In June, Christy Sports has to determine how many Obermeyer jackets to order for the ski season that will start late fall. Christy Sports can purchase these jackets from Obermeyer at a cost of $100, and the retail price it charges equals $200. Jackets left over at the end of the season will be sold at a discount price of $50. Christy Sports has to order jackets in multiples of 25.



Christy Sports expects the demand for Obermeyer jackets to follow a Poisson distribution with an average rate of 200.



a. Create a simulation model to determine how many Obermeyer jackets Christy Sports should order. What is the optimal order quantity?


b. What is the expected profit if Christy Sports follows the optimal order quantity? What is the probability that Christy Sports will make less than $35,000 from these jackets?

The area of the region bounded between the graphs of\(y = -x^2 + 8x\) and \(y = x^2 + 2x\) is 9 square units.

To find the area of the region bounded between the graphs of\(y = -x^2 + 8x\)and\(y = x^2 + 2x\), we need to find the points of intersection of the two curves and then integrate the difference of the curves between these points.

First, we find the points of intersection by setting the two curves equal to each other:

\(-x^2 + 8x = x^2 + 2x\)

Simplifying and rearranging, we get:

\(2x^2 - 6x = 0\)

Factoring out 2x, we get:

\(2x(x - 3) = 0\)

So, \(x = 0 or x = 3.\)

Substituting these values of x in either of the two equations, we get the corresponding y values:

For\(x = 0, y = 0^2 + 2(0) = 0.\)

For\(x = 3, y = 3^2 + 2(3) = 15.\)

So, the points of intersection are (0, 0) and (3, 15).

Now, we can integrate the difference of the curves between these points to find the area.

\(A = ∫[0, 3] [(x^2 + 2x) - (-x^2 + 8x)] dx\)

Simplifying the integrand, we get:

\(A = ∫[0, 3] (2x^2 - 6x) dx\)

Integrating this expression, we get:

\(A = [(2/3) x^3 - 3x^2] [0, 3]\\A = [(2/3) (3)^3 - 3(3)^2] - [(2/3) (0)^3 - 3(0)^2]\\A = (18 - 27) - (0 - 0)\\A = -9\)

Therefore, the area of the region bounded between the graphs of\(y = -x^2 + 8x\) and\(y = x^2 + 2x\) is 9 square units.

Note that the area is a positive quantity even though the integrand was negative because the area is defined as the absolute value of the integral.

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Answer:

B , D , C

Step-by-step explanation:

the central angle x is equal to the measure of the arc that subtends it, so

x = 90°

similarly

z = 22°

similarly the central angle subtended by arc y° is y°

the 3 angles on the diameter sum to 180° , that is

x + y + z = 180°

90° + y + 22° = 180°

112° + y = 180° ( subtract 112° from both sides )

y = 68°

Answer:

y = 45

Step-by-step explanation:

y = k x^2

500 = k * 10^2

500 = k*100

k = 5

y = 5*x^2

x = 3

y = 5*3^2

y = 45

When using the chi-square goodness of fit test, the smaller the value of the chi-square test statistic, the more likely we are to accept the null hypothesis rather than reject it. This statement is false.

The chi-square goodness of fit test is a hypothesis test that measures how well an observed frequency distribution fits a theoretical frequency distribution. It is used to determine whether a sample's categorical data is distributed similarly to the population's categorical data or not.

However, a low chi-square statistic suggests that the observed frequencies are close to the expected frequencies, and thus the null hypothesis should not be rejected. In contrast, a large chi-square value indicates that the observed frequencies are significantly different from the expected frequencies, indicating that the null hypothesis should be rejected.

Therefore, when using the chi-square goodness of fit test, the larger the value of the chi-square test statistic, the more likely we are to reject the null hypothesis, and vice versa.

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The solutions to matrix multiplication problems using either row or column method are: First row of AB: [45, 42, 39], Third row of AB: [54, 50, 46], Second column of AB: [3, 39, -11], First column of BA: [0, 39, -6], Third row of AA: [72, 42, 72], Third column of AA: [71, 35, 51]

a) To find the first row of AB, we must use the row method. Multiplying the first row of matrix A by matrix B, we get [3(-2) + 7(0) + 6(4) + 5(9), 3(-2) + 7(1) + 6(7) + 5(5), 3(-2) + 7(3) + 6(5) + 5(0)] = [45, 42, 39]

b) To find the third row of AB, we must use the row method. Multiplying the third row of matrix A by matrix B, we get [6(-2) + 4(0) + 6(4) + 4(9), 6(-2) + 4(1) + 6(7) + 4(5), 6(-2) + 4(3) + 6(5) + 4(0)] = [54, 50, 46]

c) To find the second column of AB, we must use the column method. Multiplying the second column of matrix A by matrix B, we get [-2(0) + 4(1) + 5(3), -2(4) + 4(7) + 5(5), -2(9) + 4(5) + 5(0)] = [3, 39, -11]

d) To find the first column of BA, we must use the column method. Multiplying the first column of matrix B by matrix A, we get [0(3) + 1(-2) + 3(6) + 9(6), 0(-2) + 1(7) + 3(5) + 9(4), 0(7) + 1(-2) + 3(4) + 9(6)] = [0, 39, -6]

e) To find the third row of AA, we must use the row method. Multiplying the third row of matrix A by matrix A, we get [6(3) + 4(-2) + 6(7) + 4(6), 6(-2) + 4(7) + 6(5) + 4(4), 6(7) + 4(-2) + 6(4) + 4(6)] = [72, 42, 72]

f) To find the third column of AA, we must use the column method. Multiplying the third column of matrix A by matrix A, we get [7(3) + 7(-2) + 5(7) + 5(6), 7(-2) + 7(7) + 5(5) + 5(4), 7(7) + 7(-2) + 5(4) + 5(6)] = [71, 35, 51]

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Answer:

-40%

Step-by-step explanation:

NV = new value

OV = old value

percent change = (NV - OV)/(OV) × 100%

percent change = (30 - 50)/(50) × 100%

percent change = -20/50 × 100%

percent change = -40%

Answer:

x=6

Step-by-step explanation:

Hypotenuse is 10 because it is the opposite of the right angle

8^2+x^2=10^2

64+x^2=100

x^2=36

x=6

Answer:

W(2) = 5

Step-by-step explanation:

Because when you look at the graph, the y value is 5 when the x value is 2.

Answer:

w(2) = 5

Step-by-step explanation:

by using rise over run to find the slope easily, you get a slope of 4 and an equation of w(x) = 4x - 3, -3 being the y-intercept

to calculate w(2):

w(2) = 4(2) - 3

w(2) = 8 - 3

w(2) = 5

or you could just look at when y is 2 and see that the corresponding x value is 5 but i wanted to provide a longer explanation in case :)

csc²(x) - 1 simplifies to sec²(x).  In conclusion, the given identity csc²(x) - 1 = sec²(x) is verified.

To verify the given identity csc²(x) - 1 = sec²(x), we can start with the definition of cosecant (csc) and secant (sec) functions.

The cosecant function is defined as the reciprocal of the sine function: csc(x) = 1/sin(x). The secant function is defined as the reciprocal of the cosine function: sec(x) = 1/cos(x).

Now, let's rewrite the left side of the equation using the definition of csc:

csc²(x) - 1 = (1/sin(x))² - 1 = 1/sin²(x) - 1.

Next, we'll use the Pythagorean identity for sine and cosine: sin²(x) + cos²(x) = 1.

We can rearrange this equation to solve for sin²(x): sin²(x) = 1 - cos²(x).

Now, substitute this expression into the previous equation:

1/sin²(x) - 1 = 1/(1 - cos²(x)) - 1.

To simplify this further, w:

e can use the concept of a common denominator. The common denominator for both terms is (1 - cos²(x)):

1/(1 - cos²(x)) - 1 = (1 - (1 - cos²(x)))/(1 - cos²(x)) = cos²(x)/(1 - cos²(x)).

Now, using the definition of sec, we can rewrite cos²(x)/(1 - cos²(x)) as sec²(x).

Therefore, csc²(x) - 1 simplifies to sec²(x).

In conclusion, the given identity csc²(x) - 1 = sec²(x) is verified.

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Answer:

The slope is 6

Step-by-step explanation:

f(x)=2(3x-7)

Distribute the 2

f(x)=2*3x-2*7

f(x) = 6x -14

This is in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is 6 and the y intercept is -14

The slope is 6

Answer:

4•(2+5)^2 -5^2 = 171

Step-by-step explanation:

Do BIDMAS
(brackets, indices, division, multipy, add, sub)

so brackets
4*7^2-5^2
then do the indices
4*49-25
then the multiply
196-25
= 171
Hope this helps

Answer: Brackets => 4 x (7)^2 - 5^2
               Indices/Orders => 4 x 49 - 25

               Multiplication => 196 - 25

               Subtraction => 171

We will have a Deficit balance of $30 at the end of the month.

"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."

Weekly net income = $380

Monthly net income = $380 * 4 weeks = $1520.

Monthly expenses = $1550

Balance = Monthly income - monthly expenses = $-30.

The negative sign shows a deficit of $30 monthly

Therefore, We will have a Deficit balance of $30 at the end of the month.

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The first and the third statements are false and second and fourth statements are true. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

Any real number can be represented using one of four basic mathematical operations, which are as follows:

1. The addition operator ('+') is used to calculate the sum of the numbers.

2. Using the "-" sign to subtract, which yields the difference between the integers.

3. When the result is the product of the numbers, multiply (×) it.

4. Division (÷), which results in the quotient of the numbers.

We are given that Jorge biked a total of 42 miles in 5 days.

The number of miles, m, Tim biked is represented by m = 8.75d for d days.

So, the number of miles, m, Tim biked in 5 days is

m = 8.75(5)

m = 43.75

Statement 1: Jorge biked more miles per day than Tim biked.

Miles per day of Jorge = 42/5 = 8.4 miles

Miles per day of Tim = 8.75 miles

The statement is false because Tim biked more miles per day than Jorge.

Statement 2: The difference between the number of miles jorge and Tim biked is 0.35 mile per day.

Difference = 8.75 - 8.4 = 0.35 miles

So, the statement is true.

Statement 3: In 5 days, the difference between the number of miles Jorge and Tim biked is 1.25 miles.

Difference = 43.75 - 42 = 1.75 miles

So, the statement is false.

Statement 4: In 7 days, the difference between the number of miles Jorge and Tim would bike would be 2.45 miles.

Miles biked in 7 days by Jorge = 8.4*7 = 58.8 miles

Miles biked in 7 days by Tim = 8.75*7 = 61.25 miles

Difference = 61.25 - 58.8 = 2.45 miles

So, the statement is true.

Hence, the first and the third statements are false and second and fourth statements are true.

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The following statements are true of valid arguments: Must have true premises; Could have true premises and a true conclusion; Cannot have true premises and a false conclusion.

Must have true premises: For an argument to be valid, the premises must be true. This means that the information or statements presented as evidence or reasons in the argument should accurately reflect reality. If any premise in the argument is false, it would affect the validity of the argument.

Could have true premises and a true conclusion: In a valid argument, it is possible for all the premises to be true and the conclusion to also be true. This means that if the premises of the argument are indeed true, then the conclusion would logically follow and be true as well. Valid arguments can have true conclusions, provided the premises are true.

Cannot have true premises and a false conclusion: A valid argument cannot have all true premises and a false conclusion. If all the premises in an argument are true, then the conclusion must also be true for the argument to be considered valid. If the conclusion is false, it indicates a logical error or flaw in the argument, making it invalid.

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In this case, the margin of safety is 4297 units

The margin of safety in units can be calculated using the formula:

Margin of Safety = (Actual Sales - Break-even Sales) / Sales per Unit

First, we need to calculate the break-even sales.

This can be done using the formula:

Break-even Sales = Fixed Costs / (Sales Price per Unit - Variable Costs per Unit)

Break-even Sales = $9,975 / ($6.99 - $2.43) = $9,975 / $4.56 ≈ 2186.40 units

Now, we can calculate the margin of safety:

Margin of Safety = (6,482 units - 2186.40 units) / 6,482 units ≈ 0.6631 or 66.31%

However, the question asks for the margin of safety in units, so we multiply the percentage by the total number of units:

Margin of Safety (in units) = 6,482 units × 0.6631 ≈ 4297 units (rounded to the nearest whole unit)

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Answer:

Step-by-step explanation:

Find the difference of corresponding coordinates

H to H'

K to K'

According to above, the rule is:

Correct choice is B

Answer:

56-5x4

Step-by-step explanation:

The reason you want to do it that way is because they will cansle eatch other out

Answer:

23

Step-by-step explanation:

3z + 2(z-1)

Let z=5

3*5 +2( 5-1)

15 +2(4)

15+8

23

Answer:

$20

Step-by-step explanation:

you would divide 60 by 12 and the times that number by 4

The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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Answer:

3 the answer is 3

Step-by-step explanation:

The vertex form of a parabola is represented by the equation y = -6 (x-0)² -36 -0.

What is a vertex form?

And this equation gives you the vertex of a parabola. h is removed from and k is inserted in the vertex form equation. We can calculate h and k from the equation. The value of h is -b/2a. It is an alternate way of writing out the vertex form. In vertex form, we use the process of completing a square. A quadratic function can also be easily solved algebraically in the vertex form (if it has a solution). Completing the square, also known as converting a quadratic function from standard form to vertex form, is the first step in solving an equation.

The given equation is y = -6x² -36

So, a= -6, b = 0, c = -36

The general formula for the vertex form is given by

y = a[x - (-b/2a))² + c - b²/4a

y = -6((x - (-0/2(-6)))² + -36 - 0²/4(-6)

y = -6 (x-0)² -36 -0

Therefore, the vertex form is y = -6 (x-0)² -36 -0.

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The correct statement is: provided that the sample size is reasonably large (for any population).

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

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The factorise form of the two expression are as follows:

b. (x - 3)(2 / 3 x - 6) = 0

Therefore, let's open the brackets

2 / 3 x² - 6x -2x + 18 = 0

2 / 3 x²  - 8x + 18 = 0

multiply through by 3

2x² - 24x + 54 = 0

Hence,

 2 (x - 3)  (x - 9)

c.

(-3x - 15)(x + 7)  = 0

Therefore,

-3x² - 21x - 15x - 105 = 0

-3x² - 36x - 105 = 0

-3(x + 5)(x + 7)

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Answer:

7d+11

Step-by-step explanation:

Pretty much just addition.

3d+4d+2+9

(3d+2)+(4d+9) = 7d+11.

A fundamental identity is an equation that relates the values of the trigonometric functions for a given angle. The equation cot θ = cos θ/sinθ is an example of a fundamental identity.

This identity states that the cotangent of an angle is equal to the cosine of the angle divided by the sine of the angle. The equation sec θ = 1/cosθ is another example of a fundamental identity. This identity states that the secant of an angle is equal to the reciprocal of the cosine of the angle. The equation sec^2 + 1 = tan^2θ is also a fundamental identity. This identity states that the square of the secant of an angle plus one is equal to the square of the tangent of the angle. The equation 1 + cot^2θ = csc^2θ is not a fundamental identity. This equation states that one plus the square of the cotangent of an angle is equal to the square of the cosecant of the angle. This equation is not a fundamental identity because it does not relate the values of the trigonometric functions for a given angle.

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Out of the given differential equations, only equation 3 is separable, and equation 4 is linear. The rest are nonlinear and neither separable nor linear.

The first-order differential equation dy/dx + exy = x2y2 is neither separable nor linear. It is a nonlinear ordinary differential equation. The presence of the term x2y2 in the equation makes it nonlinear, and the term exy makes it non-separable.

The differential equation y + ex * sin(x) = x3y' is neither separable nor linear. It is a nonlinear ordinary differential equation. The presence of the term ex * sin(x) and the term y' (derivative of y) make it nonlinear, and the term y makes it non-separable.

The differential equation ln(x) - x2y = xy' is separable but not linear. The terms ln(x) and x2y make it nonlinear, but it can be separated into two parts, one containing x and y and the other containing x and y'. Therefore, it is separable.

The differential equation dy/dx + cos(y) = tan(x) is linear but not separable. The terms cos(y) and tan(x) make it nonlinear, but it can be written in the form dy/dx + P(x)y = Q(x), where P(x) = cos(y) and Q(x) = tan(x). Therefore, it is a linear differential equation.

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The radius of convergence (r) of a power series is a value that indicates the interval within which the series converges. To find the radius of convergence for the series ∑ (-1)^n * x^n * 6^n * ln(n), we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms of a series is L, then the series converges if L is less than 1, and diverges if L is greater than 1. If L is equal to 1, the test is inconclusive.

Applying the ratio test to our series, we have:

L = lim (n→∞) |((-1)^(n+1) * x^(n+1) * 6^(n+1) * ln(n+1)) / ((-1)^n * x^n * 6^n * ln(n))|.

Simplifying, we get:

L = lim (n→∞) |(-1) * x * 6 * ln(n+1) / (x * 6 * ln(n))|.

The absolute values of -1 and 6 cancel out, and we are left with:

L = lim (n→∞) |ln(n+1) / ln(n)|.

Now, evaluating this limit, we find:

L = 1.

Since L = 1, the ratio test is inconclusive, and we need to consider the endpoint values to determine the radius of convergence. The series will converge for values of x within the interval (-1, 1) and diverge for values of x outside that interval.

Therefore, the radius of convergence (r) is 1.

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The distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the coordinates of M(6, 16) and Z(-1, 14), we get:

d = √((-1 - 6)² + (14 - 16)²) = √(49 + 4) = √53 ≈ 7.1

Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

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