My friend has $20$ stuffed animals. All of them are either cats or dogs, and all of them either have short or long fur. ${}12$ of them are cats, $15$ of them have long fur, and $4$ of them are short-furred dogs. How many stuffed animals are long-furred cats?

(a) The average cost function C*(x) is -5,500/x + 5 dollars.

(b) The marginal average cost function C'(x) is 5,500/\(x^2\) dollars.

To find the average cost function and the marginal average cost function, we start with the given total cost function:

C(x) = -5,500 + 5x

(a) To find the average cost function C*(x), we divide the total cost by the quantity produced:

C*(x) = C(x)/x

Substituting the expression for C(x):

C*(x) = (-5,500 + 5x)/x

C*(x) = -5,500/x + 5

Therefore, the average cost function C*(x) is given by -5,500/x + 5.

(b) To find the marginal average cost function C'(x), we take the derivative of the average cost function with respect to x:

C'(x) = d/dx (-5,500/x + 5)

Using the power rule for differentiation:

C'(x) = 5,500/\(x^2\)

Interpreting the results:

The marginal average cost function C'(x) is given by 5,500/\(x^2\). This means that the rate of change of the average cost function with respect to x is positive for all x greater than 0. It indicates that as the quantity produced increases, the average cost per unit decreases. This is because the fixed costs (-5,500) are spread over a larger number of units, resulting in a lower average cost per unit.

Therefore, the correct interpretation is:

Since the marginal average cost function is positive for x > 0, the rate of change of the average cost function is negative for all x > 0.

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Answer:

Step-by-step explanation:

Given m ∠ Q P S = 4 7 ∘ m∠QPS=47 ∘ m, angle, Q, P, S, equals, 47, degrees m ∠ R P S = 3 x − 3 8 ∘ m∠RPS=3x−38 ∘ m, angle, R, P, S, equals, 3, x, minus, 38, degrees m ∠ Q P R = 7 x − 9 5 ∘ m∠QPR=7x−95 ∘

Sum of angles in a triangle = 180°

47° + 3 x − 3 8 ∘ + 7x - 95° = 180°

10x + 180° = 180°

Answer: 31°

(Attached photo of work)

Answer: flat rental fee of $2

Step-by-step explanation:

independent factor that does not change. Coeffocient 0.25 will be charge for late days

Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Answer:

25%

Step-by-step explanation:

increase by = 150 - 120

=30

increase percent = 30/120 * 100%

=3000/120

=25 %

Answer:

25%

Step-by-step explanation:

Percentage increase=(new value-original value)/(original value) x 100%

Percentage increase=(150-120)/120 x 100%

Percentage increase=30/120 x 100%

Percentage increase=1/4 x 100%

Percentage increase=25%

The required point is 0.25 miles away from the nearest point on the shore.

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) =  lim h--> 0 (f(x + h) - f(x)) /(x + h - x).

here, we have,

It can be applied to minimize or maximize a function.

The given problem can be shown in the form of a diagram as follows

Suppose the underwater cable meet the shore at a distance x from the nearest point.

Then, the distance of cable in water is x² + 3.5² = x² + 12.25

And, the distance of cable in the ground is 10 - x.

As per the question, the cost of the laying cable can be represented as follows,

C(x) = 1200(10 - x) + 2400(x² + 12.25)

In order to minimize the cost the above function can be differentiated and equated to zero as,

C'(x) = -1200 + 4800x = 0

=> x = 1200/4800

      = 1/4

      = 0.25

Hence, in order to minimize the cost of the entire project the underwater cable should meet the shore at 0.25 miles away from the nearest point.

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Answer:

3285

Step-by-step explanation:

5x3144=15720

3990

15720+3990=19710

19710/6=3285

To find the percentage, we must move the decimal place to the right two times. After doing this, 0.66 written as a percentage is 66%.

Answer:

66%

Step-by-step explanation:

All you do is put the decimal places two please to the right or do the number times 100.     .66 times 100= 66%

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

In graphical form, the normal distribution appears as a "bell curve".

The normal distribution is the proper term for a probability bell curve.

In a normal distribution the mean is zero and the standard deviation is1. It has zero skew and a kurtosis of 3.

Normal distributions are symmetrical, but not all symmetrical distributions are normal.

The t-distribution describes the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.

Therefore,

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.

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The function that satisfies the requirements provided is as follows:

⇒ f(x) = [(x+1)(x-3)] / [(x-4)(x+2)] - 2

Now, Due to a factor of (x-4) in the fraction's denominator, this function has a vertical asymptote at x=4.

Because the fraction approaches the value of -2 as x increases significantly (either positively or negatively),

And, it exhibits a horizontal asymptote at y = -2.

Because there is a cancelling factor of (x+1) in both the fraction's numerator and denominator, the function has a hole at x=-1.

As a result of (x-3) becoming a factor in the numerator, the function finally crosses the x-axis at the point (3, 0).

Hence, The function that satisfies the requirements provided is as follows:

⇒ f(x) = [(x+1)(x-3)] / [(x-4)(x+2)] - 2

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Answer:

S₄₉ = 8820

Step-by-step explanation:

the sum to n terms of an arithmetic series is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 36 and d = a₂ - a₁ = 42 - 36 = 6 , then

S₄₉ = \(\frac{49}{2}\) [ (2 × 36) + (48 × 6) ]

     = 24.5 (72 + 288)

     = 24.5 × 360

     = 8820

The balloon’s vertical distance above the ground is 402.53 ft

Two legs of a right triangle are formed by the horizontal and the vertical. The tangent relation is applicable because the provided angle is the angle next to the horizontal leg:

TOA = Tangent Opposite Adjacent

Tangent = opposite / adjacent

cross multiply

opposite = tan * adjacent

The tangent is 27 degrees

The adjacent is 790 feet away

= tan 27 degrees * 790

= 402.53

This balloon can be said to be 402.53 ft above the ground.

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Answer:

402.5

Step-by-step explanation:

I got the question right

If the utilization of an M/M/1 model is 0.6, the c of time there is at least one person in the system is 100%.

In an M/M/1 model, the utilization represents the ratio of the arrival rate (λ) to the service rate (μ). If the utilization is less than 1, it means that the arrival rate is lower than the service rate, and the system is not fully utilized. However, even with a utilization of 0.6, there will still be instances where there is at least one person in the system. This is because the arrival rate is not zero, indicating that customers are still arriving, albeit at a lower rate compared to the service rate. Therefore, the percentage of time with at least one person in the system would be 100%. If you are told that the utilization rate for an M/M/1 model is 0.8 and the average number of people in the system is 4, it is impossible to determine the average number of people in the queue without further information. The average number of people in the queue depends on factors such as the arrival rate and service rate, which are not provided in this scenario. The utilization rate alone and the average number of people in the system do not provide sufficient information to calculate the average number of people in the queue accurately. Therefore, it is impossible to determine the average number of people in the queue based solely on the given information.

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Answer:15 hours

Step-by-step explanation:

15+5=20

20+20=40

13+17=30

Add

90 hours

90÷6= 15

15 hours

The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

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Step-by-step explanation:

ans is 6 bcz crossmultiplication of 3 and 4 and it gives + 12 and then 12 upon 2 than it gives 6 so the value of x is 6 may it helps u

Answer:

0.85

Step-by-step explanation:

Answer:0.83

Step-by-step explanation:

Answer:

Step-by-step explanation:  

n = the number 3n= three times the number3n - 11 = three times the number decreased by eleven

The cost for a group of 3 that include 2 children is $100.99.

Let a be the cost of an adult admission and c be the cost of a child admission.

From the first statement, we can set up the equation:

3c + 2a = 176.98

From the second statement, we can set up the equation:

2c + 4a = 245.96

Simplifying the second equation by dividing both sides by 2, we get:

c + 2a = 122.98

Now we have a system of two equations with two unknowns:

3c + 2a = 176.98

c + 2a = 122.98

Solving for c in the second equation:

c = 122.98 - 2a

Substituting this value of c into the first equation:

3(122.98 - 2a) + 2a = 176.98

Simplifying and solving for a:

368.94 - 6a + 2a = 176.98

-4a = -191.96

a = 47.99

Substituting this value of a back into the equation we found for c:

c = 122.98 - 2(47.99) = 26

So the cost for an adult admission is $47.99 and the cost for a child admission is $26.

To find the cost for a group of 3 that include 2 children, we can set up the equation:

2c + a = ?

Substituting the values we found:

2(26) + 47.99 = 100.99

So the cost for a group of 3 that include 2 children is $100.99.

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The time it will it take him to grade 150 papers is 32 minutes, 4 seconds

It is important to note that proportion is a method of comparison in which two expressions or equations are made equal to each other.

From the information given, we have that;

Mr. B grades a total of 12.5 papers in 2.7 minutes.

Then, for 150 papers, we would have;

If 12. 5 papers = 2.7 minutes

Then 150 papers = x

Cross multiply the values

12.5x = 2.7(150)

multiply the values

12.5x = 405

Divide the values by the coefficient of x, we get;

x = 405/12.5

x = 32 minutes, 4 seconds

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Answer:

dont knohfxvggxhb cbbvc

help me help me help help me help

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

A wall can be built by 6 men working 8*5*6=240 hours.

If 4 men works 5 hours a day, they work 20 hours/day.

It will take them 240 hours /20 hours = 12 days

Answer:

-4sinθcosθ

Step-by-step explanation:

Note:

1. (a + b)^2 = a^2 + 2ab + b^2

2. (a - b)^2 = a^2 - 2ab + b^2

3. sin^2θ + cos^2θ = 1

(sinθ -cosθ)^2 - (sinθ + cosθ)^2

= sin^2θ - 2sinθcosθ + cos^2θ - (sin^2θ + 2sinθcosθ + cos^2θ)

= sin^2θ + cos^2θ - 2sinθcosθ - (sin^2θ + cos^2θ + 2sinθcosθ)

= 1 - 2sinθcosθ - (1 + 2sinθcosθ)

= 1- 2sinθcosθ -1 - 2sinθcosθ

= - 2sinθcosθ - 2sinθcosθ

= -4sinθcosθ

Answer:

Step-by-step explanation:

A is y=x+4

b is y=14

Answer:

  2550 ft

Step-by-step explanation:

The difference between 2550 ft and 0 ft is 2550 ft.

The balloon must descend 2550 ft to reach an altitude of 0 ft.

II. Firms may utilize databases other than relational databases.

III. In mapping an E-R diagram to a set of tables in a relational database, only the entities in the E-R diagram are mapped to tables in the database.

II. The statement that firms may utilize databases other than relational databases is true. While relational databases are widely used, there are other types of databases available, such as hierarchical databases, network databases, and object-oriented databases. Each type has its own characteristics and may be suitable for different purposes or specific requirements of an organization.

III. The statement that, in mapping an E-R diagram to a set of tables in a relational database, only the entities in the E-R diagram are mapped to tables in the database is also true. In the entity-relationship (E-R) model, entities represent objects or concepts in the real world, and relationships define the associations between entities. When designing a relational database based on an E-R diagram, the entities are typically mapped to tables, and the relationships are represented through foreign keys and join operations between tables. Other elements, such as attributes and keys, are also considered in the mapping process, but not all of them are necessarily represented as separate tables.

IV. The statement that each attribute of an entity is given a separate table in the mapping of an E-R diagram to a set of tables in a relational database is not true. In a relational database, attributes are typically represented as columns within a table, where each row represents a record or instance of the entity. Attributes are not given separate tables, but rather they contribute to the structure and content of the table associated with the entity.

Therefore, the correct statements are II and III.

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Answer:

$18.48

Step-by-step explanation:

Find perimiter of room

4+4+7+7 =22

22•0.84 = 18.48

$18.48