Your college newspaper, The Collegiate Investigator, sels for 90t per copy. The cost of producing x copies of an edition is given by C) - 50+ 0.10+0.0012 dollars. (a) Calculate the marginal revenue A) and profit function. HINT Ser Example 2.1 RY) - PY) = 0.8 -0.002x (b) Compute the revenue and profit, and also the marginal revenue and profit, if you have produced and sold 500 copies of the latest edition revenue profit $ marginal revenue 5 per additional copy marginal profit 5 per additional copy Interpret the results The approximatelors from the sale of the 501st copy is $ (c) For which value of x is the marginal profit zero? copies X- coples Interpret your answer. The graph of the profit function is a parabola with a vertex at x = so the profit is at a maximum when you produce and sell

To apply Green's Theorem, we first need to find the curl of F.

∇ × F = (∂(x - y)/∂x - ∂(x2 + y2)/∂y)k

     = (-2y)k

Now, we apply Green's Theorem:

∮_C F · dr = ∬_R (∇ × F) · dA = ∬_R (-2y) dA

We can integrate over the region R by dividing it into two triangles, one with vertices at (0,0), (2,0), and (2,9) and the other with vertices at (0,0), (0,9), and (2,9).

For the first triangle, we have:

∫_0^2 ∫_0^(9x/2) (-2y) dy dx = -144

For the second triangle, we have:

∫_0^9 ∫_0^(2 - y/9) (-2y) dx dy = -144

Adding these two results, we get a total counterclockwise circulation of -144. Therefore, the answer is D) -144.

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Hi there!

\(\large\boxed{0, 3}\)

Find the y-intercept by substituting in 0 for x:

f(0) = 0² + 2(0) + 3

Simplify:

f(0) = 3

Answer:

0,3

hope this helped !!!

Step-by-step explanation:

The slope of the line is negative and Josh is spending money.

An algebraic description of a set of points in a coordinate system that form a line is a line equation. A line's numerous points on the coordinate axis are represented as a set of parameters x, y in order to create an algebraic equation known as a line equation. Each line's equation can be used to determine whether or not a given point is on the lines.

The equation of Line is, in fact, a one-degree linear equation.

the slope of the line is negative as he is spending money of $4 every week.

So after each week the money reduces.

Hence the slope is negative as he is spending money.

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Answer:

38°

Step-by-step explanation:

hope this helps :)

Answer:

7 . 8.9

8 . 19.5

9 . 9.9

10 .12.6

Step-by-step explanation:

7.x=11tan39

8.x=28cos46

9.x=8tan51

10.x=31sin24

side opposite of mentioned angle is opposite

longest side in triangle is hypotenuse

the side subtended by the angle is the adjacent

Answer:

the second equatin

2x+(-6)=14 that give x=10 and the other 2x=14+6 gives x= 10 so this pair is equal

£45.84

Assuming that's 7.5%

Answer: (x+5)(x+2)^2

Step-by-step explanation: Expanding (x+5)(x+4)(x+4) gives:

(x+5)(x+4)(x+4) = x(x+4)(x+4) + 5(x+4)(x+4)

= x^2(x+4) + 4x(x+4) + 5x(x+4) + 20(x+4)

= x^3 + 4x^2 + 5x^2 + 20x + 16x^2 + 80x + 20x + 80

= x^3 + 9x^2 + 45x + 80

Fully simplifying this expression gives:

x^3 + 9x^2 + 45x + 80 = (x+5)(x^2+4x+16)

= (x+5)(x+2)^2

Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

Answer:

coordinates of point g is ( -6, 14)

Step-by-step explanation:

The coordinates of the point which divides the point (x1,y1) and (x2,y2) in m:n ratio is given by (nx1+mx2)/(m+n), (ny1+my2)/(m+n).

___________________________________________

given point

F(-1, -1) to H(-8, 20)

ratio : 5:2

the coordinates of point g is

(2*-1+5*-8)/(5+2), (2*-1+5*20)/(5+2)

=> (-2 -40/7 , -2+100/7)

=> (-42/7, 98/7)

=>( -6, 14)

Thus ,  coordinates of point g is ( -6, 14)

The computed values of p(x) for each case are: a. p(x) ≈ 0.3602 , b. p(x) ≈ 0.3024 , c. p(x) = 0.008 , d. p(x) = 0.2304, e. p(x) = 0.1764 , f. p(x) = 0.027

To compute the probability mass function (PMF) for a binomial random variable, we use the formula:

p(x) = C(n, x) * p^x * (1 - p)^(n - x)

where:

- C(n, x) represents the binomial coefficient, which is the number of ways to choose x successes out of n trials, and can be calculated as C(n, x) = n! / (x! * (n - x)!)

- p is the probability of success on a single trial

- x is the number of successes we're interested in

- n is the total number of trials

Now let's calculate the values of p(x) for each case:

a. n = 5, x = 1, p = 0.3

p(x) = C(5, 1) * 0.3^1 * (1 - 0.3)^(5 - 1)

    = 5 * 0.3 * 0.7^4

    ≈ 0.3602 (rounded to four decimal places)

b. n = 4, x = 2, q = 0.7 (note: q = 1 - p)

p(x) = C(4, 2) * (1 - 0.7)^2 * 0.7^(4 - 2)

    = 6 * 0.3^2 * 0.7^2

    ≈ 0.3024 (rounded to four decimal places)

c. n = 3, x = 0, p = 0.8

p(x) = C(3, 0) * 0.8^0 * (1 - 0.8)^(3 - 0)

    = 1 * 1 * 0.2^3

    = 0.008

d. n = 5, x = 3, p = 0.4

p(x) = C(5, 3) * 0.4^3 * (1 - 0.4)^(5 - 3)

    = 10 * 0.4^3 * 0.6^2

    = 0.2304

e. n = 4, x = 2, q = 0.3 (note: q = 1 - p)

p(x) = C(4, 2) * (1 - 0.3)^2 * 0.3^(4 - 2)

    = 6 * 0.7^2 * 0.3^2

    = 0.1764

f. n = 3, x = 1, p = 0.9

p(x) = C(3, 1) * 0.9^1 * (1 - 0.9)^(3 - 1)

    = 3 * 0.9 * 0.1^2

    = 0.027

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Answer:

3b^4−2b^2+8b+6

Answer:

The answer is 2.5

o.o5 divided by o.o2 is 2.5

Answer:

10 Candies.

Step-by-step explanation:

1/3 + 1/3 + 1/3 = 15 candles.

15 Candies Divided By 1/3 is 5.

So, she lost 5 candies out of 15. Making her have 10 candies.

The number of questions on the CUNY Math Assessment Test can vary depending on the specific version of the test administered. However, typically, the CUNY Math Assessment Test consists of multiple-choice questions covering a range of math topics such as algebra, geometry, and trigonometry.

While the exact number of questions can vary, it is common for the CUNY Math Assessment Test to have around 40 to 50 questions. These questions are designed to assess your mathematical knowledge and skills in order to determine your readiness for college-level math courses.

The test is typically timed, and you will have a set amount of time to complete all the questions. It is important to manage your time effectively and pace yourself throughout the test to ensure you have enough time to answer each question.

In order to prepare for the CUNY Math Assessment Test, it is recommended to review and practice a variety of math topics, including algebraic equations, functions, graphs, geometry, and basic trigonometry concepts. Familiarizing yourself with these topics and practicing similar questions can help you become more comfortable with the content and format of the test.

Remember, it's always a good idea to consult official CUNY resources or speak with an academic advisor to get the most up-to-date and accurate information regarding the specific version of the CUNY Math Assessment Test you will be taking.

Overall, the number of questions on the CUNY Math Assessment Test can vary, but typically it consists of around 40 to 50 multiple-choice questions covering various math topics.

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Answer:

78,718.5

Step-by-step explanation:

2.1*102=214.2

3.5*105=367.5

214.2*367.5=78,718.5

Answer:

Step-by-step explanation:

percentage: 1%

decimal:0.01

fraction :1/100

When it comes to the range covered by the decision given that `x<7  Range covered: x<21`, it means that `x` is a non-negative integer, and its range covered is `x<21`.The decision given can be expressed as:x < 7 To indicate the range covered by this decision, it's important to find the largest possible value of x.

Since x is a non-negative integer, the largest possible value would be 6.When x = 6, the inequality becomes:6 < 7, which is true.This means that any value of x that is less than 6 would also make the inequality true.Therefore, the range covered by `x < 7` is:`0 ≤ x < 7`Now, let's consider the second part of the statement: Range covered: x<21`.This means that the range covered by the inequality `x < 7` is also contained within the larger inequality `x < 21`.Since the range of `x<7` is `0 ≤ x < 7`, which is less than 21, then it's true to say that the range covered by `x < 7

Range covered: x<21` is:`0 ≤ x < 21 Therefore, the range covered by the decision `x < 7 // Range covered: x<21` is `0 ≤ x < 21`.

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Answer:

the awnser is 45

Step-by-step explanation:

i just took this test on masery connect

Let x = Number of tickets

So, the equation is

Solve for x:

Answer: x = 8.33

The financing company is charging a nominal interest rate of approximately 1.359% compounded monthly on the ₱750,000 automobile loan.

The loan repayment formula is given by:

P = (R * \((1 - (1 + r)^-^n))\) / r

Where:

P = loan amount (₱750,000)

R = monthly installment payment (₱20,290)

r = nominal interest rate per period (to be determined)

n = number of periods (60 monthly installments)

Plugging in the given values, we have:

₱750,000 = (₱20,290 * (1 - \((1 + r)^-^6^0\))) / r

To solve for the nominal interest rate (r), we need to find the value that satisfies this equation.

This equation involves a non-linear relationship, making it difficult to solve algebraically. Therefore, we need to use numerical methods to approximate the value of r.

Using numerical methods, the nominal interest rate compounded monthly is determined to be approximately 1.359%.

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The expression as a single real number is \(\frac{1-\sqrt{3} }{2}\) .

What is trignomentry ?

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. It is used to study the properties of triangles and to solve problems involving angles and distances in two-dimensional space.

sin(π/6)cos(π/2) - cos(π/60)sin(π/2)

The first term in the expression, sin(π/6)cos(π/2), can be simplified as follows ,

sin(π/6) = √(3)/2, cos(π/2) = 0

so sin(π/6)cos(π/2) = (√(3)/2) * 0 = 0

The second term in the expression, -cos(π/60)sin(π/2) , can be simplified as follows ,

sin(π/2) = 1, cos(π/60) = sqrt(3)/2 - 1/2

so -cos(π/60)sin(π/2) = -(sqrt(3)/2 - 1/2) * 1 = -sqrt(3)/2 + 1/2

Now we can substitute the simplified values back into the original expression ,

0 - (-sqrt(3)/2 + 1/2)

and combining like terms, \(\frac{1-\sqrt{3} }{2}\),

Hence ,  The expression as a single real number is \(\frac{1-\sqrt{3} }{2}\) .

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The systems of inequalities are;

7G + 4H ≤ 168

14G + 2H ≤ 210

14G + 5H ≤ 252

x ≥ 0

y ≥ 0

The objective function for profit can be expressed as:

P = 28G + 8H

At least two linear inequalities in the same variables make up a system of a linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

Given:

For the information, the image is given below.

Type of Plant Square   Footage   Gallons of Soil   Cost

Giant Potted                    7                      14              $14

Hanging Basket               4                      2              $5

The objective function for profit can be expressed as:

P = 28G + 8H

where P is the total profit, G is the number of giant potted plants, and H is the number of hanging plants sold.

The systems of inequalities are;

7G + 4H ≤ 168

14G + 2H ≤ 210

14G + 5H ≤ 252

x ≥ 0

y ≥ 0

Note that the profit is the difference between the revenue earned from selling the plants and the cost of purchasing the soil. Since we are not given the cost of purchasing the plants, we cannot include it in the objective function.

Therefore, P = 28G + 8H is the required function.

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The length of arc AB in terms of pi is 16pi.

We have,

To find the length of the arc AB in terms of pi, we can use the formula:

Length of arc = (angle intercepted by arc / 360 degrees) * (circumference of the circle)

Given:

Diameter = 32 (which means the radius is half of the diameter, so the radius is 32/2 = 16)

Angle intercepted by arc AB = 180 degrees

First, we need to find the circumference of the circle using the formula:

Circumference = 2 x pi x radius

Circumference = 2 x pi x 16 = 32 x pi

Now, we can calculate the length of arc AB:

Length of arc AB = (180 / 360) x (32 x pi)

Simplifying:

Length of arc AB = (1/2) x (32 x pi)

Length of arc AB = 16 x pi

Therefore,

The length of arc AB in terms of pi is 16pi.

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The constraint that is NOT valid is " \(y > = 5x + 30\) "

To determine the constraints, we analyze the given information. The farmer has a 500-acre farm, and she wants to optimize her planting strategy for wheat and corn. Each acre of wheat requires 1 person-day of labor and $20 in expenses, while each acre of corn requires 5 person-days of labor and $30 in expenses. The farmer has a budget of $11,400 and 1480 person-days of labor available.

To maximize profit, we consider the profit per acre for each crop, which is $90 for wheat and $120 for corn. Let x represent the acres of wheat and y represent the acres of corn.

The constraints are as follows:

By considering these constraints, the farmer can determine the optimal combination of wheat and corn planting to maximize profit while adhering to resource limitations.

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Answer:

8

Step-by-step explanation:

The structure of the error term in the given model is an example of first-order autocorrelation or serial correlation. The correct answer is A.

This is because the current error term (εt) is linearly related to the past two error terms (εt-1 and εt-2) through the autoregressive coefficients (rho1 and rho2). This implies that the errors are not independently and identically distributed (i.i.d), violating one of the assumptions of the classical linear regression model.

Option A is therefore the correct answer.

Option B is incorrect because the Durbin-Watson test is used to detect the presence of autocorrelation, not any other type of error structure.

Option C is incorrect because perfect multicollinearity refers to a situation where two or more predictor variables are perfectly correlated with each other, leading to numerical problems in estimation.

Option D is incorrect because heteroskedasticity refers to a situation where the variance of the error term is not constant across observations, leading to biased and inefficient estimates of the regression coefficients. The correct answer is A.

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The mean for this binomial distribution is 12.

In probability theory, the mean of a binomial distribution is the product of the number of trials (n) and the probability of success in each trial (p).

Therefore, to find the mean of a binomial distribution with n = 20 and p = 3/5, we can simply multiply these two values together:

mean = n * p

= 20 * 3/5

= 12

So, the mean for this binomial distribution is 12. This means that on average, we can expect to see 12 successes in 20 independent trials with a probability of success of 3/5 in each trial

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