Complete Question
Leicester City Fanstore (LCF) will be selling the "new season jersey" for the 2018-2019 season. The regular price of the jersey is $80. Each jersey costs $40. Leftover jerseys will be sold at the end of the season (or later) at $30. Since jerseys are produced in China and lead time is long, Puma wants LCF to decide the quantity right now (December 2017).
a. After some analysis using historic data, LCF expects that the demand will follow a Normal distribution with a mean 40,000 and a standard deviation of 8,000 due to uncertainty in team performance. How many jerseys should LCF order?
b. If a customer cannot buy the jersey from LCF (in the case of a stock-out), they may leave the store disappointed and use other channels (such as Puma stores or puma.com) in future. LCF thinks that the lost customer goodwill is around $10. Should LCF change their decision in part (a)? If yes, please state the number of jerseys LCF should order.
c. Please state whether the following statement is always true, and give a brief explanation. If [tex]C_o =C_i[/tex], the news vendor solution is the mean.
Answer:
a
[tex]N = 46728[/tex]
b
[tex]n = 47728[/tex]
c
Yes it is always true
Step-by-step explanation:
From the question we are told that
The regular price of the jersey is [tex]P_r = \$ 80[/tex]
The cost of producing a jersey is [tex]C= \$ 40[/tex]
The left-over price of the jersey is [tex]P_o = $ 30[/tex]
The mean is [tex]\mu = 40000[/tex]
The standard deviation is [tex]\sigma = 8000[/tex]
The cost of lost customer goodwill is [tex]C_g = \$ 10[/tex]
Generally the fund that LCF will loss for one jersey if they order for too many jersey (i.e more than they need )is mathematically represented
[tex]C_o = P_o - C[/tex]
=> [tex]C_o = 40 - 30[/tex]
=> [tex]C_o = \$ 10[/tex]
Generally the fund that LCF will loss for one jersey if they order lesser amount jersey (i.e less than they need )is mathematically represented
[tex]C_i = P_r - C[/tex]
=> [tex]C_i = 80 - 40[/tex]
=> [tex]C_i = \$ 40[/tex]
Generally the critical ratio is mathematically represented as
[tex]Z = \frac{C_i }{ C_i + C_o}[/tex]
=> [tex]Z = \frac{40}{ 40 + 10}[/tex]
=> [tex]Z = 0.8[/tex]
Generally the critical value of [tex]Z = 0.8[/tex] to the right of the normal curve is
[tex]z = 0.841[/tex]
Generally the optimal quantity of jersey to order is mathematically represented as
[tex]N = \mu * [z * \sigma][/tex]
=> [tex]N = 40000 * [0.841 * 8000][/tex]
=> [tex]N = 46728[/tex]
Considering question b
Generally considering the factor of customer goodwill the fund that LCF will loss for one jersey if they order lesser amount jersey (i.e less than they need )is mathematically represented as
[tex]C_k = C_i + C_g[/tex]
=> [tex]C_k = 40 + 10[/tex]
=> [tex]C_k = \$ 50[/tex]
Now the critical ratio is mathematically represented as
[tex]Z = \frac{C_k }{ C_k + C_o}[/tex]
=> [tex]Z = \frac{50}{ 50 + 10}[/tex]
=> [tex]Z = 0.833[/tex]
Generally the critical value of [tex]Z = 0.833[/tex] to the right of the normal curve is
[tex]z = 0.966[/tex]
Generally the optimal quantity of jersey to order is mathematically represented as
[tex]n = \mu * [z * \sigma][/tex]
=> [tex]n = 40000 * [0.966 * 8000][/tex]
=> [tex]n = 47728[/tex]
Considering question c
When [tex]C_o =C_i[/tex] then
The critical ratio is mathematically represented as
[tex]Z = \frac{C_k }{ C_k + C_k}[/tex]
=> [tex]Z = \frac{1}{ 2}[/tex]
=> [tex]Z = 0.5[/tex]
Generally the critical value of [tex]Z = 0.5[/tex] to the right of the normal curve is
[tex]z = 0[/tex]
So
The optimal quantity of jersey to order is mathematically represented as
[tex]n = \mu * [z * \sigma][/tex]
=> [tex]n = 40000 * [0* 8000][/tex]
=> [tex]n = 40000 = \mu[/tex]
Hence the statement in c is true
x/x+2 -4/x-2=1 solve the equation
i will mark the brainliest plz help
Answer: x = -2/3
[tex]\frac{x}{x+2}- \frac{4}{x-2}=1\\\\<=>\frac{x(x-2)}{(x+2)(x-2)}-\frac{4(x+2)}{(x+2)(x-2)}=1\\\\\\<=>\frac{x(x-2)-4(x+2)}{(x-2)(x+2)}=1\\\\\\=>x(x-2)-4(x+2)=(x-2)(x+2)\\\\\\<=> x^{2} -2x-4x-8=x^{2} -4\\\\\\<=>-6x-8=-4\\\\\\<=>-6x=8-4\\\\\\<=>-6x=4\\\\\\<=>x=-4/6=-2/3[/tex]
Step-by-step explanation:
WHAT IS 5/6 TIMES 15
Answer:
12.5
Step-by-step explanation:
it's the awnser. I need to explain why
Guys please help me its really important i only have a bit of time
Answer:
B
A
Step-by-step explanation:
Use the graph to find the amplitude and period.
Notice amplitude is the absolute value of the number in front of either sin or cos
please give a heart for thanks :)
Determine which of the four postulates, if any, can be used to prove that the triangles are congruent.
50 points
The red lines mean the sides with the lines are the same. The red arc means those angles are the same.
Using that information you know the angle where the two same sides connect would also be the same.
So you have one side (S) and 2 angles (A) that are identical.
You can use B. ASA
Answer:
I think it is B.
Step-by-step explanation:
Hope this helped have an amazing day!
PLEASE TAKE A PIC OF YOU WORK ON A PECIE OF PAPER WITH THE AWNSER ON IT!!!! Hey! I need help with this! I’m bad at math and have a 55% in it rn it would mean a lot if you could take this seriously. Only 5 questions.
Answer:
Step-by-step explanation:
Hey if you give me your email i ca email you the aswer it wot let me link a photo lol
Which of the following is equal to 16.4 ?
O A. 32
O B. V16.4
O c.
D. 64
Answer:
b?
Step-by-step explanation:
b= v16.4
The lines represented by the equations 2y + 5x = –2 and y
- x + 3 are
parallel
Submit Answer
neither parallel nor perpendicular
perpendicular
the same line
Answer:
you should use desmos graphing. When you get there in the top left corner there are 3 lines. press that and scroll down. when you see sarcastic linear regression press that and put the coordinates points I hope this helped :))
Correctly identify the slope and y -intercept of the
slope intercept form equation:
y= mx + b
slope
intercept
Reilly, Maria, and Tamara figured out that the ratio of the times they spent painting a deck is 3:5:1. They are going to use this ratio to share the $36.90 they earned. How much will Maria get?
A parallelogram is a:
rectangle
square
quadrilateral
rhombus
Answer:
quadrilateral
Step-by-step explanation:
A quadrilateral that has two pairs of parallel sides.
–5x+4-x-1
10 points I’ll mark brainliesr I need asap
-5x+4-x-1
combine the like terms first
-5x-x+4-1
-5x-x=-6x
+4-1=3
answer:
-6x+3 or 3-6x
Answer:
-6x+3
Step-by-step explanation:
-5x+4-x-1
(-5x-x)+(4-1)
-6x+3
Joselyn saw an alligator that was 5 feet long. How many inches is 5 feet.
Answer:
The alligator is 60 Inches long.
Step-by-step explanation:
5 feet is 60 inches.
hope it helps!
Answer:
60 inches
Step-by-step explanation:
There are 12 inches in 1 foot, therefore the ratio of inches to feet is 12:1.
If the alligator is 5 feet than the amount of inches increase.
In order to find how long the alligator is in inches, multiply 5 by 12
5 x 12 = 60
Find the measure of angle A.
Answer:
I had this question and i got it right it is the measure is four
Step-by-step explanation:
This year Rachel watched 65 movies she thought that 26 of them were very good of the movies she watched what percentage did she think we’re very good
Answer:
40%
Step-by-step explanation:
26×100=2600÷65=40
40%×65=26
What could be the approximate value of the
correlation coefficient for the accompanying scatter
plor?
-X
1) -0.85
2) -0.16
3) 0.21
4) 0.90
Answer:
Step-by-step explanation:
Graph f(x) = 4[x] +5.
Answer:
See image for reference
Step-by-step explanation:
Answer:
Its b
Step-by-step explanation:
Evaluate if a = 6, b = 2, c = 9, & d = 3
Answer:
12
Step-by-step explanation:
a2 b
( )2 ( )
(–2)2 (3)
(4)(3)
please help. as soon as possible would be great thank you
(5x+3) - (2x-6) i need help ? ToT
Answer:
3x + 9
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define
(5x + 3) - (2x - 6)
Step 2: Simplify
Distribute negative: 5x + 3 - 2x + 6Combine like terms (x): 3x + 3 + 6Combine like terms (Z): 3x + 9Need help with this ASAP it’s due in 10 minutes
Answer:
Step-by-step explanation:
Formula to be used,
A = [tex]P(1+\frac{r}{n})^{nt}[/tex]
Here, A = Final amount
P = Principal amount
r = rate of interest
n = Number of compounding (In a year)
t = Duration of investment (In years)
Question (5)
P = $4250
r = 0.015
n = 4
t = 3 years
A = [tex]4250(1+\frac{0.015}{4})^{4\times 3}[/tex]
A = [tex]4250(1.00375)^{12}[/tex]
A = $4445.24
Part (C)
1). P = $6000
r = 0.03
n = 2
t = 10 years
A = [tex]6000(1+\frac{0.03}{2})^{2\times 10}[/tex]
= [tex]6000(1.015)^{20}[/tex]
= $8081.13
2). P = $9000
r = 0.05
n = 2
t = 8 years
A = [tex]9000(1+\frac{0.05}{2})^{2\times 8}[/tex]
= [tex]9000(1.025)^{16}[/tex]
= $13360.55
A court holds jurisdiction over five counties, and the juries are required to be made up in a representative manner from the eligible populations of these five counties. An investigator notices that the county where she lives has 14% of the total population of the five counties eligible for jury duty, yet records reveal that over the past five years only 122 out of the 1386 jurors used by the court reside in her county. Do you feel that this constitutes reasonable evidence that the jurors are not being randomly selected from the total population
Answer:
Yes.
I feel that since only about 9% of the jurors are being appointed from the county, instead of the more representative 14%, this constitutes reasonable evidence that the jurors are not being randomly selected from the total population.
Step-by-step explanation:
a) Data and Calculations:
County population proportion = 14%
This implies that the country is supposed to have at least 1,386 * 14% = 194 of the jurors used by the court.
Evidence from records show that the county has only 122 of 1,386 = 9% (122/1,386)
This means that about 72 (194 - 122) jurors are not being appointed from the county.
And 72 represents about 5% of 1,386 (72/1,386). This number is more than half of those being appointed from the county or more than 50% or precisely 59%.
Therefore, this constitutes reasonable evidence that the jurors are not being randomly selected from the total population. The selection is not representative of the population characteristics.
QUICK PLS HELP
The mean number of typhoon hitting US follows a Poisson distribution with
variance 0.5 per month. Find the probability that
(a) 4 typhoons will hit US in a year.
(b) at least 2 typhoons will hit US in a given half-year.
Answer:
A) 0.1339
B) 0.8078
Step-by-step explanation:
The Poisson Distribution formula is given by;
P(x; μ) = (e^(-μ) × (μ^(x))/x!
We are given;
Variance = 0.5 per month
Now, in Poisson distribution, variance = mean.. Thus, mean μ = 0.5 per month
A) We want to find the probability that 4 typhoons will hit US in a year.
Thus, x = 4
But since it's for a year, then μ = 0.5 × 12 = 6
So;
P(x = 4) = (e^(-6) × (6^(4))/4!
P(x = 4) = 0.00247875 × 1296/24
P(X = 4) = 0.1339
B) probability that at least 2 typhoons will hit US in a given half-year is;
P(X ≥ 2) = 1 - P(X < 2)
P(X < 2) = P(X = 0) + P(X = 1)
In a half given year, μ = 0.5 × 6 = 3
P(X = 0) = (e^(-3) × (6^(0))/0!
P(X = 0) = 0.0498
P(X = 1) = (e^(-3) × (6^(1))/1!
P(X = 1) = 0.1494
P(X < 2) = 0.0498 + 0.1494
P(X < 2) = 0.1922
P(X ≥ 2) = 1 - 0.1922
P(X ≥ 2) = 0.8078
PLZ HELP!! ITS ALMOST DUE!! ILL MARK BRAINLIEST!!
Answer: $32.74
Is your answer
Glad I could help!
Step-by-step explanation:
4.
IF AABD
ACBE, find the value of x.
27 cm
12 cm
SE
E
23.4 cm
Answer:
[tex] x = 10.4 [/tex]
Step-by-step explanation:
Since ∆ABD is similar to ∆CBE, therefore, the ratio of their corresponding side lengths would be equal to each other. Thus:
[tex] \frac{BD}{BE} = \frac{AD}{CE} [/tex]
BD = 12 cm
BE = x
AD = 27 cm
CE = 23.4 cm
Plug in the values
[tex] \frac{12}{x} = \frac{27}{23.4} [/tex]
Cross multiply
[tex] x \times 27 = 23.4 \times 12 [/tex]
[tex] 27x = 280.8 [/tex]
Divide both sides by 27
[tex] x = 10.4 [/tex]
evaluate this expression c^2 + d^3
Answer:
The expression is not factorable.
Step-by-step explanation:
Which set of ordered pairs represents y as a function of x ?
F {(0,0), (-1,2), (-1,-2), (-2,4), (-2,-4)}
G {(0,0), (1,1), (2,4), (3,9), (3,16)}
H {(0,0), (0,1),(0,2), (0,-1), (0, -2)}
J {(0,0), (-1,-0.5), (-2,-1), (-3,-1.5), (-4,-2)}
You run around the perimeter of a baseball field at a rate of at most 12 feet per second. Which of the following are possible amounts of time that it takes you to run around the baseball field?
Answer: 79 seconds.
Step-by-step explanation:1) we have to calculate the lenght of the baseball field.
perimeter of the baseball field=2(radius)+lenght of a semicircle.
2(radius)=2(175 ft)=350 ft
lenght of a semicircle=40% of a circumference=(40/100)(2πr)
Perimeter of the baseball field=2(175 ft) + (40/100)(2π175 ft)=
=350 ft + 140π ft=350 ft + 439.82 ft=789.82 ft,
2)Now, we calculate the amounts of time that it takes you to ruan arount the baseball field.
10 ft------------------------1 second
789,82 ft----------------- x
x=(789.82 ft * 1 second) / 10 ft=78.98 s≈79 s
The expression -25t+1250 represents the volume of liquid of a container after t seconds. The expression 50t+250 represents the volume of liquid of another container after t seconds. What does the equation -25t+1250=50t+250 mean in this situation?
Answer:
t = 13.33 second
Step-by-step explanation:
Given:
Equation first -25t+1250
Equation second 50t+250
Computation:
-25t+1250=50t+250
75 t = 1,000
t = 13.33 second
Means in t (13.33) second both container have same amount of liquid
Mr. Chen is buying cookies for the teachers and staff at Liberty Middle School. Each box contains 10 chocolate chip, 6 peanut butter, and 4 oatmeal raisin cookies. If there were 30 total peanut butter cookies, how many chocolate chip cookies did he buy? chocolate chip cookles
Answer:
50 chocolate chip cookies
Step-by-step explanation:
30÷6=5
Automobiles arrive at the drive-through window at a post office at the rate of 7 every 10 minutes. The average service time is 7 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. (Note: the given equations are NOT necessarily in the correct order.) What is the average time a car is in the system?Formulas for 13.17 What is the average number of cars in the system? What is the average time cars spend waiting to receive service? What is the average number of cars in line behind the customer receiving service? What is the probability that there are no cars at the window? What percentage of the time is the postal clerk busy? What is the probability that there are exactly two cars in the system?
Answer:
1) the average time a car is in the system is 0.1587 min
2) the average number of cars in the system 0.1111
3) the average time cars spend waiting to receive service is 0.01587 min
4) the average number of cars in line behind the customer receiving service is 0.01111
5) the probability that there are no cars at the window is 0.9
6) the percentage of time that the postal clerk is busy is 10%
7) the probability that there are exactly two cars in the system is 0.1217
Step-by-step explanation:
Given that;
Arrival rate λ = the rate of 7 every 10 minutes = 7/10 = 0.7
Average service time μ = 7 minutes
The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.
1) What is the average time a car is in the system?
Average in the system W = 1 / (μ - λ)
= 1 / (7 - 0.7) = 1 / 6.3 = 0.1587 min
therefore the average time a car is in the system is 0.1587 min
2) What is the average number of cars in the system?
Average number of cars L = λ / (μ - λ)
= 0.7 / (7 - 0.7) = 0.7/6.3 = 0.1111
Therefore the average number of cars in the system 0.1111
3) What is the average time cars spend waiting to receive service?
Average time spend waiting for services Wq = λ / μ(μ - λ)
= 0.7 / 7(7 - 0.7) = 0.7/44.1 = 0.01587 min
Therefore the average time cars spend waiting to receive service is 0.01587 min
4) What is the average number of cars in line behind the customer receiving service?
average number of cars in line behind the customer receiving service
Lq = λ² / μ(μ - λ) = (0.7)² / 7(7 - 0.7) = 0.49 / 44.1 = 0.01111
Therefore the average number of cars in line behind the customer receiving service is 0.01111
5) What is the probability that there are no cars at the window?
probability that there are no cars at the window = 1 - (λ / μ)
= 1 - (0.7 / 7) = 1 - 0.1 = 0.9
Therefore the probability that there are no cars at the window is 0.9
6) What percentage of the time is the postal clerk busy?
percentage of the time is the postal clerk busy = (λ / μ)
= (0.7 / 7) = 0.1 ≈ 10%
Therefore the percentage of time that the postal clerk is busy is 10%
7) What is the probability that there are exactly two cars in the system?
the probability that there are exactly two cars in the system = (λ²e^-λ) / 2!
= (0.7²e^-0.7) / 2! = 0.2433 / 2 = 0.1217
Therefore the probability that there are exactly two cars in the system is 0.1217