

divide area for one security guard into total area of facility  70,000 / 625 =

112 security guards

find how many people for each block = 70,000 / 625 = 112 blocks

12,000 people divided by 112 blocks = 12,000 / 112 = 107.14 rounded to nearest 10 = 110 people per block

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Step-by-step explanation:

Here is the complete question.

Dominique, Marco, Roberto , and John work for a publishing company. The company wants to send two employees to a statistics conference. To be fair, the company decides that the two individuals who get to attend will have their names drawn from a hat. This is like obtaining a simple random sample of size 2. (a) Determine the sample space of the experiment. That is, list all possible simple random samples of size n = 2. (b) What is the probability that Dominique and Marco attend the conference? (c) What is the probability that John attends the conference?  ​(d) What is the probability that John stays​ home?

Since there are four employees to select the two to send from. then for us to get the sample space for the experiment we need to merge all possible two employees and represent them as set.

Let D = Dominique, M = Marco, R = Roberto and J = John

a) The sample space for the experiment is the total number of possible outcomes that we can have. It is as given below

S = 4C2 = 4!/(4-2)!2! (Selecting 2 out of 4 employees)

Total sample space = 4!/2!2!

Total sample space = 4*3*2!/2!2

Total sample space = 12/2 = 6

The sample space are S = {DM, DR, DJ, MR, MJ, RJ}

b) Probability is the ratio of number of event to the sample space.

P = n(E)/n(S)

Given n(S) = 6

n(E) is the event of Dominique and Marco attending the conference.

E = {DM}

n(E) = 1

P(D and M) = 1/6

Hence  the probability that Dominique and Marco attend the conference is 1/6

c) For John to attend the conference, the event outcome will be given as;

E = {DJ, MJ, RJ}

n(E) = 3

n(S) = 6

Probability for John to attend the conference is 3/6 = 1/2

d) Probability that John stays at home = 1 - Prob (John attends the conference)

Probability that John stays at home = 1 - 1/2

Probability that John stays at home = 1/2

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