home security service. This private home security service guarantees to either dispatch one of their own five guards immediately if one of their customers sends in an alarm or, in the case that all five guards are responding to other calls, direct the alarm to the local police. The company receives 12 calls per hour, evenly distributed over the course of the day. The local police charges the home security company $500 for every call that the police responds to. It takes a guard, on average, 90 minutes to respond to an alarm. a. What fraction of the time are incoming alarms directed to the police? b. How much does the home security company have to pay the local police every month?

Answers

Answer 1

Answer:

a.

The fraction of the time is incoming alarms directed to the police is 74.02%

b.

The home security company has to pay $3,197,665 the local police every month.

Step-by-step explanation:

As per the given data

Numbers of guards = 5 guards

Calls received per hour = 12 calls per hour

Activity time = 90 minutes

First, calculate the inter-arrival time

Inter-arrival time = Minutes in an hour / Numbers of calls received per hour = 60 minutes per hour / 12 calls per hour = 5 minutes

a.

First, calculate the ratio of activity time to inter-arrival time

Ratio = Activity time / Inter-arrival time = 90 minutes / 5 minutses = 18

Now calculate the probability of all 5 servers are busy using ratio of activity time to inter-arrival time

Probability = [tex]P_{Servers}[/tex] ( ratio )

Probability = [tex]P_{5}[/tex] ( 18 )

Probability = 0.7402

Probability = 74.02%

Hence the probability of incoming calls directed to the police is 74.02%

b.

First, calculate the loss of customers

Loss of customers = Probability x ( 1 / Servers )

Loss of customers = 74.02% x ( 1 / 5 )

Loss of customers = 0.7402 x 0.20

Loss of customers = 0.14804 per minute

Loss of customers = 0.14804 per minute x 24 x 60 x 30 = 6,395.33 calls per month

Now calculate the total loss

Total loss =  6,395.33 calls x $500

Total loss = $3,197,665


Related Questions

GIVING BRAINLIST. 6 dimes if what percent of a dollar

Answers

Answer:

60%

Step-by-step explanation:

6 dimes is 10x6 and a dollar would have 10 dimes so 60%

You spin the spinner twice.
8
7
What is the probability of landing on an 8 and then landing on a 7?
Write your answer as a fraction or whole number.

Answers

two over four is the probability that you will land on seven or eight

Answer:

P( landing an an 8 then on  a 7 ) = 1/ 16

What is a Probability?

Its is the branch of mathematics concerning numerical description of how likely an event is to occur .

P( landing an an 8 then on  a 7 ) = P ( landing on an 8) * P ( landing on a 7 )

P(Landing on an 8) = 1/4

P(Landing on an 7) = 1/4

P = 1/4 * 1/4

P= 1 / 16

Learn more about Probability:

https://brainly.com/question/11234923?referrer=searchResults

#SPJ2

2. The sides of a triangle are in the ratio 3:7:10 and the perimeter is 80 inches.
What are the lengths of the sides of the triangle?

Can anyone help please ?​

Answers

Step-by-step explanation:

3+7+10=20

80/20=4

1 ratio =4

3(4) : 7(4) : 10(4)

= 12 : 28 : 40

The eiffel tower stands 1,986 ft tall. the chrysler building in New your city is 319 meters. Which is taller? Solve by using dimensional analysis

Answers

Answer:

The Eiffel tower is taller because 319 meters into feet is 1046

so the true equation would be 1,986 > 1,046

Step-by-step explanation:

WILL MARK BRAINLYIST

Answers

B is the correct answer

Please tell the answer​

Answers

Answer:

Step-by-step explanation:

The person I sent it to couldn't see it either. I'm going to take a chance and say the Chord (AB) and the Tangent line form a 50 degree angle. If this is incorrect, I won't know, from the diagram, what else to try.

If I'm right then <OAB = 40 degrees because 90 - 50 = 40 because <AOC is a right angle (property of radii and tangents).

<ABO also = 40 (the triangle is isosceles by two legs being radii).

That means that BOA = 180 - 40 - 40 = 100

si en una canasta saben 30 limones ¿ Cuantos canastas nesesitamos para guardar 75 ? inversa ​

Answers

Answer:

3

Step-by-step explanation:

¡¡espero que esto ayude!!

Although bats are not known for their eyesight, they are able to locate prey (mainly insects) by emitting high-pitched sounds and listening for echoes. A paper gave the following distances (in centimeters) at which a bat first detected a nearby insect. 24 41 25 68 53 83 43 63 56 34 45 A button hyperlink to the SALT program that reads: Use SALT. (a) Calculate the sample mean distance at which the bat first detects an insect. (Round your answer to four decimal places.) 48.6364 cm (b) Calculate the sample variance and standard deviation for this data set. (Round your answers to four decimal places.) Variance Standard deviation

Answers

Answer:

[tex]Mean = 48.6364[/tex]

[tex]s^2 = 331.8545[/tex] -- Sample Variance

[tex]s = 18.2169[/tex] --- Sample Standard Deviation

Step-by-step explanation:

Given

[tex]n = 11[/tex]

[tex]Data: 24, 41 ,25 ,68 ,53 ,83 ,43 ,63 ,56 ,34 ,45[/tex]

Solving (a): The sample mean

[tex]Mean = \frac{\sum x}{n}[/tex]

So:

[tex]Mean = \frac{24 +41 +25 +68 +53 +83 +43 +63 +56 +34+ 45}{11}[/tex]

[tex]Mean = \frac{535}{11}[/tex]

[tex]Mean = 48.6364[/tex]

Solving (b): Sample variance (s^2)

This is calculated as:

[tex]s^2 = \frac{\sum (x - \bar x_i)^2}{n - 1}[/tex]

Where:

[tex]\bar x = 48.6364[/tex]

So:

[tex]s^2 = \frac{(24 -48.6364)^2 +(41 -48.6364)^2 +......................+( 45 -48.6364)^2}{11-1}[/tex]

[tex]s^2 = \frac{3318.54545456}{10}[/tex]

[tex]s^2 = 331.8545[/tex]

Solving (c): Sample Standard Deviation (s)

This is calculated as:

[tex]s = \sqrt {s^2[/tex]

[tex]s = \sqrt{331.8545[/tex]

[tex]s = 18.2169[/tex]

change the following improper to mixed plz help quick!
1. 8/3

2. 9/4

3. 12/5

Answers

Answer:

Improper Fractions:

Step-by-step explanation:

1. 2 and 2/3

2. 2 and 1/4

3. 2 and 2/5

Write down in figures the number forty one thousand and ninety six.

Answers

Answer:

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Step-by-step explanation:

Answer:

41,096

Hope it helps

Please mark me as the brainliest

Thank you

How do you differentiate y = 3x3 - 2x-4

Answers

Answer:

y' = 9x^2 + 8x^-5

Step-by-step explanation:

General Principle

y' = ax^b

y' = a*b * x^(b-1)

Solution

3x^3 = 3*3x^(3-1)

3x^3 = 9x^2

-2x^-4  = -2*-4 x ^(-4 - 1)

-2x^-4 = 8 x ^-5

Answer

y' = 9x^2 + 8x^-5


A sum amounted naira 2,590
at 10% Per annum for the
Period of 4 Years. Find the sum

Answers

Answer:

1,769

Step-by-step explanation:

The computation of the sum is shown below:

Future value = Present value × (1 + rate of interest)^number of years

2,590 = Present value × (1 + 0.10)^4

2,590 = Present value × 1.10^4

So, the present value is

= 2,590 ÷ 1.10^4

= 2,590 ÷ 1.4641

= 1,769

HELP THIS WAS DUE THREE DAYS AGO!!!!!!!!!!

Answers

Answer:

Step-by-step explanation:

2. 2c(7c + 1)

3. stays as is

4. 2x^3y^4(4 - 11x^2y^2)

5. ab(10ab + 9b - a)

6. 3m^2(7m^4n^2+2m^2n+5)

7. (a - 8)(a + 8)

8. (y - 17)(y + 17)

9. stays as is

10. (1 - 5n)(1 + 5n)

11. (4x - 7y)(4x + 7y)

12. (w^2 - 10)(w^2 + 10)

13. (c - 9d)(c + 9d)

14. (14a - b)(14a + b)

pls answer i have a ton of homework

Answers

Answer:

ewqvrdvfgbt2nbvcx

Step-by-step explanation:

Answer:

the answer is 9

Step-by-step explanation:

Can someone please help me I’m desperate it due tomorrowwww

Answers

Answer:

Step-by-step explanation:

First box: m=1/2

Second box: m=2

Third box: m=1

Fourth box: m=2

any ideas on this fractions questions? (maths/fractions)

Answers

Answer:

5 9/14

Step-by-step explanation:

Let's add the whole numbers first to make the process simpler, 4+1=5. So 5 1/7 + 1/2 can be converted to 5 2/14 + 7/14, with a common denominator of 14. Add the numerators together, and you get 5 9/14.

Hope this helps! ;)

Please I need help it’s an emergency

Answers

Answer:

A. Cos θ = 16/42

Step-by-step explanation:

The angle the ladder makes with the floor = θ

Hypotenuse = length of the ladder = 42 m

Adjacent = Distance from the bottom of the ladder to the wall = 16 m

Therefore to find θ, we would apply the trigonometric function, CAH:

Cos θ = adj/hyp

Which is:

Cos θ = 16/42

How many copies of 1 twelfth are equivalent to 3 sixths? Help!

Answers

Answer:

6/12 is equal to 3/6 ( 6 twelfths is equal to 3 sixths )

Step-by-step explanation:  

multiply both sides of 3/6 by 2 to get the same denominator, doing that will get you 6/12

Answer:

6 copies

Step-by-step explanation:

Step 1:  Convert 1 twelfth to an expression

1 twelfth is the same thing as 1/12

Step 2:  Convert 3 sixths to an expression

3 sixths is the same thing as 3/6

Step 3:  Get common denominators

The lowest common denominator between 1/12 and 3/6 is 12

[tex]\frac{1}{12}[/tex] → [tex]\frac{(1 * 1)}{(12 * 1)}[/tex] → [tex]\frac{1}{12}[/tex]

[tex]\frac{3}{6}[/tex] → [tex]\frac{(3 * 2)}{(6*2)}[/tex] → [tex]\frac{6}{12}[/tex]

Step 4:  Find the amount of 1/12 there are in 6/12

In order to find out the copies, we need to add 1/12 x amount of times to get 6/12.  We find that x is going to be 6.  Therefore, there 6 copies.

[tex]\frac{1}{12}+\frac{1}{12}+\frac{1}{12}+\frac{1}{12}+\frac{1}{12}+\frac{1}{12} = \frac{6}{12}[/tex]

Answer:  6 copies

P = 2l + 2w, when P = 28 ft. and w = 5 ft.

Answers

Answer:

9

Step-by-step explanation:

5*2=10 28-10=18 18/2=9

In ΔJKL, j = 520 inches, k = 730 inches and l=640 inches. Find the measure of ∠K to the nearest degree.

Answers

Answer:

It’s 56.7

Step-by-step explanation:

Fudisks

39 inches is the right answer just did the test on edge

Answers

Yup 39 is the correct answer good job :-)

Answer:

thanks have a nice day can you please mark me brainliest im trying to rank up and i  need 2 more brainlys

Step-by-step explanation:

What is the relationship between the two quantities in the table?

Answers

D

x is multipled by 30 everytime to acheive y

Answer:

Its D

Step-by-step explanation:

I am editing the answer cause my other answer here was incorrect Your answer is D cause every time you multiply the number from the x to 30

1 x 30 = 30

2 x 30 = 60

3 x 30 = 90

4 x 30 = 120

One of the legs of a right triangle measures 11 cm and its hypotenuse measures 12 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

Answers

Answer:

4.8cm

Step-by-step explanation:

a²+b²=c² where c is the hypotenuse so

Let's plug in those values

11²+b²=12²

b²=12²-11²

b²=23

b=4.8

I really need help with this statistical/variable question, i am really struggling and would be super happy if someone could answer

Answers

Answer:

Statistic

Step-by-step explanation:

A statistic is a sample of the whole mean like

E.x( how many pink doughnuts are in the dozen pack of doughnuts.

A parameter represent the whole mean

E.x( how many donuts were made at 7:00)

Since they are sampling 25 cars, it is a statistic.

more on fraction

21×5​

Answers

Answer:

105.

Step-by-step explanation:

21+21+21+21+21=105.

The Blinking Rockets baseball team has had 127,034 visitors to their fan website. Rounded to the nearest ten thousand how many visitors have they had

Answers

Answer:

[tex]Visitors = 130000[/tex]

Step-by-step explanation:

Given

[tex]Visitors = 127034[/tex]

Required

Approximate to the nearest ten thousand

First, identify the digit at the ten thousand position

From the given numbers of visitors, the digit is 2.

So, the next digit (which is 7) will be approximated and added to 2.

7 > 5. So, 1 will be added to 2.

The number of visitors becomes:

[tex]Visitors = 130000[/tex]

what is the answer to this question 108= ​

Answers

Umm what’s the question??

emmanuel spent 20% on his savings on a new video game that cost 40$. how much was in his savings abount to begin with?

Answers

Answer:

He had $200 to begin with.

Blueberries at a farmers' market
cost $18 for 6 pounds. Jerome pays
$24.75 for blueberries to make pies.
How many pounds of blueberries did
he buy?
pounds

Answers

Answer:

8.25 pounds

Step-by-step explanation:

Its $3 per pound, so 24.75/3= 8.25

Answer: 8.25 lbs.

Steps:

18 / 6 = 3 dollars per pound

24.75 / 3 = 8.25

Which of the lines below has a negative slope?
A
B
6
-5
15
6
10
5
D
5
5

Answers

Well, negative slope has the word negative in it right? So, it will be the negative number. Answer: -5 (negative 5)
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