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.

Answer:

the probability that I chose red or blue is 75%

75%

f(0) = 56

f(2) = 42

f(-2) = 70

f(x+1) = 7|x-7|

f(x²+2) = 7|x²-6|

Answered by GAUTHMATH

Answer:

a=2, b=3,x=6

Step-by-step explanation:

We are given that

We have to find the value of the missing letters in the sum of numbers.

From given sum

1+a+b=x   ....(1)

b+b+b=9  .....(2)

a+a=4       ......(3)

From equation (2) we get

[tex]3b=9[/tex]

[tex]\implies b=3[/tex]

From equation (3) we get

[tex]2a=4[/tex]

[tex]a=4/2[/tex]

[tex]a=2[/tex]

Now, substitute the values in equation (1) we get

[tex]1+2+3=x[/tex]

[tex]x=6[/tex]

Therefore,

231+32+233=496

If we simplify, both Joe and Hope factored the polynomial correctly but Joe didn't complete it fully.

The first binomial can be further factored:

The quadratic expression needs to have two roots in order to be factored as two binomials.

The discriminant must be positive or zero:

We have a = 3, b = k, c = -8

So we get following inequality:

Since k² is positive for any value of k, the solution is any value of k:

Hope this attachment helps you.

Answer:

-2x³ - 14x² + 7x - 4

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

(3x³ - 2x² + 4x - 8) - (5x³ + 12x² - 3x - 4)

Step 2: Simplify

Answer:

Option B, 29°

Step-by-step explanation:

The diagram is a angle bisecting diagram which divides the 58° angle into two 29° angles.

Answered by GAUTHMATH

Answer:

The area of the shed=[tex]64m^2[/tex]

Step-by-step explanation:

We are given that

Side of square =8m

We have to find the area of the shed.

To find the area of shed we will find the area of square.

We know that

Area of square=[tex]side\times side[/tex]

Using the formula

Area of square=[tex]8\times 8[/tex]

Area of square=[tex]64m^2[/tex]

Area of shed=Area of square

Area of shed=64 square m

Hence, the area of the shed=[tex]64m^2[/tex]

Answer:

(a) Residents

(b) [tex]Median = 0.13[/tex]

(c)  [tex]\bar x = 0.14[/tex]

(d) Right skewed

Step-by-step explanation:

Given

The data of residents without health insurance

Solving (a): The variable

The variable is the residents

Solving (b): The median

First, we sort the data

[tex]Sorted: 0.09, 0.10, 0.11, 0.13, 0.13, 0.14, 0.16, 0.19, 0.25[/tex]

So, the median position is:

[tex]Median = \frac{n + 1}{2}[/tex]

[tex]Median = \frac{9 + 1}{2}[/tex]

[tex]Median = \frac{10}{2}[/tex]

[tex]Median = 5th[/tex]

The 5th element of the dataset is: 0.13

So:

[tex]Median = 0.13[/tex]

Solving (c): The mean

This is calculated as:

[tex]\bar x = \frac{\sum x}{n}[/tex]

[tex]\bar x = \frac{0.09+ 0.10+ 0.11+ 0.13+ 0.13+ 0.14+ 0.16+ 0.19+ 0.25}{9}[/tex]

[tex]\bar x = \frac{1.3}{9}[/tex]

[tex]\bar x = 0.14[/tex]

Solving (d): The shape of the distribution

In (b) and (c), we have:

[tex]Median = 0.13[/tex]

[tex]\bar x = 0.14[/tex]

By comparison, the mean is greater than the median.

Hence, the shape is: right skewed.

Answer:

There is not enough info to tell

Step-by-step explanation:

Khan acadamey

Answer:

100

Step-by-step explanation:

I assume you mean [tex]\frac{5}{12}[/tex] of the students in Year 9.

Basically, first you need to work out 1/12 of the students, which is just 240 divided by 12, equals 20.

So, we know 1/12 of 240 is 20, therefore, in order to work out 5/12, we must do 20 x 5, which is 100.

Answer:

8/81

Step-by-step explanation:

It's most efficient to simplify the quotient algebraically before inserting the values of the variables x and y.  

The given expression reduces to x³ / y^4.

Substituting 2 for x and 3 for y, we get:

 (2)³           8

--------- = ---------- (Agrees with first given possible answer)

 (3)^4         81

Answer:

1 ans A second phi okay yed

Explanation:

There are 8 different flavors and 3 types of cones. This means there are 8*3 = 24 different combos possible.

Imagine a table with 8 rows and 3 columns. Each row is a different flavor and each column is a different cone type. The table formed has 24 inner cells to represent a different combination of flavor + cone type. So that's why we multiplied those values earlier.

Note: This only works if you're only able to select one type of flavor.

Answer:

$2550

Step-by-step explanation:

Calculation to determine the amount of retained earnings at the beginning of Year 2

Using this formula

Beginning Retained Earnings + Revenue − Expenses − Dividends = Ending Retained Earnings

Let plug in the formula

Beginning Retained Earnings + $3,200 − $1,700 − $1,100 = $2950

Beginning Retained Earnings= $2,950-$400

Beginning Retained Earnings = $2,550

Therefore the amount of retained earnings at the beginning of Year 2 is $2550

Answer:

I got u, it is litearly 16540/83.8 = $19737.5

Step-by-step explanation:

its very simple sincen 100-16.2=83.8

Answer:

Outlier therefore could only be values below  - 12.75

or could only be values above + 121.125

Step-by-step explanation:

0, 4, 6, 14, 17

inner quartile range of 0 - 17 is 1/2 of 17 subtracted from the higher number = 17 - 1/2 of 8.5 =  8.5 - 4.25 = 4.25 - 4.25 x 3

= 4.25 to 12.75 for inner quartile

inner quartile range is 12.75-4.25 = 8.5

We then 1.5 x 8.5 to show the outlier

= 12.75 meaning there is no outlier if is below.

Lower quartile fences  = 4.25 - 1.5 = 2.75

or -1.5 x 8.5 (the range) =   -12.75

Upper quartile fence = 12.75 + 1.5 = 14.25 x 8.5 =   121.125  this would be an outlier if it is 12.75 higher than 121.125 or 12.75 lower than 5.50.

Outlier therefore could only be values below  - 12.75

or could only be values above + 121.125

An observation is considered an outlier if it exceeds a distance of 1.5 times the interquartile range (IQR) below the lower quartile or above the upper quartile. The values of the lower quartile - 1.5 x IQR and upper quartile + 1.5 x IQR are known as the inner fences.

An observation is an outlier if it falls more than above the upper quartile or more than below the lower quartile. The minimum value is so there are no outliers in the low end of the distribution. The maximum value is so there are no outliers in the high end of the distribution.

Answer:

£2120.27

Step-by-step explanation:

A = P (1 + r100)

A = 2000 (1+ 0.03/365)^365(2)

A = 2000 ( 1.00008)^730

A = 2000 (1.060)

A = £2120.27

Answer:

2n+2

_____

9 2n

Answer:

3. The scale factor is 3, which means the length of the image of segment KL will be 3 times as long.

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure. If a point A(x, y) is dilated about the center of dilation located at O(a, b), the new point is at A'[k(x - a) + a, k(y - b) + b].

Quadrilateral KLMN has vertices at K(2, 1), L(-1, -5), M(6, -5) and N(6, 1). If it is dilated by 3, about the center M(6, -5), the new points are:

K' = (3(2 - 6) + 6, 3(1 - (-5)) + (-5)) = (-6, 13)

L' = (3(-1 - 6) + 6, 3(-5 - (-5)) + (-5)) = (-15, -5)

M' = (3(6 - 6) + 6, 3(-5 - (-5)) + (-5)) = (6, -5)

N' = (3(6 - 6) + 6, 3(1 - (-5)) + (-5)) = (6, 13)

Therefore the image of segment KL will be 3 times long.

Answer:

1) a)  accepting the new drug is better based on its effectiveness when in reality the drug ain't better than the drug in current use because of its side effects

b) Accepting and using the current drug in use when it is not as effective as the new drug

c) Type 1 error

2) a) rejecting the vitamin supplement based on not knowing the harmful side effects

b) Accepting the Vitamin supplement based on just health benefits it portrays without comparison with other supplement.

c) Type II error

3) Increase the significance level  ( A )

Step-by-step explanation:

1)

a) To make a type 1 error in this situation is accepting the new drug is better and prescribing it to the millions of people based only on its effectiveness when in reality the drug ain't better than the drug in current use because of its side effects

b) A type II error in context is :Accepting and using the current drug in use when it is not as effective as the new drug

c)  Type I error

2)

a) Type 1 error is rejecting the vitamin supplement based on not knowing the harmful side effects

b) Accepting the Vitamin supplement based on just health benefits it portrays without comparison with other supplement.

c) Type II error

3) If committing a type 1 error is much worse

Increase the significance level

Answer:

Y = 2/3X + 4/3

Step-by-step explanation:

(1,2) (4,4)

M = 2/3

Y = 2/3X + b

4 = 8/3 + b

12 = 8 + 3b

4 = 3b

B = 4/3

Y = 2/3X + 4/3

Answer:

[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

Step-by-step explanation:

A

Let's start with the first function:

[tex]x^{3}cos(x^{2})=x^{3}-\frac{x^{7}}{2!}+\frac{x^{11}}{4!}-\frac{x^{15}}{6!}+...[/tex]

In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a

[tex](-1)^{n}[/tex].

This will guarantee us that the terms will always change their signs so that will be the first part of our expression.

next, the power of the x. Notice the given sequence: 3, 7, 11, 15...

we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 3. So the power is given by 4n+3.

so let's put the two things together:

[tex](-1)^{n}x^{4n+3}[/tex]

Finally the denominator, there is also a sequence there: 0!, 2!, 4!, 6!

This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2, so in this case the sequence can be written as: (2n)!

So let's put it all together so we get:

[tex]\frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

So now we can build the whole series:

[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

B

Now, let's continue with the next function:

[tex]x^{3}sin(x^{2})=x^{5}-\frac{x^{9}}{3!}+\frac{x^{13}}{5!}-\frac{x^{17}}{7!}+...[/tex]

In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a

[tex](-1)^{n}[/tex].

This will guarantee us that the terms will always change their signs so that will be the first part of our expression.

next, the power of the x. Notice the given sequence: 5, 9, 13, 17...

we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 5. So the power is given by 4n+5.

so let's put the two things together:

[tex](-1)^{n}x^{4n+5}[/tex]

Finally the denominator, there is also a sequence there: 1!, 3!, 5!, 7!

This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2 starting from a 1, so in this case the sequence can be written as: (2n+1)!

So let's put it all together so we get:

[tex]\frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

So now we can build the whole series:

[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

Answer:

The length is of 59 cm.

Step-by-step explanation:

Perimeter of a rectangle:

The perimeter of a rectangle with width w and length l is given by:

[tex]P = 2(w + l)[/tex]

Width of 49 centimeters and a perimeter of 216 centimeters:

This means that [tex]w = 49, P = 216[/tex]

The length is cm.

We have to solve the equation for l. So

[tex]P = 2(w + l)[/tex]

[tex]216 = 2(49 + l)[/tex]

[tex]216 = 98 + 2l[/tex]

[tex]2l = 118[/tex]

[tex]l = \frac{118}{2}[/tex]

[tex]l = 59[/tex]

The length is of 59 cm.

Answer:

Factors of number 52

Factors of 52: 1, 2, 4, 13, 26 and 52.

Negative Factors of 52: -1, -2, -4, -13, -26 and -52.

Prime Factors of 52: 2, 13.

Prime Factorization of 52: 2 × 2 × 13 = 22 × 13.

Sum of Factors of 52: 98.

Answer:

Atleast 4 women

Step-by-step explanation:

Ratio of

Women to men = 2 : 7

Number of women needed to maintain the ratio if there are 14 men on the roster :

The minimum number of women required :

(2 : 7) * number of men in roster

(2 / 7) * 14

2 * 2 = 4 women

Atleast 4 women are required to main the ratio

Answer:

Values of x

Step-by-step explanation:

The domain of a function is the set of all possible inputs for the function while the co-domain is the set of all possible outputs of the function.

In other words, domain is the set of x-values that you can put into any given equation while co-domain is the sex of f(x)-values that you get from substituting the values of x.

Hope it's clear

Answer:

just keep writing down outcome on a sheet of paper then count total

Step-by-step explanation: