negative five divided by five sevenths

​

The point where marginal cost equals $15 is at the production of the 7th pizza. Therefore, the firm should produce 7 pizzas.

The firm's shut-down price is the price at which the firm is indifferent between producing and shutting down.

Using the table provided, we can calculate the missing values:

Variable Cost:

For 0 pizzas, the variable cost is $0.

For 1 pizza, the variable cost is $10.

For 2 pizzas, the variable cost is $12.

For 3 pizzas, the variable cost is $2.

For 4 pizzas, the variable cost is $1.

For 5 pizzas, the variable cost is $2.

For 6 pizzas, the variable cost is $3.

For 7 pizzas, the variable cost is $13.

For 8 pizzas, the variable cost is $16.

For 9 pizzas, the variable cost is $3.

For 10 pizzas, the variable cost is $6.

For 11 pizzas, the variable cost is $4.

Total Cost: To calculate the total cost, we simply add the variable cost and the fixed cost for each level of output. The fixed cost is not given in the table, so we cannot calculate the total cost.

Average Variable Cost:

To calculate the average variable cost, we divide the variable cost by the level of output. For example, the average variable cost for 1 pizza is $10/1 = $10.

Average Fixed Cost:To calculate the average fixed cost, we divide the fixed cost by the level of output.

Average Total Cost: To calculate the average total cost, we add the average variable cost and the average fixed cost. The firm should produce pizzas up to the point where marginal cost equals marginal revenue.

This is the point where the firm maximizes its profit. From the table, we can see that the marginal cost is increasing as output increases, while the marginal revenue remains constant at $15.

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$1.25 per pound, your welcome

Answer:

$1.25 per pound

Step-by-step explanation:

Lets put $3.75 for 3 pounds in a ratio

3.75 : 3

and turn that into

3.75÷3=1.25

Now the ratio is

1.25 : 1

$1.25 for 1 pound of granola

Final answer $1.25

The given statement "The median of a quantitative data set is always one of the individual data values" is false.

When a given data set is arranged in ascending order the observation which at the between of the data is the median of that data set. It is a value in the set whose left and right both have the same number of observations.

The given statement is not true, this is because the median is the mid-value of any data set.

Hence, the given statement "The median of a quantitative data set is always one of the individual data values" is false.

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(a) Example question: "How often do you look at social media while doing schoolwork?

(b) Sofie can select a simple random sample of students by using a random number generator to assign a unique identification number to each student in the online high school.

(c) The sample for Sofie's research is the 32 completed surveys she received. These surveys represent the responses of a subset of the population. The population, in this case, refers to all the students at the online high school.

(d) If Sofie uses only the completed surveys, she can conclude that approximately 50% (16 out of 32) of the students who completed the survey reported using social media while doing schoolwork.

(a) Please select one of the following options: never, rarely, occasionally, frequently, or always."

(b) She can then use the random number generator again to select a specific number of students from the entire population of students, ensuring that each student has an equal chance of being selected. For example, if there are 500 students in total and Sofie wants a sample size of 50, she can generate 50 random numbers and select the corresponding students based on their identification numbers.

(d) However, it is important to note that this conclusion is specific to the sample of completed surveys and cannot be generalized to the entire population of high school students.

To make an inference about the percent of all high school students who use social media while doing schoolwork, Sofie would need a larger and more representative sample that covers a wider range of students in the online high school.

Additionally, she should consider potential biases in the sample, such as non-response bias if the students who chose not to complete the survey have different social media usage patterns compared to those who did respond.

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Answer:

Larger number = 34

Smaller number = 17

Step-by-step explanation:

Given that:

Sum of numbers = 51

Let,

x be the larger number

y be the smaller number

According to given statement;

x+y=51       Eqn 1

x = 2y        Eqn 2

Putting x=2y in Eqn 1

2y+y=51

3y=51

Dividing both sides by 3

\(\frac{3y}{3}=\frac{51}{3}\\y=17\)

Putting y=17 in Eqn 2

x=2(17)

x=34

Hence,

Larger number = 34

Smaller number = 17

The general solution of the system of differential equations is given by:

[x1(t); x2(t)] = c1 [2t; t] e^(5t) + c2 [t; t] e^(9t)

where c1 and c2 are constants.

Let's first find the eigenvalues of the coefficient matrix. The characteristic polynomial is given as:

λ^2 - 14λ + 65 = 0

We can factor this as:

(λ - 5)(λ - 9) = 0

So, the eigenvalues are λ = 5 and λ = 9.

Now, let's find the eigenvectors corresponding to each eigenvalue:

For λ = 5:

(A - 5I)x = 0

where A is the coefficient matrix and I is the identity matrix.

Substituting the values, we get:

[3-5 1; 1 -5] [x1; x2] = [0; 0]

Simplifying, we get:

-2x1 + x2 = 0

x1 - 4x2 = 0

Taking x2 = t, we get:

x1 = 2t

So, the eigenvector corresponding to λ = 5 is:

[2t; t]

For λ = 9:

(A - 9I)x = 0

Substituting the values, we get:

[-1 1; 1 -3] [x1; x2] = [0; 0]

Simplifying, we get:

-x1 + x2 = 0

x1 - 3x2 = 0

Taking x2 = t, we get:

x1 = t

So, the eigenvector corresponding to λ = 9 is:

[t; t]

Therefore, the general solution of the system of differential equations is given by:

[x1(t); x2(t)] = c1 [2t; t] e^(5t) + c2 [t; t] e^(9t)

where c1 and c2 are constants.

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Answer:$2800

Step-by-step explanation: Lets first figure out how much money a box of candy bars is worth. We know that each candy bar is worth $5 and that there are 7 candy bars per box. We can multiply 7*5 to figure out that each box is worth $35.

Now lets figure out how many boxes can be sold each day. Each student can sell two boxes a day. 5 students selling 2 boxes each is 5*2= 10 boxes total sold a day.

Now finally we use what we found to figure out the amount of money made per day. We know that there are 10 boxes being sold and that each box makes them $35. We just multiply 10 boxes by $35 to get $350 dollars each day.

Since they sell for 8 days we just multiply 8*$350 to get $2800.

The probability P(|X - Y| ≤ 1/2) is equal to 1 or 100%.

To find the probability P(|X - Y| ≤ 1/2), we need to determine the area of the region where the absolute difference between X and Y is less than or equal to 1/2.

Consider the unit square [0, 2] × [0, 2]. We can divide it into two triangles and two rectangles:

Triangle A: The points (x, y) where x ≥ y.

Triangle B: The points (x, y) where x < y.

Rectangle C: The points (x, y) where x ≥ y + 1/2.

Rectangle D: The points (x, y) where x < y - 1/2.

Let's calculate the areas of these regions:

Area(A) = (base × height)/2 = (2 × 2)/2 = 2

Area(B) = (base × height)/2 = (2 × 2)/2 = 2

Area(C) = 2 × (2 - 1/2) = 3

Area(D) = 2 × (2 - 1/2) = 3

Now, let's calculate the area of the region where |X - Y| ≤ 1/2. It consists of Triangle A and Triangle B, as both triangles satisfy the condition.

Area(|X - Y| ≤ 1/2) = Area(A) + Area(B) = 2 + 2 = 4

Since the total area of the unit square is 2 × 2 = 4, the probability P(|X - Y| ≤ 1/2) is the ratio of the area of the region to the total area:

P(|X - Y| ≤ 1/2) = Area(|X - Y| ≤ 1/2) / Area([0, 2]2) = 4 / 4 = 1

Therefore, the probability P(|X - Y| ≤ 1/2) is equal to 1 or 100%

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Answer:

(Answer D)

Step-by-step explanation:

Please use " ^ " to indicate exponentiation:  y = -8x^2 - 2, y = -8x^2

The graph of y = -8x^2 is an inverted parabola with vertex at (0, 0).

That of y = -8x^2 - 2 is the same as above, except that the whole graph has been shifted 2 units down (Answer D).

The problem involves finding the absolute value of the determinant of the Jacobian for a given change of coordinates.

The change of coordinates is defined as

x = e^(-2u)cos(6v) and y = e^(-2u)sin(6v),

mapping points from the uv-plane to the xy-plane.

To calculate the determinant of the Jacobian matrix, we need to find the partial derivatives of x and y with respect to u and v. Then, we form the Jacobian matrix by arranging these partial derivatives, and finally, calculate the determinant.

Taking the partial derivatives,

we find ∂x/∂u = -2e^(-2u)cos(6v), ∂x/∂v = -6e^(-2u)sin(6v), ∂y/∂u = -2e^(-2u)sin(6v), and ∂y/∂v = 6e^(-2u)cos(6v).

Constructing the Jacobian matrix with these partial derivatives, we have:

J = [∂x/∂u ∂x/∂v]

[∂y/∂u ∂y/∂v]

The determinant of the Jacobian matrix is

det(J) = (∂x/∂u)(∂y/∂v) - (∂x/∂v)(∂y/∂u).

Calculating the determinant and taking the absolute value, we get the result: ∣det[J]∣.

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The absolute value of the determinant of the Jacobian for the given change of coordinates is needed to determine the scaling factor between the uv-plane and the xy-plane.

In this case, the Jacobian matrix J is defined as follows:

J = ∂(u,v)/∂(x,y) = | ∂u/∂x ∂u/∂y |

| ∂v/∂x ∂v/∂y |

To find the absolute value of the determinant of J, we calculate:

|det[J]| = | ∂u/∂x ∂v/∂y - ∂u/∂y ∂v/∂x |

Now, let's compute the partial derivatives ∂u/∂x, ∂u/∂y, ∂v/∂x, and ∂v/∂y using the given expressions for x and y.

∂u/∂x = ∂/∂x (e^(-2u) cos(6v)) = -2e^(-2u) cos(6v)

∂u/∂y = ∂/∂y (e^(-2u) cos(6v)) = 0

∂v/∂x = ∂/∂x (e^(-2u) sin(6v)) = 0

∂v/∂y = ∂/∂y (e^(-2u) sin(6v)) = -2e^(-2u) sin(6v)

Substituting these values into the determinant expression, we have:

|det[J]| = |-2e^(-2u) cos(6v) -2e^(-2u) sin(6v)| = 2e^(-2u) |cos(6v) sin(6v)| = 2e^(-2u)

Thus, the absolute value of the determinant of the Jacobian is 2e^(-2u).

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x = 3 and y = 7 are the answers to the simultaneous equations 8x + 3y = 45 and 2x + 3y = 27.

A linear equation is an equation that describes a straight line on a coordinate plane. It is an equation of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis).

To solve the simultaneous equations:

8x + 3y = 45 ...(1)

2x + 3y = 27 ...(2)

By adding or removing equations, we can utilise the procedure of elimination to get rid of one of the variables. In this situation, y can be removed by deducting equation (2) from equation (1) as shown below:

(8x + 3y) - (2x + 3y) = 45 - 27

6x = 18

x = 3

In order to obtain the value of y, we can now change the value of x in either equation (1) or (2). Consider using equation (1):

8x + 3y = 45

8(3) + 3y = 45

24 + 3y = 45

3y = 45 - 24

3y = 21

y = 7

Therefore, the solution to the simultaneous equations 8x + 3y = 45 and 2x + 3y = 27 is x = 3 and y = 7.

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Answer:

C) 180 degree rotation

Step-by-step explanation:

I hope this helps you :)

To determine whether the series is absolutely convergent, conditionally convergent, or divergent, we can use the Ratio Test. Answer : the series is divergent.

Let's analyze the given series:

4, 7, 4 · 10, 7 · 9, 4 · 10 · 16, 7 · 9 · 11, 4 · 10 · 16 · 22, 7 · 9 · 11 · 13, ...

We will calculate the ratio of consecutive terms:

(7/4), (40/7), (63/40), (352/63), (1386/352), (7722/1386), ...

Now, we will calculate the limit of the absolute value of the ratios:

lim(n->∞) |a(n+1)/a(n)| = lim(n->∞) |(7722/1386) / (1386/352)| = lim(n->∞) |(7722/1386) * (352/1386)| = lim(n->∞) |7722/1386 * 352/1386| = |2039328/1933156| = 1.055...

The limit of the absolute value of the ratios is greater than 1. According to the Ratio Test, if the limit is greater than 1, the series diverges. Therefore, the given series is divergent.

In conclusion, the series is divergent.

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Therefore, options c and e are true regarding normal probability distribution with mean μ and standard deviation σ

To answer your question, let's briefly discuss each of the given options:
a. This statement is false. A normal probability distribution can have values beyond 4, depending on its mean and standard deviation.
b. This statement is false. Half of the normally distributed data falls below the mean, not necessarily 0.
c. This statement is true. In a normal distribution, the area to the left of one standard deviation below the mean is equal to the area to the right of one standard deviation above the mean.
d. This statement is false. A larger standard deviation results in a wider/spread-out curve, not a skinnier/tighter one.
e. This statement is true. When the standard deviation is 1 and the mean is 0, it is called the standard normal distribution.

Therefore, options c and e are true regarding normal probability distribution with mean μ and standard deviation σ.

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Answer:

2x^2-6x+4

Step-by-step explanation:

Answer:

\( p = 111.2^\circ \)

Step-by-step explanation:

Since you only have sides given, you must use the law of cosines.

\( c^2 = a^2 + b^2 - 2ab \cos C \)

Let angle p be angle C in the law of cosines formula. Then a is 2.8 cm, b is 3.6 cm, and c is 5.3 cm.

All units of length are cm, so I'll leave them out for simplicity.

\( 5.3^2 = 2.8^2 + 3.6^2 - 2(2.8)(3.6) \cos C \)

\( 28.09 = 7.84 + 12.96 - 20.16 \cos C \)

\( 7.29 = -20.16 \cos C \)

\( \cos C = \dfrac{7.29}{-20.16} = -0.361607 \)

\( C = \cos^{-1} -0.361607 \)

\( C = 111.2^\circ \)

\( p = 111.2^\circ \)

Answer:

5.22 is the answer required

The number of days in a row Makenzie could wear a different outfit using only her favorite clothes is 24 days.

Solving this problem would involve combinations. In mathematics, combination refers to a mathematical technique used to determine the number of possible arrangements in a collection of items, irrespective of the arrangements.

We are given that the number of t-shirts is four, the number of pairs of designer jeans is three, and the number of pairs of sandals is two. The number of days in a row Makenzie could wear a different outfit using only her favorite clothes is calculated as follows:

(4C₁) (3C₁) (2C₁) =

4 × 3 × 2 =

24

We have confirmed that the number of days in a row Makenzie could wear a different outfit using only her favorite clothes is indeed 24 days.

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Rosie, this is the solution to the system of equations:

___________________________________________

2x - 3y = 6

2x - 6y = 9

___________

Step 1: Let's multiply by -1 the second equation, therefore we have:

2x - 3y = 6

-2x + 6y = -9

___________

Step 2: We eliminate x and solve for y, as follows:

-3y + 6y = 6 - 9

3y = -3

Dividing by 3 at both sides:

3y/3 = -3/3

y = -1

_______________________

Step 3: We substitute y and solve for x in the first equation, this way:

2x - 3 (-1) = 6

2x + 3 = 6

Subtracting 3 at both sides:

2x + 3 - 3 = 6 - 3

2x = 3

Dividing by 2 at both sides:

2x/2 = 3/2

x = 3/2

_________________________

Step 4: Now, let's prove x = 3/2 and y = -1 are right, replacing in the second equation, as follows:

2x - 6y = 9

2 (3/2) - 6 (-1) = 9

3 + 6 = 9

9 = 9

We proved that x = 3/2 and y = -1 are correct.

So, we need to find A and B that divide (-∞, 2)U(7, ∞) into three intervals

Given that the function is

\(f(x) = √-x² + 9x 14\)

The domain of a function is the set of all the possible values of x for which the function is defined, thus exists.

Denominator of the function is

\((-x²+9x-14)=-(x²-9x+14)=-(x-2)(x-7)\)

Thus, the domain of f(x) is the set of all real numbers except for the values of x which make the denominator zero.

So, the domain of the function is (-∞, 2)U(7, ∞).

Therefore, the domain consists of two intervals and we are given three intervals.

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The series is a convergent p-series with p = 3

We would know that a series is a convergent p series when we have ∑ 1 np. Then you have to be able to tell if the series is a divergent p series or it is a convergent p series.

The way that you are able to tell this is if the terms of the series do not approach towards 0. Now when the value of p is greater than 1 then you would be able to tell that the series is a convergent series.

The value of \(\sqrt{9}= 3\)

The formular for this is

∑\(\frac{1}{n^p} \\\)

where n = 1

we know it is convergent because p is greater than 1. 3>1

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a. Factor: 3 cos² 0+2 cos 0-8

3 cos² 0 + 2 cos 0 - 8 = (3 cos² 0 - 4) + 6 cos 0 = (3 cos 0 - 4)(cos 0 + 2)

The first factor can be simplified using the Pythagorean identity, cos² 0 + sin² 0 = 1. So, 3 cos² 0 - 4 = 3(cos² 0 - 1) = 3(sin² 0) = 3 sin² 0.

Therefore, the simplified expression is (3 sin 0 - 4)(cos 0 + 2).

b. Reduce: 3 sin 8 + 6 sin² 0-4

The given expression can be reduced as follows:

3 sin 8 + 6 sin² 0-4 = 3 sin 0 (1 + 2 sin² 0) - 4 = 3 sin 0 (1 + 2(1 - cos² 0)) - 4 = 3 sin 0 (3 - 2 cos² 0) - 4

Using the Pythagorean identity again, we can simplify the expression as follows:

3 sin 0 (3 - 2 cos² 0) - 4 = 3 sin 0 (3 - 2(1 - sin² 0)) - 4 = 3 sin 0 (5 - 2 sin² 0) - 4 = 15 sin 0 - 6 sin² 0 - 4

Therefore, the simplified expression is 15 sin 0 - 6 sin² 0 - 4.

c. Change to sines and cosines, tanß + 1 then simplify: sec ß + tan p

The given expression can be changed to sines and cosines as follows:

sec ß + tan ß = 1/cos ß + sin ß/cos ß = (1 + sin ß)/cos ß

Therefore, the simplified expression is (1 + sin ß)/cos ß.

To factor the expression in part (a), we used the difference of squares factorization. To reduce the expression in part (b), we used the Pythagorean identity twice. To change the expression in part (c) to sines and cosines, we used the definitions of secant and tangent.

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Both a frequency table and a frequency distribution are tools used to organize and summarize data, particularly in statistical analysis. They both display the frequency or count of occurrences of each unique value or category in a dataset.

The main difference between a frequency table and a frequency distribution is the type of data they are used to summarize. A frequency table is typically used to display the frequency of occurrence of qualitative or categorical data. It lists the categories or classes of data and the number of observations that fall into each category. For example, a frequency table could display the number of students in a class that received an A, B, C, D, or F grade in a course.

On the other hand, a frequency distribution is typically used to display the frequency of occurrence of quantitative or numerical data. It groups the data into classes or intervals and lists the number of observations that fall into each class or interval. For example, a frequency distribution could display the number of times a coin toss resulted in 0, 1, or 2 heads in a series of 10 tosses.

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The required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.

Arithmetic progression is the series of numbers that have common differences between adjacent values.

here,
The Sequences 8, 11, 14,...

first term a = 8
common difference = 11 - 8 = 3

Now,
The explicit formula is given as,
nth terms = a + (n - 1)d
nth term = 8 + (n - 1)3

Thus, the required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.

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The given system of linear equations consists of four equations with four variables: x, y, z, and w. To solve the system, we can use various methods, such as Gaussian elimination or matrix operations.

By performing row operations, we can reduce the system to its row-echelon form or solve it directly to find the values of x, y, z, and w. We will solve the system of linear equations using the method of Gaussian elimination. The augmented matrix representation of the system is:

[1 1 2 -1 | -2]

[0 3 1 2 | 2]

[1 1 0 3 | 2]

[-3 0 1 2 | 5]

First, we'll perform row operations to transform the matrix into the row-echelon form:

R2 = R2 - 3R1

R3 = R3 - R1

R4 = R4 + 3R1

The resulting matrix after these operations is:

[1 1 2 -1 | -2]

[0 0 -5 5 | 8]

[0 0 -2 4 | 4]

[0 3 1 2 | 5]

Next, we'll perform additional row operations to further simplify the matrix:

R4 = R4 - 3R2

The matrix now becomes:

[1 1 2 -1 | -2]

[0 0 -5 5 | 8]

[0 0 -2 4 | 4]

[0 3 1 2 | -19]

Finally, we'll perform the last row operation:

R3 = R3 + 2R2

The matrix is now in row-echelon form:

[1 1 2 -1 | -2]

[0 0 -5 5 | 8]

[0 0 0 14 | 20]

[0 3 1 2 | -19]

From this row-echelon form, we can solve for the variables. Starting from the bottom row, we obtain:

3w + z + 2w = -19, which simplifies to 5w + z = -19.

Next, we have 0x + 0y - 5z + 5w = 8, which simplifies to -5z + 5w = 8.

Lastly, x + y + 2z - w = -2.

At this point, we have three equations with three variables: x, y, and z. By solving this simplified system, we can find the values of x, y, and z.

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The height of the foyer is approximately 24 feet. To find the height of the foyer, we can start by calculating the lateral area of the regular octagonal pyramid.

The lateral area of a regular pyramid can be found using the formula

LA = (perimeter of base) × (slant height) / 2.

Since we are given that the lateral area is 600 ft² and the sides of the octagonal floor have a length of 10 ft, we can calculate the perimeter of the base. The perimeter of a regular octagon can be found by multiplying the length of one side by 8.

Perimeter of base = 10 ft × 8 = 80 ft

Next, we can use the apothem to find the slant height. The apothem is the distance from the center of the base to the midpoint of any side. In this case, the apothem is given as 12 ft.

Using the formula for the lateral area, we can now solve for the slant height:

600 ft² = (80 ft) * (slant height) / 2

1200 ft² = 80 ft * (slant height)

(slant height) = 1200 ft² / 80 ft

(slant height) = 15 ft

Finally, we can use the Pythagorean theorem to find the height of the pyramid. The height, slant height, and apothem form a right triangle, where the height is the unknown side. Applying the Pythagorean theorem:

(height)² + (apothem)² = (slant height)²

(height)² + 12 ft² = 15 ft²

(height)² = 15 ft² - 12 ft²

(height)² = 9 ft²

height = √9 ft

height ≈ 3 ft

Therefore, the height of the foyer is approximately 24 feet.

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