Answer:
[tex]\displaystyle \frac{118}{125}[/tex]
Step-by-step explanation:
Trigonometry
Calculate
[tex]\sin (3\sin^{-1}(2/5))[/tex]
We use the formula for the sine of triple angle:
[tex]\sin 3x=3\sin x-4\sin^3 x[/tex]
And recall:
[tex]\sin \sin^{-1}x=x[/tex]
For this problem, we set:
[tex]x=\sin^{-1}(2/5)[/tex]
Thus:
[tex]\sin 3x=3\sin (\sin^{-1}(2/5))-4\sin^3 (\sin^{-1}(2/5))[/tex]
[tex]\displaystyle \sin 3x=3*\frac{2}{5}-4\left(\frac{2}{5}\right)^3[/tex]
[tex]\displaystyle \sin 3x=\frac{6}{5}-4*\frac{8}{125}[/tex]
[tex]\displaystyle \sin 3x=\frac{6}{5}-\frac{32}{125}[/tex]
[tex]\displaystyle \sin 3x=\frac{6*25}{125}-\frac{32}{125}[/tex]
[tex]\displaystyle \sin 3x=\frac{150-32}{125}[/tex]
[tex]\mathbf{\displaystyle \sin 3x=\frac{118}{125}}[/tex]
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 c=c, the newsvendor solution is the mean.
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
Solve: 2x + 3x? - 11x-6=0
Answer:
To solve the following equation we must first combine like terms Recognize the easiest way to manipulate the equation Lastly rearrange to isolate for x: usually done with division2x+3x-11x-6=0
Combine like x variables
-6x-6=0
Add 6 to the right side
-6x = 6
Divide by -6
x=-1
Rate positively and give brainlist
Answer:
x = - 1
Step-by-step explanation:
2x + 3x - 11x - 6 = 0
-6x = 6
x = - 1
To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded mean nicotine content of milligrams and standard deviation of milligrams for a sample of cigarettes. Construct a % confidence interval for the mean nicotine content of this brand of cigarette.
Answer:.
Step-by-step explanation:.
in eleven years ted will be 22 years old how old is he now?
Answer:
11
Step-by-step explanation:
22-11=11
-4x+3y=-2
y=x-1
x=
y=
Answer:
Easy thankyou for coming to me your answer is x= -1 and y=-2
Step-by-step explanation:
Hope that help.
Answer:
Step-by-step explanation:
here you go mate'
step 1
-4x+3y=-2,y=x-1 equation
step 2
y=x-1;-4x+3y=-2 rewrite the equation
step 3
y=x-1 1st equation
step 4
-4x+3y=-2 saubstitute
-4x+3(x-1)=-2
-x-3=-2
step 5
-x-3=-2 simplify by adding 3 to both sides
-x=1
step 6
-x/-1=1/-1 divide
x=-1
second equation
step 1
y=x-1 substitute
y=-1-1
step 2
y=-1-1 simplify
y=-2
answer
x=-1 and y=-2
Sarah read 64 1/2 pages of her book in 6 hours. What is the average number of pages that Sarah reads per hour?
Answer:
We conclude that the average number of pages that Sarah reads per hour will be: 10.75 page per hour
Step-by-step explanation:
Given
Number of pages Sarah read [tex]=64\frac{1}{2}=\frac{129}{2} = 64.5[/tex]Number of hours Sarah spent = 6 hoursThe average number of pages per hour can be calculated by simply dividing the total number of pages i.e. 64.5 pages by the number of hours spent on reading i.e. 6 hours.
Thus,
Average number of pages per hour = 64.5 pages / 6 hours
= 10.75 page per hour
Therefore, we conclude that the average number of pages that Sarah reads per hour will be: 10.75 page per hour
can u pls help me with this question asap
Answer:
$13.50
Step-by-step explanation:
5 bags is 22.50 so 22.50/5 = 4.50 for 1 bag. Multiply that by 3 for 3 bags and get $13.50
Find the prime factorization of 100. Show all of your work and write your answer using exponents.
this is the ans ..............................
VWXY is a parallelogram. Find the measure of XY and WY
Answer:
WY = 30
XZ = 10.5
Step-by-step explanation:
Paralellogram's diagonal's bisect eachother
Therefore,
[tex]n + 7 = 3 n[/tex]
Move the n over,
2n = 7
Divide both sides by 2,
n = 3.5
WY = 2(ZY) because definition of bisector
Simplify...
WY = 2(4n+1)
WY = 2(4(3.5)+1)
WY = 2(15)
WY = 30
You asked for XY, but the question asks for XZ, so I'm going to give XZ.
With n = 3.5 from above,
XZ = 3n
XZ = 3(3.5)
XZ = 10.5
The measure of XY and WY are; WY = 30 and XZ = 10.5
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Since Paralellogram's diagonal's bisect each other
Therefore,
2n = 7
Divide both sides by 2;
n = 3.5
WY = 2(ZY)
because definition of bisector
Simplify;
WY = 2(4n+1)
WY = 2(4(3.5)+1)
WY = 2(15)
WY = 30
we asked for XY,
With n = 3.5 from above,
XZ = 3n
XZ = 3(3.5)
XZ = 10.5
The measure of XY and WY are; WY = 30 and XZ = 10.5
Learn more about parallelogram;
https://brainly.com/question/28854514
#SPJ2
I need help plssssss.....
Complete the statement with the appropriate symbol.
1.42 _____ 1.420
=
>
Answer:
=
Step-by-step explanation:
After the decimal point if the zeros are on the right side they do not have any value.
Answer: = because 0 has no value
Complete the statement with the appropriate symbol.
1.42 ___=__ 1.420
>
<
=
Step-by-step explanation: = because the 0 has no value.
Which of the following letters have perpendicular line segments.
A E F H MNV X Z
Answer:
I think it's E, F, H
Step-by-step explanation:
Hope you got it.
Merry Christmas...
slove for x
(6x+4)+81+41
Picture below
mathematics
Answer:
false
Step-by-step explanation:
5/9 is .5 repeating
Please Help thank you I appreciate it
Answer:
48in sq
Step-by-step explanation:
8*12/2=8*6=48
Answer:
48in
Step-by-step explanation:
A triangle like this is like half of a rectangle. The rest fits in the upper left and right. So to find the area of the triangle, we're going to start be pretending it's a recrangle.
Our rectangle is 12 by 8.
12 x 8 = 96
If this were a rectangle, the area would be 96in.
Since it's a triangle and that's only half of a rectangle, the area is half of that.
96 / 2 = 48
The area of this triangle is 48in.
Macy wants to sell her old Playstation 4 games on decluttr.com. The wtbsite charges sellers a comission of 20%
for items sold on their website. If Macy sells a Playstation 4 game on the website for $35.00. How much willshe
actually receive?
Answer:
$28
Step-by-step explanation:
The website charges 20%, so Macy receives 80%.
Then:
80% x 35=.8 x 35=28 ....................
BRAINLIST ASAP
When marcus started school at 5 years old, his parents put $9,050 into a college fund account that earned 7.5% interest. What is the total amount in the account when he starts college at 18 years old? ____
Answer: 17873.75 dollars
Step-by-step explanation:
We can use the equation: l = p x r x t (Total Interest = principal x interest rate x years/time)
9050 will be the principal; it's the amount you deposit in the first place.
7.5% is the interest rate. You can convert it to 0.075 as a decimal.
13 is the years/time. If Marcus's parents put the college fund in when he was 5 and now he's 18, there has been 13 years in between.
9050 x 0.075 x 13 = 8823.75
8823.75 + 9050 = $17873.75
So in Conclusion, the total amount in the account when Marcus is 18 is 17873.75 dollars.
Hope this helps!
HELPP PLEASE ILL NAME YOU BRAINLIEST!!!
LOOK AT PICTURE, THEN ANWSER, WHOEVER IS CORRECT I WILL MARK BRAINIEST:)
Answer:
C
Step-by-step explanation:
It has to be either A or C because the function is decreasing as you move left to right, this only occurs when the number inside parenthesis is less than 1.
It isn't A because if you plug in x=0, the value is 2, but on the graph it is greater than 2.
pleae give thanks by hitting heart button :)
-4(x+6)-2(-3x-9) simplify
Answer:
-4x-24+6x+18
Step-by-step explanation:
For the triangles shown, which detail would have to be given to prove them congruent by the Angle Angle Side congruence criteria?
Answer:
The measure of the angle labeled d
Step-by-step explanation:
I took the quick check for "angle angle side postulate"
Which operation is NOT closed for polynomials?
es )
A)
add a trinomial to a trinomial
B)
divide a binomial by a trinomial
multiply a binomial by a binomial
D)
subtract a binomial from a trinomial
Answer:
B)
divide a binomial by a trinomial
Step-by-step explanation:
As we know that the polynomials are very closed to the addition, subtraction and the multiplication but the same cannot be happen under the division as the division of two polynomials could not become a polynomial it is not necessary
Now if we divide the binomial from a trinomial so it would give a rational expression and contain a negative exponent and negative exponent is not allowed under the same
Therefore the option B is correct
ostulate
Point D is on segment BC. Segment BC measures 8x units in length.
A line has points C, D, B. The length of line C D is 3 x + 8. The length of line D B is 4 x + 10.
What is the length of segment BC?
Answer:
144Step-by-step explanation:
If point D is on BC, then BD + DC = BC
Given
BC = 8x
CD = 3x + 8
BD = 4x + 10
Substitute and get x
8x = 3x+8 + 4x + 10
9X - 7X = 18
x = 18
Get BCBC = 8x
BC = 8(18)
BC = 144
Hence the length of segment BC is 144
Answer:
144
Step-by-step explanation:
I just had this assignment on edge 2021. Hope this helped :)
In triangle ABC shown below, point A is at (0,0)
point B is at (x subscript2, 0)
point C is ([x sub1]/ 2, [y sub1]/2
point D is [x sub1 + xsub2]/2, ysub1/2)
Prove that segment DE is parallel to segment AB.
Answer:
Proof below
Step-by-step explanation:
To prove DE and AB are parallel, we compare the slopes of both segments
Suppose we know a line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Segment AB goes through the points (0,0) and (x2,0), thus:
[tex]\displaystyle m_{AB}=\frac{0-0}{x_2-0}=0[/tex]
The slope is 0 because the line is horizontal.
Now for the segment DE, the endpoints are
[tex]\displaystyle (\frac{x_1}{2},\frac{y_1}{2}),\ (\frac{x_1+x_2}{2},\frac{y_1}{2})[/tex]
The slope is:
[tex]\displaystyle m_{DE}=\frac{\frac{y_1}{2}-\frac{y_1}{2}}{\frac{x_1+x_2}{2}-\frac{x_1}{2}}[/tex]
[tex]\displaystyle m_{DE}=\frac{0}{\frac{x_2}{2}}=0[/tex]
Segment DE is also horizontal, thus is parallel to segment AB.
Given the drawing as shown below and that p || a, which of the following cannot be supported by the evidence shown?
A -
B -
C -
D -
Answer:
D. <b ≅ <g
Step-by-step explanation:
Given that lines p and q are parallel to each other, therefore the following can be concluded:
✔️<f ≅ <h, this is because they are both Vertical angles.
✔️<d and <h are supplematry, this is because they are same side consecutive interior angles. Consecutive angles are supplematry.
✔️<a and <b are supplematry, this is because they are linear pair angles.
✔️<b cannot be congruent to <g. They are not corresponding angles, nor are they alternate interior angles.
Anyone know this answer?
the answer is =10
10
10
10
What is the elevation of the deck where Winston ate dinner?
plz helppp
Question:
What is the elevation of the deck where Winston ate dinner?
Answer:
The surf shop was higher and the distance would be 12.8 feet above the oceans surface.
12.8
Step-by-step explanation:
Y=log base(rootx) x find dy/dx
Given:
[tex]y=\log_{\sqrt{x}}x[/tex]
To find:
The value of [tex]\dfrac{dy}{dx}[/tex].
Solution:
We have,
[tex]y=\log_{\sqrt{x}}x[/tex]
It can be written as
[tex]y=\log_{\sqrt{x}}(\sqrt{x})^2[/tex]
Using property of log, we get
[tex]y=2[/tex] [tex][\because \log_aa^x=x][/tex]
Now, differentiate both sides with respect to x.
[tex]\dfrac{dy}{dx}=\dfrac{d}{dx}(2)[/tex]
[tex]\dfrac{dy}{dx}=0[/tex] [tex][\because \dfrac{d}{dx}(Constant)=0][/tex]
Therefore, the value of [tex]\dfrac{dy}{dx}[/tex] is 0.
A pound of sweet potatoes costs $1.81 at Walmart. Shelly buys 14.6 pounds to make a sweet potato pie. How much money
will she spend at Walmart?
Answer:
$26.43
Step-by-step explanation:
A pound = $1.81. Multiply the price per pound by however many pounds Shelly is buying.
Answer:
26.426
Step-by-step explanation:
1.81x14.6=26.426
A salesperson works 40 hours per week at a job where she has two options for being paid. Option
A is an hourly wage of $22. Option B is a commission rate of 10% on weekly sales. How much
does she need to sell this week to earn the same amount with the two options?
Answer:
the weekly sales are $8,800 to earn the similar amount with the two options
Step-by-step explanation:
The computation is shown below:
The earnings in option A is
= 40 hours × $22
= $880
Now let us assume the weekly sales be x
So the equation would be
10%x = $880
0.10x = $880
x = $8,800
Hence, the weekly sales are $8,800 to earn a similar amount with the two options