Mathematics High School

What is the equation of the line that passes through the point (-7, -1) and has a
slope of 1?

Answers

Answer 1

Answer:

y= x +6

Step-by-step explanation:

y=mx+b

given: m=1

y=x+b

-1 = -7 +b

6 = b

y= x +6

Related Questions

Sensitivity analysis considers how changes in objective cell coefficients would effect the optimal solution. True
False

Answers

The given point about sensitivity analysis is True.

True.

Sensitivity analysis is a technique used in linear programming (LP) to analyze the impact of changes in the objective function coefficients, the right-hand side values of constraints or the constraint coefficients on the optimal solution of the LP model.

Sensitivity analysis helps in understanding the stability of the optimal solution and provides information about the range of values for the coefficients that would keep the current optimal solution valid.

Sensitivity analysis helps in understanding the robustness of the optimal solution and provides information about the range of values for the coefficients that would keep the current optimal solution valid.

It is an important tool in decision-making, as it allows managers to evaluate the impact of changes in input parameters on the overall outcome of the optimization problem.

In summary,

Sensitivity analysis is an essential part of the LP process, and it considers changes in objective function coefficients, among other parameters to determine the impact on the optimal solution.

Therefore, sensitivity analysis does consider how changes in objective cell coefficients would affect the optimal solution.

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Given statement "Sensitivity analysis considers how changes in objective cell coefficients would effect the optimal" is True. because Sensitivity analysis is an essential part of the LP process, and it considers changes in objective function coefficients, among other parameters to determine the impact on the optimal solution.

Sensitivity analysis helps in understanding the stability of the optimal solution and provides information about the range of values for the coefficients that would keep the current optimal solution valid.

Sensitivity analysis helps in understanding the robustness of the optimal solution and provides information about the range of values for the coefficients that would keep the current optimal solution valid.

It is an important tool in decision-making, as it allows managers to evaluate the impact of changes in input parameters on the overall outcome of the optimization problem.

In summary, sensitivity analysis does consider how changes in objective cell coefficients would affect the optimal solution.

The given statement is true.

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4. Let X=(A,B,C,D,E,F,G), where
A={b,f,h},
B={b,h},

C={a,b,c,d,g},
D={c,d,e,f,g},

E={b,e,f},
F={e,f,h},

1 (a) Draw a bipartite graph G such that the problem of finding a transversal of X is equivalent to the problem of finding a matching in G. (b) Find a transversal of X, or show that it doesn't have one.

Answers

(a) A bipartite graph G can be constructed where one set of vertices represents the elements of X and the other set represents the subsets of X. The problem of finding a transversal of X is equivalent to the problem of finding a matching in G.

(b) A transversal of X can be found by analyzing the constructed bipartite graph G and identifying a matching, or it can be shown that no transversal exists.

(a) To create a bipartite graph G, we consider one set of vertices to represent the elements of X (A, B, C, D, E, F, G), and another set of vertices to represent the subsets of X (A, B, C, D, E, F, G). Each vertex in the element set is connected to the vertices in the subset set if the element belongs to that subset. For example, vertex A is connected to vertices A, C, and D, as A is present in subsets A, C, and D.

(b) In order to find a transversal of X, we need to find a matching in the bipartite graph G. A matching in a bipartite graph is a set of edges where no two edges share a common vertex. By identifying such a matching in G, we can determine a transversal of X.

To find a matching, we can employ various algorithms like the Hopcroft-Karp algorithm or the Ford-Fulkerson algorithm. These algorithms will traverse the bipartite graph and identify a set of edges that form a matching.

If it is not possible to find a matching, it indicates that no transversal exists for X. This means that there is no subset in X that contains exactly one element from each of the other subsets. In such cases, we can conclude that X does not have a transversal.

In summary, by constructing a bipartite graph G and finding a matching in it, we can solve the problem of finding a transversal of X. If a matching exists, it represents a transversal, while the absence of a matching indicates the absence of a transversal.

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What is the equation of the line that passes through the point (4, 7) and has a slope
of 0?

Answers

Answer:

I think it's y= 7

if you put it into a graph calculator such as desmos it passes straight through (4,7) and has a slope of 0

Hope this helps have a wonderful day :)

What is the distance between-2 and 2 on the number line shown below -

Answers

Answer:

Step-by-step explanation:

on less you have a picter i cant help that much

Answer: The distance is 4

Step-by-step explanation:

-(-4)-(-3)-(-2)-(-1)-0-(1)-(2)-(3)-(4)-

^ 1 2 3 4 ^

~ ~ ~ ~

Please help me solve for X
I'll give brainlyest

Answers

Answer:

1. x = 8

2. x = 12

3. x = 11

4. x = 6

Step-by-step explanation:

102 + 102 = 204

360 - 204 = 156

156 / 2 = 78

78 = 10x - 2

78 + 2 = 10x

80 = 10x

80 / 10 = x

x = 8

81 = 7x - 3

81 + 3 = 7x

84 = 7x

84 / 7 = x

x = 12

77 = 6x + 11

77 - 11 = 6x

66 = 6x

66 / 6 = x

x = 11

115 + 115 = 230

360 - 230 = 130

130 / 2 = 65

65 = 8x + 17

65 - 17 = 8x

48 = 8x

48 / 8 = x

x = 6

In point slope form write the equation of the line with slope 4 which passes through the point (7,-13).

Answers

Answer:

y + 13 = 4(x - 7)

Step-by-step explanation:

Point-slope: y - y1 = m(x - x1)

Using (7,-13) and m = 4

y - -13 = 4(x - 7)

y + 13 = 4(x - 7)

For the functions below, what is the direction of fastest increase at (1, 1, 1)? (a) f(x, y, z) = 1/x² + y² + 22
(b) f(x, y, z) = 4xy + 4yz + 4xz 6 (c) f(x, y, z) x2 + y2 + z2

Answers

Answer: For all three functions, the direction of fastest increase at the point (1, 1, 1) is the direction of the gradient vector of the function at that point.

For function (a), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:

[2/x³, 2y, 22] = [2, 2, 22].

The direction of this gradient vector is given by the direction in which each of its components is increasing the most rapidly. In this case, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.

For function (b), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:

[4y + 4z, 4x + 4z, 4x + 4y] = [4, 4, 4].

Again, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.

For function (c), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:

[2x, 2y, 2z] = [2, 2, 2].

As before, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.

Therefore, for all three functions, the direction of fastest increase at (1, 1, 1) is the direction of the positive x, y, and z axes.

Step-by-step explanation:

Two groups of participants are presented with the famous "Asian disease problem" (Tverksy & Kahneman, 1980). A new and unknown disease is threatening the nation. Group 1 is presented with two possible courses of action:
Out of 600 people
Program A: 200 will be saved
Program B: there is a 1/3 probability that 600 people will be saved and 2/3 probability that no one will be saved
Group 2 is presented with the following courses of action:
Out of 600 people
Program A: 400 will die
Program B: there is a 1/3 probability that 600 people will be saved and 2/3 probability that no one will be saved.
Notice, that both groups are given the same condition; it is the wording that matters. What will the pattern of results look like (most likely)?
Both groups will prefer A
O Group 1 will be most likely to choose B, Group 2 will be most likely to choose A
Group 1 will be most likely to choose A, Group 2 will be most likely to choose B
O Both groups will be equally likely to choose A or B

Answers

Group 1 will be most likely to choose Program A, while Group 2 will be most likely to choose Program B in the Asian disease problem, reflecting a difference in preferences due to the framing effect.

The pattern of results in the Asian disease problem is typically influenced by a cognitive bias known as the framing effect, which suggests that people's choices are influenced by the way options are presented or framed.

In Group 1, where the options are presented in terms of potential lives saved, participants are more likely to choose Program A because it guarantees the saving of 200 out of 600 people. The probabilistic nature of Program B, with a 1/3 chance of saving all 600 people and a 2/3 chance of saving no one, may seem riskier and less favorable in this framing.

On the other hand, in Group 2, where the options are presented in terms of potential deaths, participants are more likely to choose Program B. The probabilistic nature of Program B, with a 1/3 chance of no one dying and a 2/3 chance of everyone dying, may be perceived as a more favorable option compared to the certain death of 400 people under Program A. Therefore, the pattern of results will likely show that Group 1 prefers Program A, while Group 2 prefers Program B. This difference arises from the framing of the options in terms of lives saved or deaths.

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consider the given plot of absorbance vs. concentration. which line is the best-fit line to represent the black data points? plot with eight data points and three lines drawn. the green line is on top and touches three of the data points with the rest below it. the red line is in the middle; it goes through one data point, three data points are above it, and four data points are below it. the blue line is on the bottom; it has two data points below it and six data points above it. select one: red line (b) green line (a) blue line (c)

Answers

The best-fit line to represent the black data points is the blue line.

The plot of absorbance vs. concentration shows 8 data points with 3 lines drawn to represent the data. In order to determine the best-fit line, we need to evaluate the lines based on how well they represent the data points.

(a) The red line is the middle line and goes through 1 data point, with 3 data points above it and 4 data points below it. This line has a slope that is between the slopes of the other two lines. However, it doesn't go through many of the data points and the slope is not consistent with the majority of the data points.

(b) The green line is the top line and touches 3 of the data points, with the rest of the data points below it. This line has a steeper slope compared to the red line, but it doesn't touch many of the data points and has a significant deviation from the majority of the data points.

(c) The blue line is the bottom line and has 2 data points below it and 6 data points above it. This line has a slope that is more consistent with the majority of the data points, and it has the least deviation from the data points compared to the other two lines.

In mathematical terms, the blue line has the least sum of squared residuals, meaning it has the smallest difference between the observed values and the predicted values.

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consider the given plot of absorbance vs. concentration. which line is the best-fit line to represent

Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options.
18 x minus 15 = 72
50 x minus 25 = 72
18 x minus 9 = 72
3 (6 x minus 3) = 72
x = 4.5

Answers

Answer:

Option 3 ) 18x - 9 = 72

Step-by-step explanation:

Algebraic equations:

$\sf \dfrac{3}{5}(30x - 15) = 72\\\\\\$

Multiply each term of (30x - 15) by 3/5,

$\sf \dfrac{3}{5}*30x - \dfrac{3}{5}*15=72\\\\\\3*6x - 3*3 = 72\\\\18x - 9 = 72$

The given equation is same as 18x - 9 = 72

Concepts and Skills Bennet has 8 blue marbles, 7 green marbles, 15 red marbles, and 20 yellow marbles in a bag. He randomly selects a marble 200 times. He replaces the marble after each selection. Predict how many times Bennet will select a red marble. A) about 30 times B about 50 times Cabout 60 times D about 120 times

Answers

With probability we can predict that, Bennet will select a red marble about 60 times in 200 draws, which corresponds to option C.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.

According to given information:

The probability of selecting a red marble on any given draw is the number of red marbles divided by the total number of marbles in the bag:

P(Red) = 15 / (8 + 7 + 15 + 20) = 15 / 50 = 0.3

Since Bennet is replacing the marble after each selection, each draw is independent and has the same probability of selecting a red marble. Therefore, the number of red marbles selected in 200 draws follows a binomial distribution with n = 200 (the number of trials) and p = 0.3 (the probability of success on each trial).

The expected value of the number of red marbles selected can be found using the formula:

E(X) = np

where X is the number of red marbles selected, n is the number of trials, and p is the probability of success on each trial.

Substituting the values we get:

E(X) = 200 * 0.3 = 60

Therefore, we can predict that Bennet will select a red marble about 60 times in 200 draws, which corresponds to option C.

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Let n be the last digit of your register number. Consider the initial value problem y" + 4y = 4un (t), y(0) = 0, y'(0) = 1.
a. Find the Laplace transform of the solution y(t).
b. Find the solution y(t) by inverting the transform.

Answers

To solve the initial value problem y" + 4y = 4u_n(t), where y(0) = 0 and y'(0) = 1, we will follow these steps:

a. Find the Laplace transform of the solution y(t).

The Laplace transform of the given differential equation can be obtained using the properties of the Laplace transform. Taking the Laplace transform of both sides, we get:

s^2Y(s) - sy(0) - y'(0) + 4Y(s) = 4U_n(s),

where Y(s) represents the Laplace transform of y(t) and U_n(s) is the Laplace transform of the unit step function u_n(t).

Since y(0) = 0 and y'(0) = 1, the equation becomes:

s^2Y(s) - s(0) - 1 + 4Y(s) = 4U_n(s),

s^2Y(s) + 4Y(s) - 1 = 4U_n(s).

Taking the inverse Laplace transform of both sides, we obtain the solution in the time domain:

y''(t) + 4y(t) = 4u_n(t).

b. Find the solution y(t) by inverting the transform.

To find the solution y(t) in the time domain, we need to solve the differential equation y''(t) + 4y(t) = 4u_n(t) with the initial conditions y(0) = 0 and y'(0) = 1.

The homogeneous solution to the differential equation is obtained by setting the right-hand side to zero:

y''(t) + 4y(t) = 0.

The characteristic equation is r^2 + 4 = 0, which has complex roots: r = ±2i.

The homogeneous solution is given by:

y_h(t) = c1cos(2t) + c2sin(2t),

where c1 and c2 are constants to be determined.

Next, we find the particular solution for the given right-hand side:

For t < n, u_n(t) = 0, and for t ≥ n, u_n(t) = 1.

For t < n, the particular solution is zero: y_p(t) = 0.

For t ≥ n, we need to find the particular solution satisfying y''(t) + 4y(t) = 4.

Since the right-hand side is a constant, we assume a constant particular solution: y_p(t) = A.

Plugging this into the differential equation, we get:

0 + 4A = 4,

A = 1.

Therefore, for t ≥ n, the particular solution is: y_p(t) = 1.

The general solution for t ≥ n is given by the sum of the homogeneous and particular solutions:

y(t) = y_h(t) + y_p(t)

y(t) = c1cos(2t) + c2sin(2t) + 1.

Using the initial conditions y(0) = 0 and y'(0) = 1, we can determine the values of c1 and c2:

y(0) = c1cos(0) + c2sin(0) + 1 = c1 + 1 = 0,

c1 = -1.

y'(t) = -2c1sin(2t) + 2c2cos(2t),

y'(0) = -2c1sin(0) + 2c2cos(0) = 2c2 = 1,

c2 = 1/2.

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The height of a student is measured as 1.6m to the nearest tenth of a meter. Find to one significant figure, the greatest possible percentage error

Answers

Answer: 7.4

Step-by-step explanation:

Fatimah is x years old and nadia is 3 years older than fatmah. find expression, in it's simplest form in terms of x, for the sum of the girls ages in two years time and in y years time

Answers

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

How to derive an algebraic expression from a word problem

Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:

y - x = 3 (Expression that represents age difference between Fatimah and Nadia)

x + 3 = y, where x, y > 0 and y > x. (1)

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

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In eight minutes josh was able to type 496 words what’s he typing speed per minute

Answers

Answer: 62 words per minute.

Step-by-step explanation: 496/8=62.

Answer:

62 words per minute

Step-by-step explanation:

divide 496 and 8

What is an example of slope-intercept form?.

Answers

Answer:

y = 3x + 1

Step-by-step explanation:

The equation for slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

How do you do log and inverse log?

Answers

Logarithms can be calculated using the log function in a calculator or the formula loga(x) = y, where a is the base and x is the number you want to find the logarithm of.Inverse logarithms can be calculated using the 10x key on a calculator or the formula 10^y=x, where y is the logarithm and x is the number you want to find the inverse logarithm of.

Logarithms:

To calculate the logarithm of a number, use the log function in your calculator, or use the formula loga(x) = y, where a is the base and x is the number you want to find the logarithm of.

Inverse Logarithms:

To calculate the inverse logarithm of a number, use the 10x key on your calculator, or use the formula 10^y=x, where y is the logarithm and x is the number you want to find the inverse logarithm of.

Logarithms can be calculated using the log function in a calculator or the formula loga(x) = y, where a is the base and x is the number you want to find the logarithm of. Inverse logarithms can be calculated using the 10x key on a calculator or the formula 10^y=x, where y is the logarithm and x is the number you want to find the inverse logarithm of.

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2. You have $3.25 to buy bananas. Each banana costs $0.35. How many bananas can you buy? Will you use all your money? If not, how much will you have left over? Explain your answers.

Answers

Answer:

You could buy 9 bananas

Step-by-step explanation:

No you will not use all your money because $3.25 does not divide into 0.35 evenly so you will have 10 cents left.

Explain how to solve $3^x^-^4=6$ using the change of base formula log base b of y equals log y over log b Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answers

The solution of x in the equation 3^(x -4) = 6 is x = 5.63

How to determine the solution of the equation?

The equation is given as

3^(x -4) = 6

Apply the law of indices on the expression 3^(x -4) to rewrite it

So, we have

3^x/3^4 = 6

The above equation becomes

3^x = 6 * 3^4

Evaluate the product

So, we have

3^x = 486

Take the logarithm of bot sides

xlog(3) = log(486)

Divide both sides by log(3)

x = log(486)/log(3)

Evaluate

x = 5.63

Hence, the solution of x in the equation 3^(x -4) = 6 is x = 5.63

Answers

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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solve/answer the question and help me understand this question please

thank you to all user that will help me!

Answers

Answer:

5.25 m

Step-by-step explanation:

A diagram can help you understand the question, and can give you a clue as to how to find the answer. A diagram is attached. The problem can be described as finding the sum of two vectors whose magnitude and direction are known.

understanding the direction

In navigation problems, direction angles are specified a couple of different ways. A bearing is usually an angle in the range [0°, 360°), measured clockwise from north. In land surveying and some other applications, a bearing may be specified as an angle east or west of a north-south line. In this problem we are given the bearing of the second leg of the walk as ...

N 35° E . . . . . . . 35° east of north

Occasionally, a non-standard bearing will be given in terms of an angle north or south of an east-west line. The same bearing could be specified as E 55° N, for example.

the two vectors

A vector is a mathematical object that has both magnitude and direction. It is sometimes expressed as an ordered pair: (magnitude; direction angle). It can also be expressed using some other notations;

magnitude∠directionmagnitude cis direction

In the latter case, "cis" is an abbreviation for the sum cos(θ)+i·sin(θ), where θ is the direction angle.

Sometimes a semicolon is used in the polar coordinate ordered pair to distinguish the coordinates from (x, y) rectangular coordinates.

The first leg of the walk is 3 meters due north. The angle from north is 0°, and the magnitude of the distance is 3 meters. We can express this vector in any of the ways described above. One convenient way is 3∠0°.

The second leg of the walk is 2.5 meters on a bearing 35° clockwise from north. This leg can be described by the vector 2.5∠35°.

vector sum

The final position is the sum of these two changes in position:

3∠0° +2.5∠35°

Some calculators can compute this sum directly. The result from one such calculator is shown in the second attachment:

= 5.24760∠15.8582°

This tells you the magnitude of the distance from the original position is about 5.25 meters. (This value is also shown in the first attachment.)

You may have noticed that adding two vectors often results in a triangle. The magnitude of the vector sum can also be found using the Law of Cosines to solve the triangle. For the triangle shown in the first attachment, the Law of Cosines formula can be written as ...

a² = b² +o² -2bo·cos(A) . . . . where A is the internal angle at A, 145°

Using the values we know, this becomes ...

a² = 3² +2.5² -2(3)(2.5)cos(145°) ≈ 27.5373

a = √27.5373 = 5.24760 . . . . meters

The distance from the original position is about 5.25 meters.

_____

Additional comment

The vector sum can also be calculated in terms of rectangular coordinates. Position A has rectangular coordinates (0, 3). The change in coordinates from A to B can be represented as 2.5(sin(35°), cos(35°)) ≈ (1.434, 2.048). Then the coordinates of B are ...

(0, 3) +(1.434, 2.048) = (1.434, 5.048)

The distance can be found using the Pythagorean theorem:

OB = √(1.434² +5.048²) ≈ 5.248

Find the slope of the line that passes through (23, 9) and (5, -10).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Answer:

19/18

Step-by-step explanation:

To find the slope, we can use the following formula:

$m=\frac{y2-y1}{x2-x1}$, where m is the slope, and (x1,y1), (x2,y2) are two points that the line passes through.

We are given the following points: (23,9) and (5,-10). All we have to do is plug the appropriate numbers into the formula and solve for m:

$m=\frac{-10-9}{5-23}=\frac{-19}{-18}=\frac{19}{18}$

Therefore, the slope is 19/18

Consider the following 2 person, 1 good economy with two possible states of nature. There are two states of nature j € {1,2} and two individuals, i E {A, B}. In state- of-nature j = 1 the individual i receives income Yi, whereas in state-of-nature j = 2, individual i receives income y,2. Let Gij denote the amount of the consumption good enjoyed by individual i if the state-of-nature is j. State-of-nature j occurs with probability Tt; and 11 + 12 = 1. Prior to learning the state-of-nature, individuals have the ability to purchase or sell) contracts that specify delivery of the consumption good in each state-of-nature. There are two assets. Each unit of asset 1 pays one unit of the consumption good if the state- of-nature is revealed to be state 1. Each unit of asset 2 pays one unit of the consumption good in each state-of-nature. Let dij denote the number of asset j € {1,2} purchased by individual i. The relative price of asset 2 is p. In other words, it costs p units of asset 1 to obtain a single unit of asset 2 so that asset 1 serves as the numeraire (its price is normalized to one and relative prices are expressed in units of asset 1). Individuals cannot create wealth by making promises to deliver goods in the future so the total net expenditure on purchasing contracts must equal zero, that is, 0,,1 + po 2 = 0. Individual i's consumption in state-of-nature j is equal to his/her realized income, yj, plus the realized return from his/her asset portfolio. The timing is as follows: individuals trade in the asset market, and once trades are complete, the state-of-nature is revealed and asset obligations are settled. The individual's objective function is max {714(G,1)+12u(6,2)}. 1. Write down each individual's optimization problem. 2. Write down the Lagrangean for each individual. 3. Solve for each individual's optimality conditions. 4. Define an equilibrium. 5. Provide the equilibrium conditions that characterize the equilibrium allocations in the market for contracts. 6. Let the utility function u(e) = ln(c) so that u'(c) = . Solve for the equilibrium price and allocations.
Previous question

Answers

The optimization problem for individual A is to maximize their objective function: max {7A(GA1) + 12u(A,G2)}. The Lagrangean for individual A can be written as: L(A) = 7A(GA1) + 12u(A,G2) + λ1(IA1 - DA1) + λ2(IA2 - DA2) + μ1(IA1 - pIA2) + μ2(IA2 - IA1 - IA2).

To solve for individual A's optimality conditions, we take the partial derivatives of the Lagrangean with respect to the decision variables: ∂L(A)/∂GA1 = 0, ∂L(A)/∂GA2 = 0, ∂L(A)/∂IA1 = 0, and ∂L(A)/∂IA2 = 0.

An equilibrium is defined as a set of allocations (GA1, GA2) and prices (p) such that all individuals optimize their objective functions and markets clear, i.e., the total net expenditure on purchasing contracts is zero. The equilibrium conditions that characterize the equilibrium allocations in the market for contracts are: ∑AIA1 + ∑BIB1 = 0, ∑AIA2 + ∑BIB2 = 0, and IA1 + IB1 = IA2 + IB2.

Given the utility function u(e) = ln(c), we can solve for the equilibrium price and allocations by setting the optimality conditions equal to zero and solving the resulting system of equations.

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The temperature outside changed from 94°F to 46°F over a period of eight days. If the temperature changed by the same amount each day, what was the daily temperature change?

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Answer:

6°F

Step-by-step explanation:

First, subtract 46 from 94 (94-46) and you will get 48.

Then, divide 48÷8 (because the time period is 8 days) and you will get 6.

Therefore, the daily temperature change is 6°F.

press the picture lol, i’ll mark you as brain

Answers

Answer: (1,4) is the answer

y= -x+5

y= x+3

since both expressions -x+5 and x+3 are equal to y, set them equal to each other forming an equation in x

-x+5=x+3

solve for x, so x=1

Then, substitute the given value of x into the equation y=x+3

y=1+3 which equals to y=4

Check:

Check if the ordered pair is the solution of the system of equations

4= (-1) +5

4= (1)+3

Which equals to

4=4

since all od the equalities are true, the ordered pair is the solution of the system

(x,y) = (1,4)

I’m doing this too :((

A television normally sells for $320. This week, it's on sale at %60 off the normal price. What is the sale price?

Answers

Answer:

$128

Step-by-step explanation:

60% of 320 is 192

320

- 192

128

$128 is the cost of the tv during the sale

Answer:

$192

Step-by-step explanation:

change 60% to a decimal: 0.60

then you will multiply:

0.60 × 320 = $192

Which equation can be used to solve for b?

Triangle A B C is shown. Angle B C A is a right angle and angle C A B is 30 degrees. The length of side B C is 5 centimeters, the length of B A is 10 centimeters, and the length of C A is b.

tan(30o) = StartFraction 5 Over b EndFraction

tan(30o) = StartFraction b Over 5 EndFraction

tan(30o) = StartFraction 10 Over b EndFraction

tan(30o) =

Answers

The equation can be used to solve for b is b = 5 / tan30°

What is an equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a triangle, ∠ BCA = 90°, ∠ CAB = 30°, we need to find the equation for AC,

The equation for AC(b) =

tan30° = 5/b

b = 5 / tan30°

Hence, the equation can be used to solve for b is b = 5 / tan30°

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PLSSSSS SOMEONE HELP ME!!!!!!!!
Subtract the polynomials (3^5 + 8^3) − (7^2 − 6^3). Show all work

Answers

Answer:

We can simplify each term in the polynomials and then perform the subtraction:

(3^5 + 8^3) − (7^2 − 6^3)

= 243 + 512 − 49 + 216

= 752 - 33

= 719

So, (3^5 + 8^3) − (7^2 − 6^3) = 719

Hello! :3

Correct Answer: 716

The answer below is incorrect! solved with 3^3 instead of 3^5! OOPS!!!

( 27 + 8^3) - (7^2-1x6^3)( 27 + 512 ) - (7^2-1x6^3) (539) - (7^2-1x6^3)(539) - (49-1x6^3)(539) - (49-1x216)539 - (49-216)539 - (-167)539 + 167706

Hope this helps! :)

Find the vertex of the quadratic polynomial, f(x) = 4x² -8x + 6

Answers

The equation of a parabola with vertex (h,k) is given by:

$y=a(x-h)^2+k$

Starting from the given equation, complete the square to write the function in vertex form:

$\begin{gathered} f(x)=4x^2-8x+6 \\ =4(x^2-2x)+6 \\ =4(x^2-2x+1-1)+6 \\ =4(x^2-2x+1)+4(-1)+6 \\ =4(x-1)^2-4+6 \\ =4(x-1)^2+2 \end{gathered}$

By comparing that equation with the vertex form of a parabola, we can see that h=1 and k=2.

Therefore, the vertex of the given quadratic polynomial, is:

$(1,2)$

Answer:

I think its -128x + 6

Step-by-step explanation:

solve the inequality
|7x|+3<21

Answers

Answer:

The inequality is, -18/7 less than x less than 18/7

Step-by-step explanation:

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What is the equation of the line that passes through the point (-7, -1) and has a slope of 1?

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What is the equation of the line that passes through the point (-7, -1) and has a
slope of 1?