Question 5
What is the equation of the line?

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

Answer:

it is thr 3rd answer hope it help you

Answer:

D

Step-by-step explanation:

A. Does not have to have symmetry

B. Opposite angles are congruent.

C. Opposite sides are parallel.

D. All sides are NOT congruent.

Answer:

#25 is left, #27 is between, #28 is below, and #26 is first i think.

Step-by-step explanation:

Answer: #25 is left, #27 is between, #28 is below, and #26 is first i think.

Step-by-step explanation:

Answer:

67 monedas de 5, 34 de 10 y 11 de 25.

Step-by-step explanation:

Representemos el primer enunciado de manera algebraica:

[tex]5x+10y+25z =950[/tex]  (1)

Donde:

Ahora, el número de monedas de 10 centavos era el triple de las de 25 centavos y que las de 5 centavos era el doble de las de 10 centavos, se puede representar como:

[tex]y=3z[/tex]  (2)              

[tex]x=2y[/tex]  (3)    

Combinado las eacuaciones (1), (2) y (3) tenemos:

[tex]5(2y)+10y+25(\frac{y}{3}) =950[/tex]

[tex]10y+10y+\frac{25}{3}y =950[/tex]

[tex]\frac{85}{3}y =950[/tex]  

[tex]y =34[/tex]

Por lo tanto el valor de x y z seran:

[tex]x=2(34)[/tex]          

[tex]x=68[/tex]          

[tex]z=11[/tex]    

Si ponemos cada valor en la equacion (1), tenemos:

[tex]5(68)+10(34)+25(11) =955[/tex]

Como el resultado da 955 hay un excedente de 5 pesos, asi que finalmente tendremos.

x = 67

y = 34

z = 11  

Espero te haya serrvido!

Answer:

720 cherries

Step-by-step explanation:

3 pies need 240 cherries so the equation would be:

3c = 240

so, c = 80

But, he needs to make 9 "perfect" pies so you make the equation:

9c = 80*9

9c = 720

So Greg needs 720 cherries to make 9 perfect cherry pies.

Answer:

C & D

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

More participants caught 6 fish than any other number.

We have given that,

The dot plot shows a random sample of the number of fish caught and released by 30 participants during a two-day fishing derby.

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.

More participants caught 6 fish than any other number.

To learn more about the random sample visit:

https://brainly.com/question/17831271

#SPJ2

Answer: 10x5

(10 blocks wide, 5 blocks long) or (5 blocks wide, 10 blocks long)

Step-by-step explanation:

3 blocks = 18 meters, so

1 block = 6 meters

60meters/ 6meters= 10 blocks

30 meters/ 6 meters = 5 blocks

Answer:

Table number 3

Step-by-step explanation:

25+25=50

50+25=75

Answer:

C

Step-by-step explanation:

For every 1 hour(h) 25 dollars(d) gets added. You can multiply 25 with however many hours you need to get the answer.

example: 4 hours would be 100 because 25×4=100

Answer:

This would be (5.5,0)

Step-by-step explanation:

Hope it helped!

Answer:

it's 86

Step-by-step explanation:

150-(2+x)^3=150-(2+2)^3

    =150-4^3

    =150-64

    =86

The value of the expression 150 - (2 + x)³, when x = 2 is, 86.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression 150 - (2 + x)³, when x = 2.

This can be obtained by replacing x = 2 in the expression.

Therefore, 150 - (2 + x)³.

= 150 - (2 + 2)³.

= 150 - 4³.

= 150 - 64.

= 86.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ5

Answer:

12 cm

Step-by-step explanation:

Well first we can cut the triangle in half and use the Pythagorean theorm

a^2+b^2=c^2

In this case we are going to be doing c^2-a^2=b^2

10^2-8^2=b^2

(10*10)-(8*8)=b^2

100-64=b^2

36=b^2

Now we just square root 36 (what number times itself is 36)

[tex]\sqrt{36}[/tex]

b=6

Since half of the one side equals 6 (DC) then the length of AC is 12!

Answer:

hey mate here is your answer...

Step-by-step explanation:

by using Pythagoras theorem...

hope it helps you ❣️

Answer:

x = 5

Step-by-step explanation:

The diagonals of a parallelogram bisects each other, which means that each diagonal is splitter into two equal parts.

Therefore:

x - 2 = 2x - 7

Collect like terms

x - 2x = 2 - 7

-x = -5

Divide both sides by -1

x = 5

Answer: perhaps a rectangle with length L=6

if so , then P = 12 + 2w ---> (P-12)/2 = 2

and area A = 6w ---> w = A/6

IF i get it wrong im swwy ❤️✨

Step-by-step explanation:

Answer: sphere

Step-by-step explanation:

Answer:

Sphere

Step-by-step explanation:

The formula given is the formula for volume of a sphere, where 'r' is the radius of the sphere.

The formula for volume of a sphere is the only formula with '4/3' in it, compared to the other option choices given.

Hope this helps.

Answer:

37.69

Step-by-step explanation:

Answer:r=7r =9 r=10

Step-by-step explanation:

Answer:

187

Step-by-step explanation:

1870/210=187

Also / means divide

Answer:

3.9 in^2

Step-by-step explanation:

Split it up into a top rectangle and a bottom rectangle. Find the area of the top rectangle and subtract the combined area of the two quarter circles.

The area of the rectangle is 6  * 3 = 18. The area of the two quarter circles is the same as the area of one semicircle, and since the radius is 3 you can do:

3^2 * pi / 2 = 9pi/2. As a decimal this would be: 14.14.

Then, you can do rectangle - circle = 18 - 14.14 = 3.86. Rounded to the nearest tenth, this is 3.9

Answer:

6x2 =12

Step-by-step explanation: when ever u see that just multiply

Answer:

Yes, Elias got his food before reaching the potluck.

Step-by-step explanation:

Elias left home at 7:00 one morning, determined to make the ten-mile trip to Leaders on a bicycle. Soon thereafter, Elias' parent noticed he had forgotten his potluck dish on the kitchen table, got into the family car, and tried to catch up with the forgetful child. Elias had a fifteen-minute head start, and was pedaling at 12 mph, while the parent pursued at 30 mph. Was Elias reunited with his potluck food before reaching Leaders that day? If so, where? If not, at what time was the food delivered?

Let's set x as the time after the parent leaves as x (time after the first 15-minute headstart)

When the two meet, it means that the distance is equal. Remember, distance = time * speed.

Using this, we know that Elias had a 15-minute headstart at 12 mph, which means that he had 0.25 of an hour. Thus, Elias had a 0.25 * 12 mile headstart.

We can write this equation for the distance Elias traveled.

0.25 * 12 + 12 * x

And this equation for the distance his parent traveled.

30 * x

These equations need to be equal so that the two meet.

0.25 * 12 + 12 * x = 30 * x

Simplify.

3 + 12x = 30x

Subtract 12x from both sides.

3 = 18x

Divide both sides by 18.

x = 1/6

So, it took 1/6 of an hour, which is 10 minutes, for the parent and Elias to meet.

If Elias were to get the food before he reached the potluck, the distance he traveled (0.25 * 12 + 12 * x) needs to be less than 12.

Plug 1/6 in for x.

0.25 * 12 + 12 * 1/6 =

3 + 2 = 5

Elias traveled 5 miles before his parent met him.

So, Elias did get his food before reaching Leaders.

Just in case, let's double-check this answer.

Using the distance = speed * time formula, we know that time = distance/speed. Elias's parent had to travel 5 miles at 30 mph, so it would have taken 1/6 of an hour to drive 5 miles.

Elias traveled at 12 mph for 1/6 + 1/4 of an hour, so he traveled:

(1/6 + 1/4) * 12 =

(4/24 + 6/24) * 12 =

10/24 * 12 =

120/24 = 5 miles

Thus, the previous answer is right.

I hope this helps! Feel free to ask any questions!

Answer:40 hours

Step-by-step explanation:divide 237.36 by 6 and you will get 39.5633

so basically what you're going to do is round it up and your answer will be 40

Answer:

Step-by-step explanation:

1. (a + b)2 = a2 + 2ab + b2; a2 + b2 = (a + b)2 − 2ab

2. (a − b)2 = a2 − 2ab + b2; a2 + b2 = (a − b)2 + 2ab

3. (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

4. (a + b)3 = a3 + b3 + 3ab(a + b); a3 + b3 = (a + b)3 − 3ab(a + b)

5. (a − b)3 = a3 − b3 − 3ab(a − b); a3 − b3 = (a − b)3 + 3ab(a − b)

6. a2 − b2 = (a + b)(a − b)

7. a3 − b3 = (a − b)(a2 + ab + b2)

8. a3 + b3 = (a + b)(a2 − ab + b2)

9. an − bn = (a − b)(an−1 + an−2b + an−3b2 + ··· + bn−1)

10. an = a.a.a . . . n times

11. am.an = am+n

12. am

an = am−n if m>n

= 1 if m = n

= 1

an−m if m<n; a ∈ R, a 6= 0

13. (am)n = amn = (an)m

14. (ab)n = an.bn

15. a

b

n

= an

bn

16. a0 = 1 where a ∈ R, a 6= 0

17. a−n = 1

an , an = 1

a−n

18. ap/q = √q ap

19. If am = an and a 6= ±1, a 6= 0 then m = n

20. If an = bn where n 6= 0, then a = ±b

21. If √x, √y are quadratic surds and if a + √x = √y, then a = 0 and x = y

22. If √x, √y are quadratic surds and if a+ √x = b+ √y then a = b and x = y

23. If a, m, n are positive real numbers and a 6= 1, then loga mn = loga m+loga n

24. If a, m, n are positive real numbers, a 6= 1, then loga

m

n

= loga m−loga n

25. If a and m are positive real numbers, a 6= 1 then loga mn = n loga m

26. If a, b and k are positive real numbers, b 6= 1, k 6= 1, then logb a = logk a

logk b

27. logb a = 1

loga b where a, b are positive real numbers, a 6= 1, b 6= 1

28. if a, m, n are positive real numbers, a 6= 1 and if loga m = loga n, then

m = n