In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $100,000. The variable cost, which includes material, labor, and shipping costs, is $34 per doll. During the holiday selling season, FTC will sell the dolls for $42 each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who has agreed to pay FTC $10 per doll. Demand for new toys during the holiday selling season is extremely uncertain. Forecasts are for expected sales of 60,000 dolls with a standard deviation of 15,000. The normal probability distribution is assumed to be a good description of the demand. FTC has tentatively decided to produce 60,000 units (the same as average demand), but it wants to conduct an analysis regarding this production quantity before finalizing the decision.
(a) Create a what-if spreadsheet model using formulas that relate the values of production quantity, demand, sales, revenue from sales, amount of surplus, revenue from sales of surplus, total cost, and net profit. What is the profit corresponding to average demand (60,000 units)? $
(b) Modeling demand as a normal random variable with a mean of 60,000 and a standard deviation of 15,000, simulate the sales of The Dougie doll using a production quantity of 60,000 units. What is the estimate of the average profit associated with the production quantity of 60,000 dolls? $ How does this compare to the profit corresponding to the average demand (as computed in part a)? The input in the box below will not be graded, but may be reviewed and considered by your instructor
(c) Before making a final decision on the production quantity, management wants an analysis of a more aggressive 70,000-unit production quantity and a more conservative 50,000-unit production quantity. Run your simulation with these two production quantities. What is the mean profit associated with each? When ordering 50,000 units, the average profit is approximately $. When ordering 70,000 units, the average profit is approximately $.
(d) Besides mean profit, what other factors should FTC consider in determining a production quantity? Compare the four production quantities (40,000; 50,000; 60,000; and 70,000) using all these factors. What trade-offs occur? If required, round Probability of a Loss to three decimal places and Probability of a Shortage to two decimal places. What is your recommendation? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Let

ATQ

[tex]\\ \sf\longmapsto x+4x-6=94[/tex]

[tex]\\ \sf\longmapsto 5x-6=94[/tex]

[tex]\\ \sf\longmapsto 5x=94+6[/tex]

[tex]\\ \sf\longmapsto 5x=100[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{100}{5}[/tex]

[tex]\\ \sf\longmapsto x=20[/tex]

Answer:

$20

Step-by-step explanation:

T is Ted

K is Katie

T+K=94.

T=4K-6

I mostly just tried a bunch of numbers.

To check:

T+20=94

T=74

74=4(20)-6

74=80-6

74=74

I hope this helps!

pls ❤ and give brainliest pls

Let missing side be x

Using basic proportionality theorem

[tex]\\ \sf\longmapsto \dfrac{6}{4}=\dfrac{x}{20-x}[/tex]

[tex]\\ \sf\longmapsto 6(20-x)=4x[/tex]

[tex]\\ \sf\longmapsto 120-6x=4x[/tex]

[tex]\\ \sf\longmapsto 120=6x+4x[/tex]

[tex]\\ \sf\longmapsto 120=10x[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{120}{10}[/tex]

[tex]\\ \sf\longmapsto x=20[/tex]

Answer: k = 2/-3

Step-by-step explanation: Option (B)

Taking the test as we speak

Answer:

5% annual population growth rate

Step-by-step explanation:

Let the percent the population grows by be [tex]X\%[/tex]. The total population, [tex]f(x)[/tex], after [tex]t[/tex] years can be modeled by the function:

[tex]f(x)=40,000\cdot (\frac{X}{100}+1)^t[/tex]

Why?

Let's take a look at a simple example. If we said a number [tex]n[/tex] grew by 10%, we could represent the number after it grew by multiplying [tex]n[/tex] by [tex]1.10[/tex]. This is because growing by 10% is equivalent to taking [tex]100\%+10\%=110\%[/tex] of that number and we convert a percentage to a decimal by dividing by 100.

Therefore, if the population grew [tex]X\%[/tex], we would divide it by 100 to convert it to a decimal, then add 1 (100%) and raise to the power of [tex]t[/tex] (number of years) to multiply by the initial population of 40,000 to get the total population after [tex]t[/tex] years.

Since the population of the town after two years is 44,100, substitute [tex]f(x)=44,100[/tex] and [tex]t=2[/tex] into [tex]f(x)=40,000\cdot (\frac{X}{100}+1)^t[/tex]:

[tex]44,100=40,000\cdot (\frac{X}{100}+1)^2,\\\\(\frac{X}{100}+1)^2=\frac{44,100}{40,000},\\\\(\frac{X}{100}+1)^2=1.1025,\\\\(\frac{X}{100}+1)^2=\pm \sqrt{1.1025},\\\\\begin{cases}\frac{X}{100}+1=1.05,\frac{X}{100}=0.05, X=\boxed{5\%},\\*\text{negative case is extraneous since X must be positive}\end{cases}[/tex]

Therefore, the city has an annual population growth rate of 5%.

Answer:

because the power of variable is -2

Step-by-step explanation:

polynomials are a combination of constant and variable or only variable, being that power of variable is always positive natural no.

7/x^2 denotes 7x^-2

Answer:

Below!

Step-by-step explanation:

Please provide the two points (A & B) so I can help you out with the question or...

use the distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

where the first point = [tex](x_1,y_1)[/tex] & the second point: [tex](x_2,y_2)[/tex]

Answer:

100.48

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h where r is the radius and h is the height

V = 3.14 ( 2)^2 * 8

V = 3.14 (4)(8)

V = 100.48

Answer:

Step-by-step explanation:

If you mean √200, you cannot write it as V200.

√200 = √(10²×2) = 10√2

Answer:

B.) 2/10

Step-by-step explanation:

Answer:

RS 17.10

Step-by-step explanation:

If they earn 0.95 a day, you can multiply that income by the number of days, which is 18.

RS 17.10

Answer:

1

Step-by-step explanation:

Since the y value is the same, we only need to find the distance between the x points

1-0 = 1

The distance between the point is 1

Answer : 1 unit.

Explanation: Since ( 0,0 ) is at 0 on the x axis, ( 1,0 ) is one unit to the right of 0, 1.

Complete Question

Complete Question is attached below

Answer:

[tex]M=160[/tex]

Step-by-step explanation:

From the question we are told that:

Standard models contribute $20

Deluxe  models contribute $30

Availability Average :

Stamping machine S= 30 minutes per hour

Motor installation Production M=60 minutes

Wiring is W=90 minutes per hour

Generally the formulation of the linear program is given as

[tex]Maximium (M)=20x + 30 y[/tex]

Where

For Stamping machine

[tex]S= 3x + 6y \leq 30.....Equ 1[/tex]

For Motor installation Production

[tex]10x + 10y \leq 60....Equ 2[/tex]

For Wiring

[tex]10x + 15y \leq 90....Equ3[/tex]

Therefore

Solving Equ...(1,2,3) simultaneously we have

[tex]x=2\\\\y=4[/tex]

Therefore

[tex]Maximium\ (M)=20x + 30 y[/tex]

[tex]M=20(2)+30(4)[/tex]

[tex]M=160[/tex]

Answer:

Step-by-step explanation:

(-4 - 5i)⋅(1 - i) = (-4)(1) + (-4)(-i) + (-5i)(1) + (-5i)(-i)

= -4 + 4i - 5i + 5i²

= -4 - i -5

= -9 - i

The maximum length of the seesaw is option c  4.00 meters.

A right-angled triangle is one in which one of the angles is equal to 90 degrees. A 90 degree angle is called a right angle, which is why a triangle made up of right angle is termed a right angled triangle.

A right-angled triangle has three sides- hypotenuse, base and height. Hypotenuse is the longest and also the opposite side of the right angle of the triangle, base and height of a right triangle are always the sides adjacent to the right angle.

The formula for measuring the hypotenuse is,

Height / Hypotenuse = Sinθ , where θ is the angle opposite to the height of the triangle.

In the given question, the seesaw should make an angle of 30° with the ground and the maximum height it should rise is 2 meters so the height here is 2 meters. So the seesaw will make a right angled triangle.

Height = 2 meters, θ = 30°,

Now using the formula,

2 / Hypotenuse = Sin30°

Rearranging we get,

Hypotenuse = 2 / Sin30°

The value of Sin30° is 1/2 and putting the value we get,

Hypotenuse = 2 / (1/2)

                     = 2 × 2

                     = 4 meters.

Therefore, the maximum length of the seesaw (that is the hypotenuse ) is 4 meters.

To learn more about right-angled triangles and finding sides of it click here-brainly.com/question/10331046

#SPJ2

Answer:

Step-by-step explanation:

3-(2x-5)=-4(x+2)

We simplify the equation to the form, which is simple to understand

3-(2x-5)=-4(x+2)

Remove unnecessary parentheses

3-2x+5=-4*(x+2)

Reorder the terms in parentheses

3-2x+5=+(-4x-8)

Remove unnecessary parentheses

+3-2x+5=-4x-8

We move all terms containing x to the left and all other terms to the right.

-2x+4x=-8-3-5

We simplify left and right side of the equation.

+2x=-16

We divide both sides of the equation by 2 to get x.

x=-8

Answer:

x < - 8

Step-by-step explanation:

Given

3 - (2x - 5) < - 4(x + 2) ← distribute parenthesis on both sides

3 - 2x + 5 < - 4x - 8

- 2x + 8 < - 4x - 8 ( add 4x to both sides )

2x + 8 < - 8 ( subtract 8 from both sides )

2x < - 16 ( divide both sides by 2 )

x < - 8

Answer:

1/13

Step-by-step explanation:

There are 52 cards in a deck of cards and 13 of them are hears

P(heart) = hearts / total

              = 13/52 = 1/13

Answer:

The key difference between simple interest and compound interest is that in simple interest, the interest is calculated based on the principal amount of the loan.

The formula is principal multiplied by time by rate divided by 100.

Compound interest on the other hand, has to do with the principal amount and accumulated interest on previous periods.

The difference affects the effectiveness of each because in SI, interest is calculated once, while in CI, there's accumulated interest.

I think the given integral reads

[tex]\displaystyle \int_{-3}^3 \int_0^{9-x^2} \int_{x^2+y^2}^{9-x^2-y^2} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

In cylindrical coordinates, we take

x ² + y ² = r ²

x = r cos(θ)

y = r sin(θ)

and leave z alone. The volume element becomes

dV = dx dy dz = r dr dθ dz

Then the integral in cylindrical coordinates is

[tex]\displaystyle \boxed{\int_0^\pi \int_0^{(\sqrt{35\cos^2(\theta)+1}-\sin(\theta))/(2\cos^2(\theta))} \int_{r^2}^{9-r^2} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta}[/tex]

To arrive at this integral, first look at the "shadow" of the integration region in the x-y plane. It's the set

{(x, y) : -3 ≤ x ≤ 3 and 0 ≤ y ≤ 9 - x ²}

which is the area between a paraboloid and the x-axis in the upper half of the plane. So right away, you know θ will fall in the first two quadrants, so that 0 ≤ θ ≤ π.

Next, r describes the distance from the origin to the parabola y = 9 - x ². In cylindrical coordinates, this equation changes to

r sin(θ) = 9 - (r cos(θ))²

You can solve this explicitly for r as a function of θ :

r sin(θ) = 9 - r ² cos²(θ)

r ² cos²(θ) + r sin(θ) = 9

r ² + r sin(θ)/cos²(θ) = 9/cos²(θ)

(r + sin(θ)/(2 cos²(θ)))² = 9/cos²(θ) + sin²(θ)/(4 cos⁴(θ))

(r + sin(θ)/(2 cos²(θ)))² = (36 cos²(θ) + sin²(θ))/(4 cos⁴(θ))

(r + sin(θ)/(2 cos²(θ)))² = (35 cos²(θ) + 1)/(4 cos⁴(θ))

r + sin(θ)/(2 cos²(θ)) = √[(35 cos²(θ) + 1)/(4 cos⁴(θ))]

r  = √[(35 cos²(θ) + 1)/(4 cos⁴(θ))] - sin(θ)/(2 cos²(θ))

Then r ranges from 0 to this upper limit.

Lastly, the limits for z can be converted immediately since there's no underlying dependence on r or θ.

The expression above is a bit complicated, so I wonder if you are missing some square roots in the given integral... Perhaps you meant

[tex]\displaystyle \int_{-3}^3 \int_0^{\sqrt{9-x^2}} \int_{x^2+y^2}^{9-x^2-y^2} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

or

[tex]\displaystyle \int_{-3}^3 \int_0^{\sqrt{9-x^2}} \int_{x^2+y^2}^{\sqrt{9-x^2-y^2}} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]

For either of these, the "shadow" in the x-y plane is a semicircle of radius 3, so the only difference is that the upper limit on r in either integral would be r = 3. The limits for z would essentially stay the same. So you'd have either

[tex]\displaystyle \int_0^\pi \int_0^3 \int_{r^2}^{9-r^2} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]

or

[tex]\displaystyle \int_0^\pi \int_0^3 \int_{r^2}^{\sqrt{9-r^2}} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]

Answer:

[tex]thank \: you[/tex]

$121 and $12 ok isn't available in your ma er bishal bishal bishal

Answer:

Y= -9x+45

y = -9 X + b

-9 = -9(6) + b

-9 = -54 + b

b=45

Step-by-step explanation:

Answer:

the lower limit is 35% women believed and 65% of men believed in serial discrimination

Hi! I'm happy to help!

To solve this problem, we need to divide the recipe amount in 1/6 amounts. So, we will do a fraction division problem like this:

15[tex]\frac{1}{6}[/tex]÷[tex]\frac{1}{6}[/tex]

This problem is hard to do with mixed numbers, so we need to turn 15[tex]\frac{1}{6}[/tex] into an improper fraction. To do that we need to multiply 15 by 6, because that is our denominator, then add the extra [tex]\frac{1}{6}[/tex].

(15×6)+1

90+1

91

So, our improper fraction would be[tex]\frac{91}{6}[/tex], now, let's solve.

[tex]\frac{91}{6}[/tex]÷[tex]\frac{1}{6}[/tex]

It is difficult to do division problems on their own, so we can change this into an easier problem. We can do the inverse operation and turn this into multiplication. We do this by changing it to multiplication (obviously), then flip the second fraction.

[tex]\frac{91}{6}[/tex]×[tex]\frac{6}{1}[/tex]

Now, we just multiply the top by the top, and bottom by the bottom.

[tex]\frac{546}{6}[/tex]

We could end it here, but we want a whole number, so, we simplify the number by dividing both the top and bottom by 6.

[tex]\frac{91}{1}[/tex]

Anything over 1, is just a whole number

91.

Therefore, the recipe should require 91 uses of the 1/6 cup.

I hope this was helpful, keep learning! :D

ans: 257,256.59

if it was sold for $3.99

it would have been 86,047 × $3.99 = 343,303.59 and it was sold for $1 instead so automatically it's $86,047

therefore

343, 303.59

-86, 047 which is equal to a loss of $257, 256.59

Answer:

-12

Step-by-step explanation:

that is b

Answer:

C

Step-by-step explanation:

sin(theta)=7/8, theta=arcsin(7/8)=61

Answer:

please tell me the complete question

Answer: hello your question is poorly written attached below is the complete question

answer:

1 ) =  I (

2) = F

3) = Z

4) = D

Step-by-step explanation:

attached below is the required solution.

1 ) =  I ( The sequence diverges to infinity )

2) = F ( The sequence has a finite non-zero limit )

3) = Z ( The sequence converges to zero )

4) = D ( The sequence diverges )

Answer:

3

Step-by-step explanation:

Please Mark me brainliest

Answer:

aren't one of the numbers in the equations supposed to be negative?