The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of three jobs per 8-hour day. The company's repair facility is a single-server system operated by a repair technician. The service time varies, with a mean repair time of 2 hours and a standard deviation of 1.5 hours. The company's cost of the repair operation is $28 per hour. In the economic analysis of the waiting line system, Robotics uses $35 per hour cost for customers waiting during the repair process. What are the arrival rate and service rate in jobs per hour
Answer:
The correct answer is:
[tex]\lambda=0.375 \ jobs \ per \ hour[/tex][tex]\mu=0.5 \ jobs \ per \ hour[/tex]Step-by-step explanation:
The given values are:
Service time varies,
Repair time = 2 hours
Standard deviation = 1.5 hours
Robotics uses per hour cost,
= $35
Company's cost per hour,
= $28
(a)
⇒ Arrival rate = Jobs per hours
then,
= [tex]\frac{8 \ hours}{3 \ jobs}[/tex]
= [tex]2.666 \ hours \ per \ job[/tex]
The jobs per hour will be:
⇒ [tex]\lambda=\frac{1}{2.666}[/tex]
[tex]=0.375[/tex]
(b)
⇒ Service rate = jobs per hour
then,
μ = [tex]\frac{1 \ repair \ job}{2 \ hours}[/tex]
= [tex]0.5 \ jobs[/tex]
In a school of 1200 students, the ratio of
the number of teachers to students is 1 : 15.
After some teachers join the school, the ratio of
the number of teachers to students becomes 3:40.
Find
(i) the initial number of teachers in the school,
(ii) the number of teachers who join the school.
Step-by-step explanation:
i)Initial School population,
given 15 units = 1200
1 unit =
[tex]1200 \div 15 \\ = 80[/tex]
Number of teachers (initial) = 1 unit = 80.
ii)take j = number of teachers joining the school.
New teacher population = 80+j
[tex] \frac{3}{43} (1280 + j) = 80 + j \\ \frac{3840}{43} + \frac{3}{43} j = 80 + j \\ j - \frac{3}{43} j = \frac{3840}{43} - 80 \\ \frac{40}{43} j = \frac{400}{43} \\ 40j = 400 \\ j = 400 \div 40 \\ = 10[/tex]
When driving in England, Brian drove through several speed cameras. On one drive, Brian left his hotel and after 7 minutes he was 2.5 km away and at that moment was measured going 0.5 kpm (kilometers per minute). Later, 18 minutes after he started driving, he was 14.8 km from the hotel and at that moment was measured going 0.8 kpm.
A. Find the linearization at 7 minutes.
B. Find the linearization at 18 minutes.
C. Compute two approximations for Brian's distance from his hotel at 14 minutes, using the linearizations from parts a and b.
D. Which approximation do you think is better? Why?
Solution :
The formula for the linearization of a function [tex]$f(x)$[/tex] at a point [tex]$x$[/tex] = a is given as
[tex]$L(x)=f(a)+(x-a)f'(a)$[/tex]
Assuming the time is t and the distance travelled is [tex]$f(t)$[/tex], that makes the speed as [tex]$f'(t)$[/tex].
So substituting them in the linearization formula,
A. At t = 7 minutes
f(7) = 2.5 km
f'(7) = 0.5 kpm
∴ [tex]$L_7(t)=f(7)+(t-7)f'(7)$[/tex]
[tex]$=2.5+(t-7)0.5$[/tex]
[tex]$=2.5+0.5t-3.5$[/tex]
[tex]$=0.5t-1$[/tex]
B. At t = 18 minutes
f(18) = 14.8 km
f'(18) = 0.8 kpm
∴ [tex]$L_{18}(t)=f(18)+(t-18)f'(18)$[/tex]
[tex]$=14.8+(t-18)0.8$[/tex]
[tex]$=14.8+0.8t-14.4$[/tex]
[tex]$=0.8t-0.4$[/tex]
C. Substituting the value of t as 14 in both the linearization to determine the position at 14 minutes, we get
[tex]$L_7(14)=0.5(14)-1.0$[/tex]
= 7 - 1
= 6 km
[tex]$L_{18}(14)=0.8(14)+0.4$[/tex]
= 11.2 + 0.4
= 11.6 km
D. According to the linearization at 7, the distance travelled between the 7 minutes and 14 minutes is = 6 km - 2.5 km
= 3.5 km
And between the 14 minutes and 18 minutes is = 14.8 km - 6 km
= 8.8 km
This is an average speed of 0.5 kpm in the first interval and an average speed of 2.2 kpm.
Now, according to the linearization of 18, the distance travelled between the 7 minutes and the 14 minutes is = 11.6 km - 2.5 km
= 9.1 km
And between 14 minutes and 18 minutes is = 14.8 km - 11.6 km
= 3.2 km
This gives an average speed of 1.3 kpm in the first interval and 0.8 kpm in the second interval.
Therefore, the second approximation is the better one since the average speed are closer to the actual readings in the second linearization.
Please tell me if I got it right
Answer:
1/9
Step-by-step explanation:
1/3 / 3 = 1/9
she will run 1/9
jog 1/9
and walk 1/9
to check all of them equal 1/3
1/9+1/9+1/9 = 3/9 = 1/3
Lucy drank 6 liters of water after 2 days. How many liters of water did she drink after 6 days?
Answer:
18 Liters of water
24 13
10) Find the midpoint of a line segment AB. A(3, 10) and B (-9,3)
Answer:
(-3 ;13/2)Step-by-step explanation:
hello :
the midpoint of the line segment is : ((3-9)/2 ;(10+3)/2 )
(-3 ;13/2)
Tomas drew a rectangle with an area of 6 square centimeters.what is the greatest possible perimeter of this rectangle?Explain please. i want 20 answers please
Determine the intercepts of the line I need help quick!!!!!
Answer:
x-inter = (-40,0), y-inter= (0,15)
Step-by-step explanation:
the fitnessgram pacer test is an automated aerobic capacity test that progressively gets more difficult as it continues.
Can somebody help please
A child weighing 59 lb has a bad infection and is to be given Cefaclor.
The dosage is 15 mg per kg.
The drug will be delivered in an oral suspension with concentration 250 mg/5 mL.
How many mL will she receive?
Round to the nearest whole number.
You will need to convert her weight to kg, using 1 kg = 2.2 lb.
Answer:
Step-by-step explanation:
59:2,2=26,81
15*26,81:250=1,6086
May you solve this for me?
Answer: 23.94 cm
Step-by-step explanation: I am totally not sure if this is the answer, but think of it this way: Those are 2 semi circles. The formula for the area of a semi circle is A = π * r^2 / 2. For the semi circle with 6 cm, the radius is 3. So we can plug it in the formula. 3.14 * 3^2 / 2, which is 14.13. For the semi circle with 5 cm, the radius is 2.5. Again plug it in and it will be 3.14 * 2.5^2 / 2, which is 9.8125. Then, to get the total area, add the 2 final values together. 9.8125 + 14.13, which is 23.9425. Then it said "round to the nearest hundredth if necessary. We can round to the nearest hundredth, which is 23.94, so that would be the answer. That is just my thought process.
I am not really sure if it's the answer, but take a gander at my thought process and hopefully, you can agree with me.
Use the shell method to compute the volume (CALCULUS HELP!!!)
Use the shell method. The volume is
V = 2π ∫₅⁸ (x - 5) x ² dx
V = 2π ∫₅⁸ (x ³ - 5x ²) dx
V = 2π (1/4 x ⁴ - 5/3 x ³) |₅⁸
V = π/6 (3x ⁴ - 20x ³) |₅⁸
V = π/6 ((3 × 8⁴ - 20 × 8³) - (3 × 5⁴ - 20 × 5³))
V = 891π/2
Find the slope of the line.
33) 90÷18-18÷6-6÷3=
Preciso de ajudaaaa
Answer:
67
Step-by-step explanation:
(90÷18)-(18÷6)-(6÷3)= 72-3-2= 67
Nancy bought a vase as wedding gift .The cost excluding vat was R250.How much must she pay with VAT inclusive
Step-by-step explanation:
VAT = 250*15%
VAT = 250*15/100
VAT = 37.5 therefore
total price add VAT =250+37.5
=287.5
The ratio of dogs to cats at the local
shelter is 2 to 5. There are 20 dogs at
the shelter. What is the total number
of cats and dogs at the shelter?
A. 28
B. 50
C.
70
D. 8
Need
Answer:
B 50
Step-by-step explanation:
Option 1) 2/5 = 20/x | 20/2 = 10 so x = 10 | 5 times x 10 =50
Option 2) dogs 2 to cats 5 | 2/5 = 20/x | .40 = 20/x | .40x = 20 | x = 50
Option 3) you can look and see that 20 is 10 times more than 2 and therefore infer that x is 10 times more than 5 which is 50
Algebra 2
L.3 Multiply polynomials BGN
Answer:
x² + 4x
Step-by-step explanation:
Area of the rectangle = length × width
length = x + 4
width = x
Therefore,
Area = x(x + 4)
Area = x*x + x*4
x² + 4x
Please help me thanks! :)
Answer:
eyjdnfbhs
Step-by-step explanation:
QUICK PLEASE HELP!!!
I’LL MARK BRAINLIEST!!!
Answer:
C) 50
Step-by-step explanation:
50
Answer:
C: 50
Step-by-step explanation:
The inner diamond has congruent sides
Half of the line segment on the left is 25.
The other half of the left line segment is also 25
Together, the left line segment is 50 units
The inner diamond has both 90 degree angles and 18 unit long sides
Thus, we know that both sides are congruent
Finally, the right side is the same length as the left side
The right side is 50 units long
3 mugs have the same capacity as 2 bottles. The capacity of 10 mugs and
8 bottles is 15.4 l. Find the capacity of a mug.
Answer:
0.70L
Step-by-step explanation:
3m=2b
convert 8 b to mugs
therefore 8b=12m
12m+10m=22m
15.4/22=0.700l
Emiliano firmó hoy un pagaré por la cantidad de $ 92.000. la tasa de interés estipulada es un 20% anual
Cuantos dias se necesitan para los intereses de la playa $ 8.000
Answer:
159 días.
Step-by-step explanation:
Dado que Emiliano firmó hoy un pagaré por la cantidad de $ 92.000 a una tasa de interés estipulada de un 20% anual, para determinar la cantidad de días que se necesitan para que dicho interés genere unos $8.000 se debe realizar el siguiente calculo:
92.000 x 0.2 = X
18.400 = X
18.400 / 365 = 50,41
8.000 / 50,41 = X
158.69 = X
Así, se necesitarán 159 días para que se generen $8.000 en intereses.
Nevaeh’s bag contains 2 red marbles, 3 blue marbles, and 5 green marbles. Nevaeh randomly selects a marble from the bag, records the color, and then puts the marble back in the bag. If she does this 150 times, how many times would she expect to select blue?
A 10 times
B 30 times
C 45 times
D 75 times
Answer:
30
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
mark me brainlest
The diameter of a cylindrical water tank is 10 ft, and its height is 9 ft. What is the volume of the tank?
Use the value 3.14 for w, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
225w
Step-by-step explanation:
volume formula: w*r²*9
w*5²*9
25*9w
225w
Answer: V=707
Step-by-step explanation:
6) A spinner is
divided into 5 sections
lettered A to E. Lena
spins the pointer on
the spinner 25 times.
She records her
results in the table.
Based on these results,
lands on the letter B?
B is 5
Answer:
1/5
Step-by-step explanation:
there are 5 sections regardless of how many time she rolls it ti does not change the probability of landing on b so it's 1/5
Given f z please help
Answer:
z = -11, z = -2
Step-by-step explanation:
Given that, ([tex]f(z)=\sqrt{z+27} -z[/tex]) and ([tex]f(z)=7[/tex]), set up an equation that puts the first value of ([tex]f(z)[/tex]) equal to the other given value of the function.
[tex]f(z)=\sqrt{z+27}-z=7[/tex]
Use inverse operations to solve,
[tex]\sqrt{z+27}-z=7\\\\\sqrt{z-27}=7+z\\\\z+27 = (7+z)^2\\\\z + 27 = 49+14z+z^2\\ -(27+z)\\\\0 = z^2+13z+22[/tex]
Factor,
[tex]0=(z+11)(z+2)[/tex]
Solve using the zero product property, the zero product property states that any number times zero equals zero;
[tex]z=-11,z=-2[/tex]
Answer:
Then solve the rest using the quadratic formula
what does noncollinear
9514 1404 393
Answer:
not on the same line
Step-by-step explanation:
Any two distinct points define a line. Additional points may or may not be on that line. If they are on the line, they are collinear with other points on the same line.
Any point not on the line is noncollinear with the points that are on the line.
square root of 27 lies between which two natural numbers?
Answer:
5,6
Step-by-step explanation:
Answer:
5 and 6
Step-by-step explanation:
5² = 25
6² = 36
help please! need asap
Answer:
2
Step-by-step explanation:
6×3÷4=2
Hope this helps you
Determine the Geometric mean of 18 and 27
Answer:
The geometric mean of 18 and 27 is 22.045407685
Step-by-step explanation:
I hope this helps and pls mark me brainliest :)
Answer:
22.045407685
Step-by-step explanation:
Which could be the function graphed below?
9514 1404 393
Answer:
(a) f(x) = √x -2
Step-by-step explanation:
The square root function has no horizontal shift, so the expression under the radical is simply x with no added terms. There is only one such answer choice, which also shows the necessary translation downward by an added negative constant.
[tex]f(x)=\sqrt{x}-2[/tex]
Answer:
the answer is A.
Step-by-step explanation:
:))))))