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jeka57 [31]
3 years ago
10

The entertainment sports industry employs athletes, coaches, referees, and related workers. Of these, 0.35 work part time and 0.

52 earn more than $20,540 annually. If 0.3 of these employees work full time and earn more than $20,540, what proportion of the industry's employees are full time or earn more than $20,540
Mathematics
1 answer:
Alona [7]3 years ago
7 0
<h2>0.87</h2>

Step-by-step explanation:

let A be the event that employees work full time

Pr(A) =  1 - 0.35=  0.65   (  given : Pr( employee work part time) = 0.35)

let B be the event that employees earn more than $20,540

Pr(B) =  0.52

Pr(  employee work full time and earn more than $20,540) =  0.3

Pr( A∩B) = 0.3

we know that

Pr( employee work full time or earn more than $20,540) = Pr( A∪B)

Also

Pr( A∪B)   =  Pr(A)  + Pr(B)  -  Pr(A∩B)

                   =  0.65   + 0.52  -   0.3

                    =    1.17    -   0.30

                     =    0.87

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The fox population in a certain region has a continuous growth rate of 5% per year. It is estimated that the population in the y
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Answer:

P(t) = A * (1 + r)^t ;

14,922 ;

Year 2013

Step-by-step explanation:

Given the following :

Continuous growth rate(r) = 5% = 0.05

Population in year 2000 = Initial population (A) = 10,100

Time(t) = period (years since year 2000)

A)

Find a function that models the population,P(t) , after (t) years since year 2000 (i.e. t= 0 for the year 2000).

P(t) = A * (1 + r)^t

Trying out our function for t = year 2000, t =0

P(0) = 10,100 * (1 + 0.05)^0

P(0) = 10,100 * 1.05^0 = 10,100

B.)

Use your function from part (a) to estimate the fox population in the year 2008.

Year 2008, t = 8

P(8) = 10,100 * (1 + 0.05)^8

P(8) = 10,100 * 1. 05^8

P(8) = 10,100 * 1.4774554437890625

= 14922.29

= 14,922

c) Use your function to estimate the year when the fox population will reach over 18,400 foxes. Round t to the nearest whole year, then state the year.

P(t) = A * (1 + r)^t

18400 = 10,100 * (1.05)^t

18400/10100 = 1.05^t

1.8217821 = 1.05^t

1.05^t = 1.8217821

In(1.05^t) = ln(1.8217821)

0.0487901 * t = 0.5998151

t = 0.5998151 / 0.0487901

t = 12.293787

Therefore eit will take 13 years

2000 + 13 = 2013

4 0
3 years ago
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