Line g passes through points (1, 1) and (10,9). Line h is perpendicular to g. What is the
slope of line h?

The provided questions cover various aspects of a 2-period production economy, including the household's problem, firm's problem, market clearing conditions, Social Planner's Problem, competitive equilibrium, and welfare theorems.

(a) The Household's problem is to maximize its utility over two periods subject to its budget constraint. The household's problem can be formulated as follows:

Max U(Co, C1) = log(Co) + ß log(C1)

subject to the budget constraint:

Co + (1+r)C1 ≤ (1+r)Ko + W0 + W1,

where Co and C1 are consumption in period 0 and 1 respectively, ß is the discount factor, r is the interest rate, Ko is the initial capital endowment, W0 and W1 are the wages in periods 0 and 1 respectively.

(b) The Firm's problem is to maximize its profit by choosing the optimal combination of capital and labor. The firm's problem can be formulated as follows:

Maximize F(K, L) - RK - WL,

where F(K, L) is the production function, K is capital, L is labor, R is the rental rate of capital, and W is the wage rate.

(c) The market clearing conditions are:

Capital market clearing: K1 = (1 - δ)K0 + S - C0, where δ is the depreciation rate, S is savings, and C0 is consumption in period 0.

Labor market clearing: L = L0 + L1, where L0 and L1 are labor supplies in periods 0 and 1 respectively.

(d) The Social Planner's Problem is to maximize social welfare, which is the sum of the household's utility and the firm's profit. The Social Planner's Problem can be formulated as follows:

Maximize U(C0, C1) + F(K, L) - RK - WL,

subject to the production function F(K, L) and the market clearing conditions.

(e) A Competitive Equilibrium is a situation where all markets clear and agents (household and firm) make optimal decisions based on prices and market conditions. It is characterized by the following conditions:

Household's problem is solved optimally.

Firm's problem is solved optimally.

Market clearing conditions hold.

(f) To solve the Social Planner's Problem, we need to set up the Lagrangian and solve for the optimal values of consumption, capital, and labor. The Lagrangian can be written as:

L = U(C0, C1) + F(K, L) - RK - WL + λ1[(1+r)K0 + W0 + W1 - Co - (1+r)C1] + λ2[K1 - (1 - δ)K0 + S - C0] + λ3[L - L0 - L1],

where λ1, λ2, and λ3 are the Lagrange multipliers.

(g) To solve the Competitive Equilibrium, we need to determine the prices of capital (R) and labor (W) that clear the markets. This can be done by equating the demand and supply of capital and labor, and solving the resulting equations.

(h) The First Welfare Theorem states that under certain conditions, a competitive equilibrium is Pareto efficient. It implies that a competitive equilibrium is a socially optimal allocation of resources. To verify the theorem, we need to demonstrate that the competitive equilibrium allocation is Pareto efficient.

(i) The Second Welfare Theorem states that any Pareto efficient allocation can be achieved as a competitive equilibrium with appropriate redistribution of initial endowments.

To verify the theorem, we need to show that given an initial Pareto efficient allocation, we can find prices and redistribution of endowments that lead to a competitive equilibrium that achieves the same allocation.

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The dressmaker can cut 30 pieces of 12-inch long ribbon from 10 of these rolls of ribbon.

A dressmaker needs to cut 12-inch pieces of ribbon from rolls of ribbon that are 3 feet in length.

We are to determine how many 12-inch pieces the dressmaker can cut from 10 of these rolls of ribbon.

To do this, we need to find out the number of 12-inch pieces in 3 feet of ribbon and multiply that number by 10 (since we have 10 rolls of ribbon).

Let's begin by converting 3 feet into inches as follows;1 foot = 12 inches

Therefore,

3 feet = 3 × 12 inches

= 36 inches

From the above, we know that the dressmaker has 36 inches of ribbon to cut into 12-inch pieces.

Thus, the number of 12-inch pieces that can be cut from 36 inches of ribbon is given by dividing 36 by 12 as follows;

Number of 12-inch pieces = 36 ÷ 12

= 3 pieces

Therefore, from one roll of ribbon, the dressmaker can cut 3 pieces of 12-inch long ribbon

From 10 rolls of ribbon, the number of 12-inch pieces that can be cut is 10 × 3 = 30 pieces.

Hence, the dressmaker can cut 30 pieces of 12-inch long ribbon from 10 of these rolls of ribbon.

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Answer:

5.006

41.056

31.289

51.977

7.884

Step-by-step explanation:

1) sin x = opposite side / hypotenuse

sin 24.3° = 2.06 / hyp

hyp = 2.06 / sin 24.3  = 5.0059006616019108320511866543651

rounding to 3 significant figures

= 5.006

2)cos x = adjacent side / hypotenuse

cos 47 = 28 / x

x = 28 / cos 47 = 41.055817197909497891901840157945

= 41.056

3) cos x = adjacent side / hypotenuse

cos 56.1 = x / 56.1

x = 56.1 * cos 56.1 = 31.289500613760617368691451544764

= 31.289

4) tan x = opposite side / adjacent side

tan 68 = x / 21

x = 21 * tan 68 = 51.9768239217422123300402781676

= 51.977

5) sin x = opposite side / hypotenuse

sin 21 = x / 22

x = 22 * sin 21 = 7.8840948899966060166510313670963

= 7.884

Answer: Toya Todoroki

Step-by-step explanation:

Answer:

Touya Todoroki

Step-by-step explanation:

i used to watch the show

Answer:

a or b (probably a)

Step-by-step explanation:

\(\textbf{Heya !}\)

the mode is the number that occurs the most

All numbers here occur once, except \(\sf{100}\).

so 100 is the mode.

`hope it was helpful to u ~

angle has a measure equal to the sum of the the question is ∠DQS.


According to the problem, we need to find an angle whose measure is equal to the sum of the measures of ∠SQR and ∠QRS. We can use the angle addition postulate which states that the measure of an angle formed by two adjacent angles is equal to the sum of their measures.

Let's consider angle ∠DQS. This angle is formed by adjacent angles ∠SQR and ∠QRS. Therefore, according to the angle addition postulate, the measure of angle ∠DQS is equal to the sum of the measures of ∠SQR and ∠QRS.



Thus, we can conclude that the angle ∠DQS has a measure equal to the sum of the measures of ∠SQR and ∠QRS.

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(a) Starting with the expression Var(X)=E[(X−μ)2], we can rearrange to get E[(X−μ)2] = Var(X)+μ2. Therefore, Var(X)=E(X2)−μ2.

(b) A random variable Z that is constructed by standardizing X is written as Z = (X-μ)/σ.

(c) E(Z) = E[(X-μ)/σ] = (E[X] - μ)/σ = 0.

(d) Var(Z) = Var[(X-μ)/σ] = (Var[X] - μ2)/σ2 = 1.

(e) The sample mean of a random sample of size n drawn from the population is an unbiased estimator for the population mean μ if E[sample mean] = μ.

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To model the given data points, we can use a linear function of the form y = mx + b.

First, we need to find the slope (m) of the line:

m = (y2 - y1) / (x2 - x1)

m = (-6 - (-2)) / (1 - 0)

m = -4/1

m = -4

Now, we can use the slope and one of the points to find the y-intercept (b):

y = mx + b

-2 = (-4)(0) + b

b = -2

Therefore, the linear function that models the given data is:

y = -4x - 2

Question:

What is the measure of an interior angle of a 21-gon?

Concept:

Define a 21-gon

A 21-gon is a 21 sided polygon also know as An icosikaihenagon

In the case of this polygon, the value of n is

We will then calculate the sum of interior angles of a 21-gon and then divide the sum by the number of sides n...

Therefore,

The formula we will use to calculate the measure of an interior angle of a 21-gon is given below as

The formula for the sum of interior angles is given below as

Hence,

We will have

Step 2:

Substitute the value of n=21 in the formula above, we will have

Hence,

The final answer = 162.86°

You will have $5,333.85 in your CD at the end of the 5 years.

The formulation for the future value of an investment with monthly compounding is:

\(CD = P(1 + \frac{r}{n} )^{(nt)}\)

Wherein:

Plugging in the given values:

\(CD= 5000(1 + \frac{0.0125}{12} )^{(12*5)}\)

\(CD = 5000(1.00104)^{60}\)

CD = 5000(1.06677)

CD = $5,333.85

Consequently, you will have $5,333.85 in your CD at the end of the 5 years.

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The equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).

If we assume that the growth rate of the world population was constant from 1997 to 2017, then we can use the following equation:

Population in 2017 = Population in 1997 × (1 + r)²⁰

where r is the annual growth rate, and the exponent 20 represents the number of years between 1997 and 2017.

We can rewrite this equation to solve for r:

(7.53 ) = (5.88 ) × (1 + r)²⁰

Divide both sides by (5.88 ):

(7.53 ) / (5.88 ) = (1 + r)²⁰

Take the 20th root of both sides:

\((7.53 / 5.88 )^{(1/20)} = 1 + r\)

Subtract 1 from both sides:

\(r = (7.53 / 5.88 )^{(1/20)} - 1\)

Therefore, the equation that can be used to find r, the rate of growth per year of the world population, is \(r = (7.53 / 5.88 )^{(1/20)} - 1\).

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George receives £112 based on the given data regarding the 4:5 ratio.

Felix receives 30% of £360 which is:

The total amount remaining for George and Harry is:

The ratio of the amount that the George receives to the amount that the Harry receives is 4:5. This means that the total ratio of the amount they receive is:

4+5 = 9

To find out how much George receives, we need to divide the total of the amount by the total of the ratio and then multiply by George's share of the ratio:

£252 ÷ 9 x 4 = £112

Therefore, George receives £112.

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The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b. This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

To find the equation for the tangent plane to the graph of the function f(x, y) = 2e^x - y at a given point (x0, y0), we need to calculate the partial derivatives of f with respect to x and y at that point.

The partial derivative of f with respect to x, denoted as ∂f/∂x or fₓ, represents the rate of change of f with respect to x while keeping y constant. Similarly, the partial derivative of f with respect to y, denoted as ∂f/∂y or fᵧ, represents the rate of change of f with respect to y while keeping x constant.

Let's calculate these partial derivatives:

fₓ = d/dx(2e^x - y) = 2e^x

fᵧ = d/dy(2e^x - y) = -1

Now, we have the partial derivatives evaluated at the point (x0, y0). Let's assume our point of interest is (a, b), where a = x0 and b = y0.

At the point (a, b), the equation for the tangent plane is given by:

z - f(a, b) = fₓ(a, b)(x - a) + fᵧ(a, b)(y - b)

Substituting fₓ(a, b) = 2e^a and fᵧ(a, b) = -1, we have:

z - f(a, b) = 2e^a(x - a) - (y - b)

Now, let's substitute f(a, b) = 2e^a - b:

z - (2e^a - b) = 2e^a(x - a) - (y - b)

Rearranging and simplifying:

z = 2e^a(x - a) - (y - b) + 2e^a - b

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b.

This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

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What are the slope and y-intercept of

25x - 20y = 100

-20y = 100 - 25x

20y = 25x - 100 (dividing by 20)

y= (25/20)x - 5

y= (5/4)x - 5

So, the slope is 5/4 and the y-intercept is 5.

Answer:

2 distinct solutions

Step-by-step explanation:

discriminant is b²-4ac

b = 3

a = 1

c = -7

discriminant = 9-4(-7) = 9+28 = 37

Answer:

x

Step-by-step explanation:

Solution :

It is given that the Precision Scientific Instrument company Manufactures thermometers that provide readings at 0 degree Celsius for the freezing point of water.

A quality control analyst examines the thermometers which provide readings in the bottom of 4%.

Using the standard normal table, we get

P(z < z) = 4%

P(z < z) = 0.04

See the probability of 0.04 in the standard normal corresponding to the z-value is = -1.75

Therefore,

P(z < -1.75) = 0.04

z = -1.75

So the temperature reading that separates the bottom of 4% from the other thermometers is - 1.75°C

Therefore correct option is (D). -1.75

To compute the Galois groups and determine if the field extensions are normal, we need to know the specific field extensions in question. However, I will provide a general method for computing Galois groups and determining normal field extensions.

Step 1: Identify the field extension
Let's say our field extension is given by K/Q, where K is the extension field and Q is the base field (the field of rational numbers).

Step 2: Determine the minimal polynomial
Find the minimal polynomial f(x) of the field extension K/Q. This is the smallest degree polynomial with rational coefficients for which the elements of K are roots.

Step 3: Compute the Galois group
The Galois group, G(K/Q), is the group of automorphisms of the field K that fix the base field Q. To compute G(K/Q), determine the set of automorphisms of K that keep the elements of Q fixed.

Step 4: Check for normality
A field extension K/Q is normal if and only if the minimal polynomial f(x) splits into distinct linear factors over K. If this is true, then K/Q is a normal field extension.

Step 5: Find a normal extension if necessary
If K/Q is not normal, we can find a normal extension L/Q containing K by considering the splitting field of the minimal polynomial f(x) over Q. The splitting field L is the smallest field containing Q and all the roots of f(x), and the extension L/Q will be normal.

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Using Pythagoras theorem to set a system of equations, the longer side is 11 unit and shorter side is 3 unit

A system of equations is a set of two or more equations containing two or more variables. The goal of a system of equations is to find the values of the variables that satisfy all of the equations simultaneously.

In this problem, we can define our unknown variables as;

Let;

Using Pythagoras theorem;

x² + y² = (√130)²

x² + y² = 130 ...(i)

The perimeter of the triangle is the sum of sides in the triangle.

x + y + √130 = 14 + √130

x + y = 14 + √130 - √130

x + y = 14 ...eq(ii)

From equ(ii)

x = 14 - y ...eq(iii)

Put eq(iii) into eq(i)

x² + y² = 130

(14 - y)² + y² = 130

y² - 28y + 196 + y² = 130

2y² - 28y + 66 = 0

Solving the quadratic equation

y = 11

Put y = 11 into equ(ii)

x + y = 14

x + 11 = 14

x = 3

The shorter side is 3 units and longer side is 11 units

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The probability that a customer will wait in a line between 3 to 6 minutes is about 16.58%.

To solve this problem, we need to use the Poisson process and the exponential distribution.

Let X be the number of arrivals in a 3-minute interval. Since customers arrive at a rate of 25 per hour, the expected number of arrivals in a 3-minute interval is:

λ = (25/60) x 3 = 1.25

Thus, X is Poisson distributed with parameter λ = 1.25.

Let Y be the service time for a customer. Since Linda serves a customer, on average, in 1.5 minutes, Y is exponentially distributed with parameter μ = 1/1.5 = 0.6667.

Let Z be the waiting time for a customer in the line. Z is the sum of X independent service times, so Z is gamma distributed with parameters X and μ.

We want to find the probability that Z is between 3 and 6 minutes:

P(3 ≤ Z ≤ 6) = ∫∫ f(x,y) dx dy

where f(x,y) is the joint probability density function of X and Y:

f(x,y) = (λ^x / x!) e^(-λ) μ e^(-μy) = (1.25^x / x!) e^(-1.9167) e^(-0.6667y)

Now we can evaluate the double integral:

P(3 ≤ Z ≤ 6) = ∫∫ f(x,y) dx dy

= ∫∫ (1.25^x / x!) e^(-1.9167) e^(-0.6667y) dx dy

= ∫ e^(-0.6667y) e^(-1.9167) ∑ (1.25^x / x!) dx dy (x=0 to ∞)

= e^(-1.9167) ∫ e^(-0.6667y) e^(1.25) dy ∑ (1.25^x / x!) (x=0 to ∞)

The sum in the integral is the Taylor series expansion of e^1.25, which is equal to e^1.25 = 3.4903.

Using a table of integrals or a computer software, we can evaluate the integral:

∫ e^(-0.6667y) e^(1.25) dy = (1/0.6667) (e^(1.25) - e^(-0.6667(6))) = 3.7225

Therefore, the probability that a customer will wait in a line between 3 to 6 minutes is:

P(3 ≤ Z ≤ 6) = e^(-1.9167) ∫ e^(-0.6667y) e^(1.25) dy ∑ (1.25^x / x!) (x=0 to ∞)

= e^(-1.9167) (3.7225) (3.4903) = 0.1658 or about 16.58% (rounded to four decimal places).

Therefore, the probability that a customer will wait in a line between 3 to 6 minutes is about 16.58%.

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Answer:

9 2/5

Step-by-step explanation:

6 38/45 + 2 5/9 ​

6 38/45 + 2 25/45 = 8 63/45 = 9 18/45 = 9 2/5

Answer:

335 Miles

Step-by-step explanation:

804/12 = 67 MPH

5 × 67 = 335

Answer:

74 inches

Step-by-step explanation:

1 yard = 36 inches

then 2 yards = 72

and 72 + 2 inches = 74 inches

Answer:

6 free throws

Step-by-step explanation:

you do 120 divided by 0.05 (which is 5 percent in decimal form) and get 6.