Consider a two person exchange economy where each agent has utility given by u
i
​
(x
i1
​
,x
i2
​
)=v(x
i1
​
)+x
i2
​
. Suppose that v is a strictly concave and increasing function that has a continuous first derivative. Suppose also that v(0)=0 and v(x)<1 for all x. Agent 1 has endowment (1,10) and agent 2 has endowment (0,10). a) Describe the Walrasian equilibria of this economy, including specifying the unique ratio of equilibrium prices (p
1
​
/p
2
​
). b) What are the Pareto efficient allocations of this economy? c) For each Pareto efficient allocation, suggest how we might change the endowments so that the Pareto efficient allocation in question is a Walrasian equilibrium.

Answer:

vertex = (- 4, - 2 )

Step-by-step explanation:

given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

f(x) = 2x² + 16x + 30 ← is in standard form

with a = 2 , b = 16 , then

\(x_{vertex}\) = - \(\frac{16}{2(2)}\) = - \(\frac{16}{4}\) = - 4

substitute x = - 4 into f(x) for corresponding y- coordinate

f(- 4) = 2(- 4)² + 16(- 4) + 30

      = 2(16) - 64 + 30

      = 32 - 34

     = - 2

vertex = (- 4, - 2 ) or x = - 4 , y = - 2

Answer:

12 in.

Step-by-step explanation:

Formula: a^2 + b^2 = c^2

This case: c^2 - a^2 = b^2

1) 15^2 + 9^2 = b^2

2) 225 - 81 = 144

3) \(\sqrt{144\) = 12

the length of the dotted line is measured by find first the length of the upper part of the diagram

now from the triangle on the upper part

9 square + 8 squared = the square of the lower part.

that is X squared = 81. + 64.

x squared = 146

x =. 12. 1 or approximately 12

therefore the dotted line is

y squared = 10 ². +. 12²

y squared = 100+144

y squared = 244

y = the square root of 244

y is equal to 15.6

Answer:

Noah's center is 85 1/2 I believe

And Gabe's is 86 I think

AND WELCOME TO BRAINLY!

Answer:

$375.32

Step-by-step explanation:

100% - 40% = 80%

80/100 = 0.8 (multiplier)

521.28 x 0.8 = 417.024

417.024 to 417.02 (2 d.p.)

100 - 10 = (ans)/100 = 0.9

417.02 x 0.9 = 375.318

$375.32

Step 1: Find the sales price

The surfboard was marked down 40% of its original price, $521.28.

0.40(521.28) = 208.512

521.28 - 208.512 = 312.768

Step 2: Find the final price

We add the tax on the sales price, not the original price. The tax is 10% in this case.

0.10(312.768) = 31.2768

312.768 + 31.2768 = 344.0448

Final price = $344.04

---I did not round until the end in this case, but rounding at every step leads to an answer of $344.05

Hope this helps!

Answer:

d

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The slope is -1/2 and the y-int is 2.

Answer:

$48

Step-by-step explanation:

so since the column on the right says n is 4 (next to yellow box), you would substitute 4 for n.

c=12n

c=12(4)

c=48

The obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

(x-3)² + 9 = 0

(x-3)²= -9

(x-3)=√-9

(x-3)=√9×√-1

(x-3)=±3i

x=3±3i

Thus, the obtained value of x after solving the equation (x-3)² + 9 = 0 by the square root principle will be x=3+31,3-3i. Option d is correct.

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Answer: The rate of the boat in still water is 74 km/hr ,and the rate of the current is 19 km/hr

Explanation:

Let:

x= the speed of the boat

y=the speed of the stream

Then,

x-y = the speed upstream

x+y = the speed downstream

So, the upstream speed is:

and, the downstream speed is:

To find the value of x and y, we use the following equations:

x-y= 55

x+y=93

Then, solve for x in x-y =55.

x=55 +y

Substitute x=55 + y into x+y=93.

x+y=93

(55 +y) + y=93

55+2y = 93

Substitute y=19 into x+y = 93.

x+y= 93

x+ 19 =93

Simplify and rearrange

x=93-19

Calculate

x=74

Therefore, the rate of the boat in still water is 74 km/hr ,and the rate of the current is 19 km/hr.

The inequality that can be used to determine the maximum number of people, x, who can go to the amusement park is: 20x + 6.50 ≤ 555Let's break down the components of the inequality.

We have x, representing the number of people going to the amusement park. Since each ticket costs $20, the total cost of tickets for x people is 20x. In addition to the ticket cost, there is also the cost of parking. The parking fee is $6.50, which is a fixed amount regardless of the number of people. The total amount spent on tickets and parking should not exceed $555, as mentioned in the problem. Therefore, we can set up the inequality: 20x + 6.50 ≤ 555 This inequality combines the cost of tickets (20x) and the cost of parking ($6.50) and ensures that the total amount spent does not exceed $555. By solving this inequality, we can determine the maximum value of x, representing the number of people who can go to the amusement park without exceeding the available budget.

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Answer:

\( \frac{7}{2} \\ = 3 \frac{1}{2} \)

Answer:

Fraction: x= 8/5

Decimal: x= 1.6

Mixed Number: x= 1 3/5

Using the proportional rule of Similar Triangles, the length of SD is 12 m.

Given a truss bridge.

From it,

The triangles BCD and RSD are similar.

For similar triangles, corresponding sides are proportional.

Corresponding sides are,

BC and RS, CD and SD, BD and RD.

BC / RS = CD / SD = BD / RD.

Consider BC / RS = CD / SD.

2 / 1 = 24 / SD

2 (SD) = 24

SD = 12

Hence the length of SD is 12 m.

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The probability that the mean daily revenue for the next 30 days will exceed $7000 is 47.60%.

The formula for the z score is-

z = (x - μ)/σ

In which,

Put the value in formula

z = (7000 - 7200)/1200

z = - 0.16

Thus,

P(x > $7000) = P(z >  - 0.16)

See the p- value for obtained z from negative z score table.

P(x > $7000) = 0.4760

Thus, the probability that the mean daily revenue for the next 30 days will exceed $7000 is 47.60%.

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Answer:

2.5

Step-by-step explanation:

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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As per the distributive property, the expression -3x⁴(5x³ - 2x⁶) is equivalent to -15x⁷ + 6x¹⁰

Distributive property:

Distributive property states that the expression has been simplified when you multiply a number by a sum or difference.

Give,

Here we have the expression -3x⁴(5x³ - 2x⁶).

Now, we have to use the distributive property in order to find the equivalent expression.

Based on the distributive property, here we have to multiply the outer term with the individual inner terms, then we get,

=> -3x⁴(5x³ - 2x⁶)

=> (-3x⁴ × 5x³) + (-3x⁴ ×- 2x⁶)

Now we have to multiply the signs and the numbers then we get.

=> -15 (x⁴ × x³) + 6 (x⁴ × x⁶)

As per the rule of exponent, we have to add the exponents of the expression to find the solution,

=> -15x⁷ + 6x¹⁰

Therefore, the equivalent expression is -15x⁷ + 6x¹⁰.

Therefore, the option A is correct.

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The inequalities equation which will shade all the points except target point are, y >= 2, y >= -3.5x + 4.5 and y <= 1.25x - 1.5.

The line passing through P(-1,2) and P(-4,2) has a slope of 0 and a y-intercept of 2, so its equation is y = 2. The line passing through P(-1,2) and P(-2,0.5) has a slope of -3.5 and a y-intercept of 4.5, so its equation is y = -3.5x + 4.5. The line passing through P(-2,0.5) and P(-4,2) has a slope of 1.25 and a y-intercept of -1.5, so its equation is y = 1.25x - 1.5.

Now we can create a system of inequalities that will shade all of the points except for T(-2,2). We can do this by making sure that the inequality for each line is greater than or equal to the target point on one side of the line, and less than or equal to the target point on the other side of the line.

For the line y = 2, we can write the inequality y >= 2 on the side of the line that contains the target point T(-2,2). For the line y = -3.5x + 4.5, we can write the inequality y >= -3.5x + 4.5 on the side of the line that contains the point T(-2,2). For the line y = 1.25x - 1.5, we can write the inequality y <= 1.25x - 1.5 on the side of the line that contains the point T(-2,2).

Putting all of these inequalities together, we get:

y >= 2 (for the line passing through P(-1,2) and P(-4,2))

y >= -3.5x + 4.5 (for the line passing through P(-1,2) and P(-2,0.5))

y <= 1.25x - 1.5 (for the line passing through P(-2,0.5) and P(-4,2))

These inequalities should shade all of the points except for the target point T(-2,2), and they should do so with the fewest number of inequalities possible.

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--The complete question is, With the fewest inequalities, shade all the points but leave the targets exposed. Write the inequality equations to do this.

Points are P(-1,2), P(-4,2) and P(-2, 0.5)

T(-2,2)
Graph is show in the image.--

The pοint that satisfies bοth inequalities is the pοint inside this triangular regiοn.

An inequality is a mathematical statement that cοmpares twο values οr expressiοns and indicates whether they are equal οr nοt, οr which οne is greater οr smaller.

Since the shading is nοt included, we will need tο use the lines themselves tο determine the cοrrect regiοn οf the cοοrdinate plane.

The first inequality y > (3/2)x - 5 has a slοpe οf 3/2 and a y-intercept οf -5. This means the line will have a pοsitive slοpe and will be lοcated belοw the pοint (0,-5).

The secοnd inequality y < (-1/6)x - 6 has a negative slοpe οf -1/6 and a y-intercept οf -6. This means the line will have a negative slοpe and will be lοcated abοve the pοint (0,-6).

Tο find the pοint that satisfies BOTH inequalities, we need tο lοοk fοr the regiοn οf the cοοrdinate plane that is belοw the line y = (3/2)x - 5 AND abοve the line y = (-1/6)x - 6. This regiοn is the triangular-shaped area that is bοunded by the twο lines and the x-axis.

The pοint that satisfies bοth inequalities is the pοint inside this triangular regiοn.

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The procedure for finding the area between two curves Find the intersection points, set up the integral using the difference between the curves, integrate, take the absolute value, and evaluate the result and the area between the two curve in excercise 1 is 40/3

The procedure for finding the area between two curves involves the following steps:

Identify the two curves: Determine the equations of the two curves that enclose the desired area.

Find the points of intersection: Set the two equations equal to each other and solve for the x-values where the curves intersect. These points will define the boundaries of the region.

Determine the limits of integration: Identify the x-values of the intersection points found in step 2. These values will be used as the limits of integration when setting up the definite integral.

Set up the integral: Depending on whether the curves intersect vertically or horizontally, choose the appropriate integration method (vertical slices or horizontal slices). The integral will involve the difference between the equations of the curves.

Integrate and evaluate: Evaluate the integral by integrating the difference between the two equations with respect to the appropriate variable (x or y), using the limits of integration determined in step 3.

Calculate the absolute value: Take the absolute value of the result obtained from the integration to ensure a positive area.

Round or approximate if necessary: Round the final result to the desired level of precision or use numerical methods if an exact solution is not required.

In summary, to find the area between two curves, determine the intersection points, set up the integral using the difference between the curves, integrate, take the absolute value, and evaluate the result.

Here's the procedure explained using the exercises:

Exercise 1:

Consider the functions F(x) = \(x^2 + 2x + 1\)and f(x) = 2x + 5. To find the area between these curves, follow these steps:

Set the two functions equal to each other and solve for x to find the points of intersection:

\(x^2 + 2x + 1 = 2x + 5\)

\(x^2 - 4 = 0\)

(x - 2)(x + 2) = 0

x = -2 and x = 2

The points of intersection, x = -2 and x = 2, give us the bounds for integration.

Now, determine which curve is above the other between these bounds. In this case, f(x) = 2x + 5 is above F(x) =\(x^2 + 2x + 1.\)

Set up the integral to find the area:

Area = ∫[a, b] (f(x) - F(x)) dx

Area = ∫\([-2, 2] ((2x + 5) - (x^2 + 2x + 1)) dx\)

Integrate the expression:

Area = ∫\([-2, 2] (-x^2 + x + 4) dx\)

Evaluate the definite integral to find the area:

Area = \([-x^3/3 + x^2/2 + 4x] [-2, 2]\)

Area = [(8/3 + 4) - (-8/3 + 4)]

Area = (20/3) + (20/3)

Area = 40/3

Therefore, the area between the curves F(x) = \(x^2 + 2x + 1\)and f(x) = 2x + 5 is 40/3 square units.

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Answer:

Step-by-step explanation:

(A). y = 110 , z = 63

Answer:

8

one fourth

2

4

Step-by-step explanation:

hope with helped ^^

Answer:

Mr. Reed still needs to run 7 5/12 miles to reach his goal.

Step-by-step explanation:

2 3/4 and 2 1/3 need to be converted to a common denominator of 12:

2 9/12 and 2 4/12

Then we need to convert the original 12 1/2:

12 6/12

Add the miles he's already run:

2 9/12 + 2 4/12 = 5 1/12

Subtract the total amount run from the total goal:

12 6/12 - 5 1/12 = 7 5/12

Therefore, he still needs to run 7 5/12 miles to meet his total 12 1/2 (or 12 6/12) miles goal.

Answer:

the answer is 20abc

Step-by-step explanation:

5ab 4c

20abc

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Answer:

The equation in slope-intercept form is y = 6x + 5

Step-by-step explanation:

The slope-intercept form of the linear equation is y = m x + b, where

Let us solve the question

∵ A line has a slope of 6

∵ m is the slope of the line

∴ m = 6

∵ The line has a y-intercept of 5

∵ b is the y-intercept

∴ b = 5

→ Substitute the values of m and b in the slope-intercept form

∵ y = m x + b

∴ y = 6x + 5

∴ The equation in slope-intercept form is y = 6x + 5

Answer:

add 1;6 and 6,2 hope this helps ;)

The distance between the two points (5, 2) and (−3,−5) is √113.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that the two points are (5, 2) and (−3,−5). The distance between the two points is calculated by the formula given below,

D = √ [ ( y₂ - y₁ )² + ( x₂ - x₁ )² ]

D = √ [ ( -3 - 5 )² + ( -5 - 2 )² ]

D = √ [ 64 + 49 ]

D = √113 units

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