Supply and demand coordinate to determine prices by working

together.
competitively.
with other factors.
separately.

The marginal propensity to save when x = 3 is approximately 0.651.

To find the marginal propensity to save (dx) for the given consumption function C(x) = 0.774 \(x^1^.^1\) + 26.9 billion per billion dollars when x = 3:

To find the marginal propensity to save, we need to differentiate the consumption function C(x) with respect to x and evaluate it at x = 3.

Taking the derivative of C(x) = 0.774 \(x^1^.^1\)  + 26.9 with respect to x, we get:

dC/dx = 0.774 * 1.1 * \(x^1^.^1^-^1\) = 0.8514\(x^0^.^1\)

Now, we evaluate the derivative at x = 3:

dC/dx = 0.8514 * \(3^0^.^1\)= 0.6507 (rounded to three decimal places)

Therefore, the marginal propensity to save when x = 3 is approximately 0.651. This value represents the rate of change of savings with respect to a change in income, indicating the proportion of additional income saved in the economy at that specific level of income.

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Answer:

-4x -y :)

Step-by-step explanation:

Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

Answer:

A. 450 B. 1 C. 2

Step-by-step explanation:

A : B : C

15 : 1/30 : 1/15

MULTIPLYING BY 30 ON NUMERATOR (as 30 is LCM OF 15, 30, 15 :

15 × 30 : 1/30 × 30 : 1/15 × 30

450 : 1 : 2

The particular solution is y = -0.5t - 1 + 4e^(2x). To plot the solution curve, we can use any graphing software or tool.

The differential equation y′ − 2y = 4 − t is a first-order linear differential equation, which has the form y' + p(x)y = q(x), where p(x) = -2 and q(x) = 4 - t.

To solve this equation, we first find the integrating factor:

mu(x) = e^∫p(x) dx

= e^∫-2 dx

= e^(-2x)

Multiplying both sides of the original equation by the integrating factor, we get:

e^(-2x) y' - 2e^(-2x) y = (4-t)e^(-2x)

Applying the product rule on the left-hand side, we have:

d/dx (e^(-2x) y) = (4-t)e^(-2x)

Integrating both sides with respect to x, we obtain:

e^(-2x) y = ∫(4-t)e^(-2x) dx + C

= (-2t-4)e^(-2x)/4 + Ce^(-2x)

= -0.5t e^(-2x) - e^(-2x) + Ce^(-2x)

where C is the constant of integration.

Simplifying further, we have:

y = -0.5t - 1 + Ce^(2x)

Therefore, the general solution of the differential equation is y = -0.5t - 1 + Ce^(2x).

To find the particular solution for the initial condition y(0) = 3, we substitute x = 0 and y = 3 into the general solution and solve for C:

3 = -0.5(0) - 1 + Ce^(2(0))

C = 4

Thus, the particular solution is y = -0.5t - 1 + 4e^(2x).

To plot the solution curve, we can use any graphing software or tool. Here's an example plot using Python and Matplotlib:

python

import numpy as np

import matplotlib.pyplot as plt

# define the function for y

def y(t, x):

   return -0.5*t - 1 + 4*np.exp(2*x)

# generate values for t and x

t_vals = np.linspace(-10, 10, 100)

x_vals = np.linspace(-10, 10, 100)

# create a meshgrid for t and x

t_mesh, x_mesh = np.meshgrid(t_vals, x_vals)

# calculate y values for each point in the meshgrid

y_mesh = y(t_mesh, x_mesh)

# plot the solution curve using contourf plot

plt.contourf(t_mesh, x_mesh, y_mesh, levels=20, cmap="coolwarm")

plt.xlabel("t")

plt.ylabel("x")

plt.colorbar()

plt.title("Solution Curve of y' - 2y = 4 - t")

plt.show()

This will produce a plot of the solution curve for the given differential equation.

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Answer:

Belt = $34

wallt = $22

Step-by-step explanation:

The company sold 66 wallets and 83 belts for a total of $4,274 the previous month and sold 66 wallets and 86 belts for a total of $4,376 this month.

Let w represent wallets and b represent belts:

66w + 83b = $4,274

66w + 86b = $4,376

66w + 86b - 66w + 83b = $4,376 - $4,274

3b = $102

b = $34 this is the price for a belt.

To find the price of a wallet we need to replace b with 34 in the equation:

34×83 + 66w = $4,274

2,822 + 66w = $4,274

66w = $1,452

w = $22

The change in speed equals 2m/s and Magnitude of acceleration = 2.

What is meant by zero acceleration is the rate of change in speed. Thus, the rate of change in speed is zero while the car is moving at a constant pace. As a result, there is no acceleration. Magnitude is the length of any vector that points in the direction of the vector and is denoted by its unit. As a result, the acceleration's magnitude is equal to the acceleration vector's length and is directed in the same direction. For any vector quantity, this is true.

the sense, or the direction the vector is moving (left/right, up/down); the orientation, or the angle(s) governing the vector's alignment (transversal, longitudinal); and

The "strength" of the function is represented by the magnitude, or the value derived from the scalar quantities.

Change in speed = 5 m/s - 3m/s = 2m/s

As acceleration = rate of change in speed

Magnitude of acceleration = 2

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Answer:

True

Step-by-step explanation:

All straight lines angles are 180 degrees

-4 is less than -3

so:

By the using this method. We get, the correct determinant is 68.

Given Determinant:

\(\left|\begin{array}{ccc}1&0&-4\\3&-4&0\\-1&-4&1\end{array}\right|\)

\((-1)\left|\begin{array}{cc}-4&0\\-4&1\end{array}\right] +0\left|\begin{array}{cc}3&0\\-1&1\end{array}\right|+(-4)\left|\begin{array}{cc}3&-4\\-1&-4\\\end{array}\right|\)

= (-1)(-4-0) +0 - 4(-12 -4)

= -1 (-4) + 0 -4(-16)

= 4 + 64

= 68.

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Complete Question:

The expansion of a 3×3 determinant can be remembered by this device. write a second copy of the first two columns to the right of the​ matrix, and compute the determinant by multiplying entries on six diagonals. add the downward diagonal products and subtract the upward products. use this method to compute the following determinant.

\(\left|\begin{array}{ccc}1&0&-4\\3&-4&0\\-1&-4&1\end{array}\right|\)

Answer:

Let s = each square foot of wood installed

Step-by-step explanation:

Total cost of laying wood = base price + price for each square foot installed

Base price = $250

Price for each square foot installed = $3.50

Let

s = number of each square foot installed

Total cost of laying wood = $250 + $3.50s

The correct answer is

Let s = each square foot of wood installed

Answer:23.7

Step-by-step explanation:

The skip interval should be 40 if the sampling frame has 2000 names and the desired sample size is 50.

Systematic sampling is a type of sampling which uses the probability method where researchers select members of the group or population at a regular interval.

To determine the skip interval, it is necessary to first determine the sample size. Then the skip interval can be determined by dividing the total population by the target/desired sample size. Therefore;

skip interval = population / target sample size

Substituting the given values;

skip interval = 2000 / 50

skip interval = 40

Hence, the skip interval is calculated to be 40 if the frame has 2000 names and the desired sample size is 50.

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Answer:

GCF of 10 and 21 is 1.2.

Step-by-step explanation:

I hope it's helpful!

Answer:

\(Probability = 0.533\)

Step-by-step explanation:

Given

\(Hits = 8\)

\(Throws = 15\)

Required

Determine the experimental probability

This is calculated by dividing the number of hits by the total throws.

\(Probability = \frac{Hits}{Throws}\)

\(Probability = \frac{8}{15}\)

\(Probability = 0.533\)

Answer:

no

Step-by-step explanation:

x + 15 = 42

Subtract 15 from each side

x + 15-15 = 42-15

x = 27

x = 17 is not 27 so it is not a solution

Answer:

No.

Step-by-step explanation:

If you substitute 17 in for x in the equation you get 17+15=42.  Simplify to get 32=42.  This is not a true statement, so x=17 is not the answer.

Answer:

- 12/7|x-9.6|+12.8

Step-by-step explanation:

Answer:

\( \boxed{ \bold{ \huge{\boxed{ \sf{14x - 6}}}}}\)

Step-by-step explanation:

Given,

Length of a rectangle ( l ) = 6x - 2

Width of a rectangle ( w ) = x - 1

Perimeter of a rectangle ( P ) = ?

Finding the expressions that represents the perimeter of the rectangle

\( \boxed{ \sf{perimeter \: of \: rectangle = 2(l + w)}}\)

⇒\( \sf{2(6x - 2 + x - 1)}\)

Collect like terms

⇒\( \sf{2(7x - 2 - 1)}\)

Calculate

⇒\( \sf{2(7x - 3)}\)

Distribute 2 through the parentheses

⇒\( \sf{14x - 6}\)

Hope I helped!

Best regards!!

The required scale factor with respect to the pre-image and image is equal to 2.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures, which can be used to either vertically or horizontally enlarge or reduce a function representing their size.

In Mathematics, the scale factor of any geometric figure can be calculated by using this mathematical expression:

Scale factor = Dimension of image/Dimension of pre-image

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = -10/-5 = -4/-2

Scale factor = 2.

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Answer:

\(y = 2\)

Step-by-step explanation:

1) Simplify 5y/9 - y/9 to 4y/9.

\( \frac{4y}{9} = \frac{8}{9} \)

2) Multiply both sides by 9.

\(4y = \frac{8}{9} \times 9\)

3) Cancle 9.

\(4y = 8\)

4) Divide both sides by 4.

\(y = \frac{8}{4} \)

4) Simplify 8/4 to 2.

\(y = 2\)

Hence, the answer is y = 2.

We have shown that r is reflexive and circular if it is an equivalence relation by showing it is reflexive, symmetrical and has transitivity.

To prove that a relation r is reflexive and circular if and only if it is an equivalence relation, we need to show two things:

1. If r is reflexive and circular, then it is an equivalence relation.
2. If r is an equivalence relation, then it is reflexive and circular.

Let's start with the first part. If r is reflexive and circular, then it satisfies the following properties:

Reflexivity: For any a, aRa (that is, a is related to itself).
Circularity: If arb and brc, then cra.

To show that r is an equivalence relation, we need to prove that it satisfies the following three properties:

1. Reflexivity: For any a, aRa.
2. Symmetry: If aRb, then bRa.
3. Transitivity: If aRb and bRc, then aRc.

Reflexivity is already given, so we just need to show symmetry and transitivity.

For symmetry, suppose that aRb. Then by circularity, we have arb and bra. Since r is reflexive, we also have bRb. Combining these, we can apply circularity again to get bra and arc. Therefore, aRb implies bRa, and symmetry is satisfied.

For transitivity, suppose that aRb and bRc. Then by circularity, we have arb and brc, and by transitivity of r we have arc. Therefore, aRc, and transitivity is satisfied.

Thus, we have shown that r is an equivalence relation if it is reflexive and circular.

For the second part, suppose that r is an equivalence relation. Then it satisfies the following properties:

1. Reflexivity: For any a, aRa.
2. Symmetry: If aRb, then bRa.
3. Transitivity: If aRb and bRc, then aRc.

To show that r is reflexive and circular, we need to prove the following two properties:

1. Reflexivity: For any a, aRa.
2. Circular: If arb and brc, then cra.

Reflexivity is already given, so we just need to show circularity.

Suppose that arb and brc. Then by transitivity of r, we have arc. Since r is symmetric, we also have cra. Therefore, r is circular.

Thus, we have shown that r is reflexive and circular if it is an equivalence relation.

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Answer:

the solution  is (1,-4)

Step-by-step explanation:

Answer:

{x,y} = {-1,-9}  

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

I think

Answer:

0.15 cents

Step-by-step explanation:

1.80 (price) divided by 12 (amount) = 0.15 cents per pencil