A store purchases food processors
from the manufacturer for $18 each.
Calculate the sticker price for the
food processors in order to achieve a
60% gross margin.
A. $21.33
C. $45.00
B. $72.00
D. $30.00

The value of C in the area of the region enclosed by the parabolas is 6.206.

We have,

The two parabolas intersect at points (c,0) and (-c,0).

We can find the area enclosed by them by integrating the difference of their equations with respect to x from -c to c:

A = ∫[-c,c] (x² - c² - c² + x²) dx

= 2 ∫[0,c] (2x² - 2c²) dx

= 4 ∫[0,c] (x² - c²) dx

= 4 [x³/3 - c² x] [0,c]

= 4 (c³/3 - c³)

= 4c³/3

We want this area to be 400, so we have:

4c³/3 = 400

Solving for c, we get:

c³ = 300

c = (300)^(1/3)

Therefore,

C ≈ 6.206.

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The discount amount was $232.80, and the new selling price of the computer system after the discount was applied was $543.20.

First, we need to calculate the amount of the discount. We can do this by multiplying the original price of the computer system by the percentage discount:

Discount = 30% x $776

Discount = 0.30 x $776

Discount = $232.80

So, the discount offered by the store is $232.80.

Next, we need to calculate the new selling price of the computer system after the discount has been applied. To do this, we need to subtract the discount amount from the original price:

New Selling Price = Original Price - Discount

New Selling Price = $776 - $232.80

New Selling Price = $543.20

Therefore, the new selling price of the computer system after the discount is $543.20.

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Complete Question:

A computer store buys a computer system at a cost of $465.60. The selling price was first at $776, but then the store advertised a 30% markdown on the system.

A) Find the new selling price. Round to the nearest cent if necessary.

The magnitude of the resultant vector is 96.77 and its direction is -78.95°.

To find the magnitude and direction of the resultant vector, we can use vector addition. We can break down each vector into its horizontal and vertical components using trigonometry:

For the first vector with magnitude 35 and direction 55°:

Horizontal component = 35 cos(55°) = 19.77

Vertical component = 35 sin(55°) = 28.25

For the second vector with magnitude 80 and direction 130°:

Horizontal component = 80 cos(130°) = -39.06

Vertical component = 80 sin(130°) = 66.68

To find the horizontal and vertical components of the resultant vector, we can add the corresponding components of the two vectors:

Horizontal component of the resultant vector = 19.77 - 39.06 = -19.29

Vertical component of the resultant vector = 28.25 + 66.68 = 94.93

The magnitude of the resultant vector is the square root of the sum of the squares of its horizontal and vertical components:

Magnitude of the resultant vector = sqrt((-19.29)^2 + (94.93)^2) = 96.77

The direction of the resultant vector can be found using trigonometry:

Direction of the resultant vector = arctan(94.93/-19.29) = -78.95° (measured counterclockwise from the positive x-axis)

Therefore, the magnitude of the resultant vector is 96.77 and its direction is -78.95°.

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So the correct answer is: A. fog(x) = 4x and go f(x) = 2x² + 2 for the given function.

In mathematics, a function is a rule that assigns a unique output value to each input value in a specified set. The input values are often called the domain of the function, while the output values are called the range. Functions are often represented using function notation, such as f(x), where f is the name of the function and x is the input value. The value of f(x) is the output value that corresponds to the input value x. Functions can be defined using a variety of methods, including algebraic equations, tables of values, graphs, and verbal descriptions. Some common types of functions include linear functions, quadratic functions, exponential functions, trigonometric functions, and logarithmic functions. Functions are an important concept in mathematics and have many practical applications in fields such as physics, engineering, economics, and computer science. They are used to model and analyze real-world phenomena, to make predictions, and to solve problems.

Here,

We have:

f(x) = x² - 1

g(x) = -2x

To find fog(x), we first substitute g(x) into f(x) wherever we see an "x":

fog(x) = f(g(x))

= f(-2x)

= (-2x)² - 1

= 4x² - 1

To find go f(x), we first substitute f(x) into g(x) wherever we see an "x":

go f(x) = g(f(x))

= g(x² - 1)

= -2(x² - 1)

= 2x² + 2

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The two ways of expressing the null hypothesis for a hypothesis test of the difference of means for two independent populations are: H0: μ1 - μ2 = 0, assuming no significant difference between the means.

H0: μ1 - μ2 = d, assuming a specific difference between the means equal to a constant value d.

Null Hypothesis H0: μ1 - μ2 = 0: This form of the null hypothesis assumes that there is no significant difference between the means of the two populations x1 and x2. In other words, the null hypothesis states that the difference between the means is exactly zero, indicating that the two populations have identical means.

Null Hypothesis H0: μ1 - μ2 = d: This form of the null hypothesis assumes that the difference between the means of the two populations x1 and x2 is equal to a specified value d. This specified value could be based on prior knowledge, theoretical expectations, or practical considerations. For example, if you are comparing the effectiveness of two different medications, you might specify d to be the minimum clinically important difference, which represents the smallest difference between the means that would be considered clinically meaningful.

Therefore, the two ways of expressing the null hypothesis for a hypothesis test of the difference of means for two independent populations are:

H0: μ1 - μ2 = 0, assuming no significant difference between the means.

H0: μ1 - μ2 = d, assuming a specific difference between the means equal to a constant value d.

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The equation of the tangent to the circle at the point where x=4 and y is negative is y = (4/3)x - 16/3, where m = 4/3 and c = -16/3.

The equation of a circle with center (a,b) and radius r is (x-a)² + (y-b)² = r². In our problem, the equation of the circle is x² + y² = 65. This means that the center of the circle is at the origin (0,0) and the radius is √65.

We can find the derivative of x² + y² = 65 using implicit differentiation. Taking the derivative with respect to x, we get:

2x + 2y(dy/dx) = 0

Simplifying this equation, we get:

dy/dx = -x/y

At the point where x=4 and y is negative, we have x=4 and y=-3. Plugging these values into the equation above, we get:

dy/dx = -4/(-3) = 4/3

This means that the slope of the tangent to the circle at the point (4,-3) is 4/3.

To find the equation of the tangent, we can use the point-slope form of a line, which is y - y₁ = m(x - x₁), where (x₁,y₁) is a point on the line and m is the slope. Plugging in the values we found, we get:

y - (-3) = (4/3)(x - 4)

Simplifying this equation, we get:

y = (4/3)x - 16/3

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The total number of eggs Dale collected is 187 eggs.

To find the total number of eggs, you would use operations, specifically, multiplication and addition. First, multiply the number of cartons (15) by the number of eggs per carton (12). This gives you a total of 180 eggs (15 x 12) in the cartons.

In addition to the eggs in the cartons, Dale also has 7 eggs left over. To find the total number of eggs Dale collected, you simply add the number of leftover eggs (7) to the total number of eggs in the cartons (180). This results in a grand total of 187 eggs (180 + 7) that Dale collected from his chickens.

In summary, Dale collected 187 eggs in total: 180 eggs from filling 15 cartons with 12 eggs each and 7 additional leftover eggs.

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(a)  The formula for the squirrel population is:

P(t) = 1500 / (1 + 1125 e^(-0.7t))

(b) It will take about 2.5 years for the squirrel population to double.

(a) Using separation of variables, we have:

dP/P(1500-P) = 0.7 dt

Integrating both sides, we get:

ln|P| - ln|1500 - P| = 0.7t + C

where C is the constant of integration.

Applying the initial condition P(0) = 375, we get:

ln|375| - ln|1125| = C

C = ln(3)

Therefore, the formula for the squirrel population is:

P(t) = 1500 / (1 + 1125 e^(-0.7t))

(b) To find the doubling time, we need to solve the equation:

2P(0) = P(d)

where P(0) = 375 and P(d) is the population after time d. Substituting the formula for P(t) from part (a), we get:

2(375) = 1500 / (1 + 1125 e^(-0.7d))

Simplifying and solving for d, we get:

d = ln(3) / 0.7

d ≈ 2.5 years

Therefore, it will take about 2.5 years for the squirrel population to double.

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The answer to the student's question falls under the criteria of a result being undefined, because division of any number by 0 proceeds to the number being labelled indeterminate. Then the required answer to the question is Option D.

Let us take this into consideration that whenever we associate with a number being divided by 0 it automatically gets into a phase where it is no longer able to project its value like before, this phase of being unnoticed is refered to as being indeterminate.

Since, in this case we are given to perform division of  0 ÷ 0 and derive result, it is not possible to do so because of the above reason.

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The amount that must be paid back at the end of the [tex]10[/tex]-year period is approximately $[tex]42,748.37[/tex].

To calculate the amount that must be paid back for a loan of $[tex]19,000[/tex] borrowed for [tex]10[/tex] years at [tex]7.5[/tex]% interest, compounded annually, we can use the formula for compound interest:

[tex]A = P(1+\frac{r}{n} )^{nt}[/tex]

Where:

A = the amount to be paid back

P = the principal amount (initial loan amount) = $[tex]19,000[/tex]

r = annual interest rate (as a decimal) = [tex]7.5[/tex]% or [tex]0.075[/tex]

n = number of times interest is compounded per year = [tex]1[/tex] (compounded annually)

t = time period in years = [tex]10[/tex]

According to the problem,

A = [tex]19000(\frac{1+0.075}{1} )^{1*10}[/tex]

A =[tex]= 19000(1.075)^{10}[/tex]

A ≈ $[tex]42,748.37[/tex]

Therefore, the amount that must be paid back at the end of the [tex]10[/tex]-year period is approximately $[tex]42,748.37[/tex].

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To find out after how many weeks the siblings will have the same amount of money in their savings accounts, we need to solve the system of linear equations. We can do this by setting the two equations equal to each other and solving for x:

7x + 40 = 5x + 60 7x - 5x = 60 - 40 2x = 20 x = 10

So, after 10 weeks, the siblings will have the same amount of money in their savings accounts. The correct answer is 10 weeks

After 10 weeks, their savings accounts will have the same amount of money. The correct answer is option (C).

A linear equation is defined as an equation in which the highest power of the variable is always one.

To find when their savings accounts will have the same amount of money, we need to solve for x in the equation:

7x + 40 = 5x + 60

Subtracting 5x from both sides, we get:

2x + 40 = 60

Subtracting 40 from both sides, we get:

2x = 20

Dividing both sides by 2, we get:

x = 10

Therefore, after 10 weeks, their savings accounts will have the same amount of money.

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To minimize the total cost, about 4,286 units should be produced on machine A and 18,364 units on machine B.

To minimize the total cost of producing x+y=22,650 units on two machines, A and B, we need to find the optimal distribution of units produced on each machine. Let's start by setting up the equations:

Machine A: C(x) = 20x^2
Machine B: C(y) = 240y^3 + 79y

Total cost: C(x, y) = C(x) + C(y)

Since x + y = 22,650, we can express y in terms of x: y = 22,650 - x.

Now, let's substitute this expression for y into the total cost equation:

C(x, y) = 20x^2 + 240(22,650 - x)^3 + 79(22,650 - x)

Now, to find the minimum total cost, we need to find the critical points by taking the derivative of C(x, y) with respect to x and set it to zero:

dC(x)/dx = 40x - 240(3)(22,650 - x)^2 + 79 = 0

Solve for x to get the optimal number of units to be produced on machine A:

x ≈ 4,286

Now, find the corresponding number of units to be produced on machine B using the relationship y = 22,650 - x:

y ≈ 22,650 - 4,286 = 18,364

Thus, to minimize the total cost, about 4,286 units should be produced on machine A and 18,364 units on machine B.

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g(x) = -4cosx + (1/3)x⁶ - [tex]2x^(3/2)[/tex] + C, where C is any constant, satisfies g'(x) = 4sinx + (2x⁵-√x/x).

To find all capabilities function g that fulfill g'(x) = 4sinx + (2x⁵-√x/x), we really want to coordinate the two sides of the situation concerning x. In the first place, we can coordinate the right-hand side by separating it into two sections:

∫[4sinx + (2x⁵-√x/x)]dx = ∫4sinxdx + ∫(2x⁵-√x/x)dx

We can incorporate the initial segment involving the reconciliation recipe for sine:

∫4sinxdx = -4cosx + C₁,

where C₁ is a consistent of coordination.

For the subsequent part, we can utilize the power rule and the chain rule to incorporate the articulation:

∫(2x⁵-√x/x)dx = (2/6)x⁶ - [tex]2x^(3/2)[/tex]+ C₂,

where C₂ is one more steady of incorporation.

Assembling the two sections, we get:

g(x) = - 4cosx + (1/3)x⁶ - [tex]2x^(3/2)[/tex]+ C,

Where C = C₁ + C₂ is the steady of joining.

Hence, the arrangement of all capabilities g that fulfill g'(x) = 4sinx + (2x⁵-√x/x) is given by g(x) = - 4cosx + (1/3)x⁶ - [tex]2x^(3/2)[/tex] + C, where C is any steady.

As such, there are limitlessly many capabilities g that fulfill g'(x) = 4sinx + (2x⁵-√x/x), and they contrast exclusively by a consistent. This is on the grounds that the reconciliation of a capability generally presents a consistent of coordination, and any two capabilities that vary by a steady have a similar subordinate.

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Answer:

------------------------------------

a) Use the following formula:

The total cost is the cost of the copier plus the cost of the materials for each order. So, we have:

We can simplify this equation to:

Hence the average cost per order is $40.

b) As more orders are printed, the average cost per order will decrease because the fixed cost of the copier is spread over a larger number of orders. In other words, the more orders that are printed, the lower the average cost per order will be.

The company accrues a profit of $908,404 each month, assuming 1 month is 4 weeks.

To calculate the profit accrued each month, we need to first calculate the total cost of producing 55728 shirts. The supplies cost $13.5 per shirt, so the total cost of supplies is 55728 x $13.5 = $752,736.

The fixed monthly costs are $700. We also need to factor in employee wages and other monthly supply costs, but we don't have enough information to calculate those. So, we'll assume they amount to $10,000 per month.

The total cost of production each month is $752,736 + $700 + $10,000 = $763,436.

Now, to calculate the profit, we need to subtract the total cost of production from the revenue generated from selling the shirts. The revenue generated from selling 55728 shirts at $30 per shirt is 55728 x $30 = $1,671,840.

So, the profit accrued each month is $1,671,840 - $763,436 = $908,404.

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The term that is used to describe a situation where two variables are correlated but there is no apparent connection between them is "spurious correlation."

Spurious correlation refers to a situation where two variables appear to be correlated or associated, but in reality, there is no actual causal relationship or meaningful connection between them. This can happen due to various reasons, such as coincidence, sampling errors, or confounding variables that are not accounted for in the analysis.

In other words, the observed correlation between the variables is merely coincidental or occurs by chance, and there is no true underlying relationship between them. It is important to be cautious when interpreting correlations, as spurious correlations can lead to incorrect or misleading conclusions.

Therefore, the correct term used for this phenomenon is "spurious correlation."

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The mean is 13 and the mean absolute deviation (MAD) is 3.9

From the box plot, we have the following readings that can be used in our computation:

4  8  10  10  10  10  12  14  14  16  16  18  20  20

The mean is calculated as

Mean = Sum/Count

So, we have

Mean = (4 + 8 + 10 + 10 + 10 + 10 + 12 + 14 + 14 + 16 + 16 + 18 + 20 + 20)/14

Evaluate

Mean = 13

The mean absolute deviation is calculated as

MAD = 1/n * ∑|xi - mean|

So, we have

MAD = 1/14 * (|4 - 13| + |8 - 13| + |10 - 13| + |10 - 13| + |10 - 13| + |10 - 13| + |12 - 13| + |14 - 13| + |14 - 13| + |16 - 13| + |16 - 13| + |18 - 13| + |20 - 13| + |20  - 13|)

Evaluate

MAD = 3.9

Hence, the mean is 13

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