Suppose xy = 3 and dy/dt = - 4. Find dx/dt when x = 2

Answer:

3:45 pm

Step-by-step explanation:

..............

Answer:

Step-by-step explanation:

1256cm^2

(a) The profit of the firm at the current employment levels of 25 units of labor and 50 units of capital can be calculated by subtracting the total cost from total revenue.

The total revenue is given by the output multiplied by the market price, which is $2. The total cost is the sum of the wage cost (W) and the rental cost of capital (R), multiplied by their respective quantities.

Profit = Total Revenue - Total Cost

Profit = (Output * Price) - (Wage * Labor + Rental * Capital)

Given that the output is determined by the production function Y = 100K^(1/2) + 40L^(1/2), the profit can be calculated as follows:

Profit = (100K^(1/2) + 40L^(1/2)) * $2 - ($8 * 25 + $10 * 50)

(b) The profit-maximizing quantity of capital for this firm can be determined by setting the marginal revenue product of capital (MRPK) equal to the rental cost of capital (R). MRPK represents the additional revenue generated by employing an additional unit of capital.

MRPK = R

The marginal revenue product of capital can be calculated as the partial derivative of the production function with respect to capital (K), multiplied by the market price (P):

MRPK = (∂Y/∂K) * P

Using the production function Y = 100K^(1/2) + 40L^(1/2), we can calculate the marginal revenue product of capital as follows:

MRPK = (∂Y/∂K) * P = (50K^(-1/2)) * $2

Setting this equal to the rental cost of capital (R) of $10, we have:

(50K^(-1/2)) * $2 = $10

Simplifying the equation, we find:

K^(-1/2) = 1/5

Squaring both sides of the equation, we get:

K = 25

Therefore, the profit-maximizing quantity of capital for this firm is 25 units.

(c) To raise profits, the firm should decrease its capital employment from 50 to 25 units. This is because the profit-maximizing quantity of capital is determined to be 25 units, as calculated in part (b). By employing fewer units of capital, the firm can reduce its rental cost while still maintaining the optimal level of capital for production. As a result, the firm can lower its total cost and increase its profit. Employing more capital beyond the profit-maximizing level would lead to diminishing returns, where the additional costs outweigh the additional revenue generated. Therefore, reducing capital employment to the optimal level of 25 units would be the most favorable decision for the firm to maximize its profits.

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The shortest distance from the point (1,2) to the line x+2y=2 is 1 / sqrt(5), which is approximately 0.447.

The shortest distance from a point to a line can be found by using the formula for the perpendicular distance between a point and a line. In this case, the given point is (1,2) and the line is x+2y=2.

To find the shortest distance, we can follow these steps:

Write the equation of the given line in slope-intercept form (y = mx + b):

x + 2y = 2

2y = -x + 2

y = (-1/2)x + 1

Identify the slope of the line, which is -1/2. The perpendicular line will have a slope that is the negative reciprocal of -1/2, which is 2.

Use the formula for the perpendicular distance between a point (x1, y1) and a line y = mx + b:

Distance = |2x1 - y1 + b| / sqrt(1² + m²)

Substitute the coordinates of the point (1,2) and the slope of the perpendicular line (m = 2) into the formula:

Distance = |2(1) - 2 + 1| / √(1² + 2²)

= |2 - 2 + 1| / √(1 + 4)

= |1| / √(5)

= 1 / sqrt(5)

Therefore, the shortest distance from the point (1,2) to the line x+2y=2 is 1 / sqrt(5), which is approximately 0.447.

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Research on aging uses a **longitudinal** design.

A longitudinal design is a research design in which the same participants are studied over time. This is in contrast to a **cross-sectional** design, in which different participants are studied at different times.

Because age cannot be manipulated as an independent variable, research on aging must use a longitudinal design. This allows researchers to track changes in participants' behavior, cognition, and other factors as they age.

Longitudinal studies can be expensive and time-consuming to conduct, but they can provide valuable insights into the aging process. For example, longitudinal studies have shown that cognitive decline is not inevitable with age, and that certain lifestyle factors, such as exercise and social engagement, can help to protect against cognitive decline.

Here are some examples of longitudinal studies on aging:

* The Baltimore Longitudinal Study of Aging, which has been following a group of adults for over 70 years.

* The Framingham Heart Study, which has been following a group of adults for over 70 years.

* The Study of Adult Development and Aging, which has been following a group of adults for over 80 years.

These studies have provided valuable insights into the aging process, and they continue to be an important source of information for researchers and policymakers.

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1) In this question, we need to remember that in any boxplot the line in the middle of the box indicates the median.

Based on that, we can tell the Median is 140

2) In the Interquartile Range, we need to find the range between the lower quartile and the upper one, based on that boxplot. We can tell the IQR is:

Note that the boundaries of the box show us the lower and the upper quartile:

Answer:

\(m=\frac{2}{3}\)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-2, -1)

Point (4, 3)

Step 2: Find slope m

The system of inequalities did not have any solution, but after reversing the  sign we will get a solution of the system of inequalities.

The inequalities are : y > 2x + 2/3 and y < 2x + 1/3

There is no intersection and no solution to the system since the region above the line y = 2x + 2/3 and the region below the line y = 2x + 1/3, respectively, are the solutions to the inequality y > 2x + 2/3 and y <2x + 1/3, respectively.

Now when the signs are changed we get:

y < 2x + 2/3 and y > 2x + 1/3

The region below the line y = 2x + 2/3 is the solution of the inequality

y= 2x + 2/3, and the region above the line y = 2x + 1/3 is the solution of the inequality y > 2x + 1/3. This implies that the area between the two lines is where the system's solution lies.

Disclaimer: The complete question is :

How will the solution of the system y>2x+2/3 and y<2x+1/3 change if the inequality sign on both inequalities is reversed to y<2x+2/3 and y>2x+1/3?

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Answer:

There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions. 

Step-by-step explanation:

Sample answer

1.6 hours

152 km total divided by her speed, 95 km/h =1.6

Answer:

8

Step-by-step explanation:

-4(2)+8(-3)+12-8(2)-2(-3)+6=-8-24+12-16+6+6=8

Answer:

-24

Step-by-step explanation:

-4b + 8c + 12 - 8b - 2c + 6

Combine like terms

6c+18-12b

Let b=2  c=-3

6(-3) +18-12(2)

-18 +18 -24

-24

Answer:

22

13

6

9

8

Step-by-step explanation:

Remember, the triangle-sides inequatily, which states that the sum of smaller two sides must be greater the larger side.

Hence there are two situtations, in this case "x" represents the unknown side. For an answer to be valid, at has to satisfy one of these inequalities.

x + 9 > 15; x<15

15 + 9 > x

Answers;

22

13

6

9

8

The probability that the mean annual salary of a simple random sample of 14 graduates is more than $200,000 is approximately 0.1134.

Based on the given information, the mean annual salary for graduates 10 years after graduation is $187,000, with a standard deviation of $40,000.

Suppose you take a simple random sample of 14 graduates.

To find the probability that the mean annual salary of this sample is more than $200,000, we can use the Central Limit Theorem.

First, we need to calculate the standard error of the sample mean, which is equal to the standard deviation divided by the square root of the sample size.

The standard error (SE) = $40,000 / √(14)

= $10,697.0577 (rounded to four decimal places).

Next, we can calculate the z-score using the formula:

z = (sample mean - population mean) / standard error.

In this case, the population mean is $187,000 and the sample mean is $200,000.

z = ($200,000 - $187,000) / $10,697.0577

= 1.2147 (rounded to four decimal places).

Finally, we can use a standard normal distribution table or a calculator to find the probability associated with the z-score of 1.2147.

The probability is approximately 0.1134 (rounded to four decimal places).

Therefore, the probability that the mean annual salary of a simple random sample of 14 graduates is more than $200,000 is approximately 0.1134.

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The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer:

true

Step-by-step explanation:

:)

Answer:

45-45-90 isosceles triangle

Step-by-step explanation:

The group that would be the most stable based on size would be 10 people. So, the correct answer is c. 10 people.

A group is a set of people or objects that are deemed to be equivalent or share a common feature. Group members may collaborate and share knowledge to achieve a common goal. The group's performance is frequently greater than the sum of its members' individual efforts, and this is known as the group effect.

Group stability is defined as the ability of a group to remain together and keep working toward its objective over time. It is essential for a group to achieve its objectives and is typically linked to the group's size and objective. A stable group can withstand external pressures and is less susceptible to breaking up or being disbanded.

A group's size has a significant influence on its stability. Small groups are often more cohesive and productive than large groups. On the other hand, as a group's size grows, it becomes more challenging to sustain cohesion and productivity. A group of 10 people would be the most stable since it's not too large or too small. Thus, the correct option is c. 10 people.

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As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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Variables:

x is the small sack’s weight.

Equation:

x = small sack’s weight - 25

x + 35 = bigs sack‘s weight - 60

2x + 35 = 85

x = 25

Answer:

0.25

Step-by-step explanation:

The answer is 0.25 i think

Answer:

Height is 0.5

Step-by-step explanation:

height of parallelogram = area ÷ base

= 2.5 ÷ 5 = 0.5

Answer:

√{12+3}=√16=√4²=±4 is your answer

Answer:

hope it helps you........

Answer:

x = 5

Step-by-step explanation:

1. Subtract 22 from both sides.

15x = 7x + 62 - 22

2. Simplify 7x + 62 - 22 to 7x + 40.

15x = 7x + 40

3. Subtract 7x from both sides.

15x - 7x = 40

4. Simplify 15x - 7x to 8x.

8x = 40

5. Divide both sides by 8.

x = \(\frac{40}{8}\)

6. Simplify \(\frac{40}{8}\) to 5.

x = 5

2,184 possibilities are there for the win, place, and show (first, second, and third) positions in a horse race with 14 horses if all orders of finish are possible.

What is permutation?

A permutation is the number of ways a set can be arranged or the number of ways things can be arranged.

P(n, r) = n!/(n-r)!

where n is number of elements and r is number of permutation

According to the given data:

We used the permutation formula

P(n, r) = n!/(n-r)!

Here n = number of elements = 14

and r = number of permutation = 3 ( 1st,2nd,3rd)

By putting the values in the formula

P(14,3) = 14!/(14–3)!

           = 14.13.12.11!/11!

           = 14.13.12

           = 2,184

Hence 2184 possibilities are there for the win, place and show positions.

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Answer:

The cost of 1 scarf is $12.25 each.

Step-by-step explanation:

Answer:

she took 6 courses

Step-by-step explanation:

1.  200-50= 150

2. 150÷25 = 6

B. 6 courses

sign-up cost = $50

cost per course = $25

Piper paid = $200

First, subtract the sign-up cost from the amount paid:

$200 - $50 = $150

Now, divide the cost per course to the amount that is left to get the number of courses she took:

$150 ÷ $25 = 6 courses

Answer:

y = 5

Step-by-step explanation:

All angle measures in a triangle add up to 180°.

Solving for Y:

Step 1: Combine like terms.

Step 2: Subtract 145 from both sides.

Step 3: Divide both sides by 7.

Step 4: Check if solution is correct.

Therefore, y = 5.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

The property agent will receive a commission of $1,310 if he sells the property for $46,000.

The property agent charges a commission of 5% on the first $10,000 of the selling price and 2 1/4% on the remainder of the selling price.

To find the amount of commission he will receive if he sells a piece of property for $46,000, we can break it down into two parts:

1. First, let's calculate the commission on the first $10,000. Since the commission rate is 5%, we can multiply $10,000 by 0.05 to find the commission on this portion:
  Commission on first $10,000 = $10,000 * 0.05 = $500

2. Next, let's calculate the commission on the remainder of the selling price. To find the remainder, we subtract $10,000 from the selling price:
  Remainder = Selling price - $10,000
  Remainder = $46,000 - $10,000 = $36,000

  The commission rate on the remainder is 2 1/4%, which can be expressed as a decimal as 0.0225. We can then multiply the remainder by this commission rate to find the commission on this portion:
  Commission on remainder = $36,000 * 0.0225 = $810

Now, we can add the commission on the first $10,000 to the commission on the remainder to find the total commission:
Total commission = Commission on first $10,000 + Commission on remainder
Total commission = $500 + $810 = $1,310

Therefore, the property agent will receive a commission of $1,310 if he sells the property for $46,000.

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The probability values  of the Poisson distribution are P(y ≤ 2) = 0.423 and P(y = 3) = 0.140

Probability 1

The given parameters here are:

P(y ≤ 2) when λ=3

The probability of a Poisson distribution is represented as

P(x) = λˣe⁻λ/x!

In this case,

x = y ≤ 2

This means that

y = 0, 1 and 2

So, we have

P(y ≤ 2) = P(0) + P(1) + P(2)

This gives

\(P(y \le 2) = \frac{3^0 \times e^{-3}}{0!} + \frac{3^1 \times e^{-3}}{1!} +\frac{3^2 \times e^{-3}}{2!}\)

Evaluate

\(P(y \le 2) = \frac{1 \times e^{-3}}{1} + \frac{3 \times e^{-3}}{1} +\frac{9 \times e^{-3}}{2}\)

Solving further, we have

P(y ≤ 2) = 0.050 + 0.149 +0.224

P(y ≤ 2) = 0.423

Probability 2

The given parameters here are:

P(y = 3) when λ = 5

The probability of a Poisson distribution is represented as

P(x) = λˣe⁻λ/x!

In this case,

x = y = 3

This gives

P(y = 3) = 5³ * e⁻⁵/3!

Evaluate

P(y = 3) = 125 * e⁻⁵/6

Solving further, we have

P(y = 3) = 0.140

Hence, the probability is 0.140

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Answer:

tanA = \(\frac{55}{48}\)

Step-by-step explanation:

tanA = \(\frac{opposite}{adjacent}\) = \(\frac{BC}{AC}\) = \(\frac{55}{48}\)