What is the slope of the line that passes
through the points (9.8) and (8.1)?

To derive the demand function from the given utility function and endowment, we need to determine the optimal allocation of goods that maximizes utility. The utility function is U(x, y) = -e^(-x) - e^(-y), and the initial endowment is (1, 0).

To derive the demand function, we need to find the optimal allocation of goods x and y that maximizes the given utility function while satisfying the endowment constraint. We can start by setting up the consumer's problem as a utility maximization subject to the budget constraint. In this case, since there is no price information provided, we assume the goods are not priced and the consumer can freely allocate them.

The consumer's problem can be stated as follows:

Maximize U(x, y) = -e^(-x) - e^(-y) subject to x + y = 1.

To solve this problem, we can use the Lagrangian method. We construct the Lagrangian function L(x, y, λ) = -e^(-x) - e^(-y) + λ(1 - x - y), where λ is the Lagrange multiplier.

Taking partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we can find the values of x, y, and λ that satisfy the optimality conditions. Solving the equations, we find that x = 1/2, y = 1/2, and λ = 1. These values represent the optimal allocation of goods that maximizes utility given the endowment.

Therefore, the demand function derived from the utility function and endowment is x = 1/2 and y = 1/2. This indicates that the consumer will allocate half of the endowment to each good, resulting in an equal distribution.

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Answer:Jesus

Step-by-step explanation: Jesus is always the answer, kiddo

The fraud triangle is a model that describes the three key factors that must be present for fraud to occur: opportunity, rationalization, and pressure.

These factors are often represented as the three sides of a triangle, with fraud being the result at the center.

Opportunity refers to the ability of an individual to commit fraud, either due to a lack of internal controls or the ability to override existing controls. Rationalization refers to the mental process by which an individual justifies the fraudulent behavior to themselves, often by convincing themselves that it is not really wrong or that they have a valid reason for doing it. Pressure refers to the external factors that motivate an individual to commit fraud, such as financial difficulties, job insecurity, or a desire to meet performance targets.

In summary, the fraud triangle indicates that all three conditions of opportunity, rationalization, and pressure must be present for fraud to be perpetrated.

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The option A is correct, the linear equation x + y = 34. and 10x + 15y = 410 represent the the statement.

According to the statement

we have given that the

Jody earns $10 per hour babysitting And jody earns $15 per hour doing yardwork.

And she worked 34 hours and earned $410

and we have to express in the linear equation terms.

So, For this purpose,

Let x represents the number hours she babysat

Let y represents the number of hours she did yardwork

And the equations become

x + y = 34.

10x + 15y = 410

And with the help of these linear equations we find the hours which are x and y.

So, The above written equations perfectly express the given conditions in the statement.

The option A is correct, the linear equation x + y = 34. and 10x + 15y = 410 represent the the statement.

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Answer:

11 + x

i took the test

Answer:

Its D

Step-by-step explanation:

The calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

To determine the number of significant figures in the answer to the calculation (3.4876)/(4.11+1.2), we need to consider the number of significant figures in the given values and apply the rules for significant figures in mathematical operations.

First, let's analyze the number of significant figures in the given values:

- 3.4876 has five significant figures.

- 4.11 has three significant figures.

- 1.2 has two significant figures.

To perform the calculation, we divide 3.4876 by the sum of 4.11 and 1.2. Let's evaluate the sum:

4.11 + 1.2 = 5.31

Now, we divide 3.4876 by 5.31:

3.4876 / 5.31 = 0.6567037...

Now, let's determine the number of significant figures in the result.

Since division and multiplication retain the least number of significant figures from the original values, the result should be reported with the same number of significant figures as the value with the fewest significant figures involved in the calculation.

In this case, the value with the fewest significant figures is 5.31, which has three significant figures.

Therefore, the answer to the calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

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Answer: x = 9 and x  = 6

Step-by-step explanation:

\(x^2-15x+54=0\\(x-9)(x-6)\\x-9=0\\x=9\\x-6=0\\x=6\)

Therefore, x = 9 and x  = 6

The mathematical expression that shows the number of math problem left for Ernest is 16-p

Linear expressions are expression that it's highest power in of it's variable is 1. Linear expression can have more than one variables.

Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.

Ernest has 16 math problem , he has solved p out of it.

To actually know the remaining math problem left, we subtract the number he has done from the number of original problem

This means the number r of problem left = 16-p

therefore the expression is 16-p

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Answer:

this is one of the property

Step-by-step explanation:

(-2)×2=(-4)

hope it helps

Answer: The picture is black lol

Step-by-step explanation:

Answer:

9 cm^2

Step-by-step explanation:

The area of a triangle is calculated with the following formula:

1/2*b*h (b: base, h: height)

The base is given as 3 and height is 6 so

1/2*3*6 = 9 cm^2 is the answer we are looking for.

Answer:

c = d/a - b

Hope that helps

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

5(4)-2(1)=

20-2=

18

Answer:

B

Step-by-step explanation:

Answer:

\(sin(\theta_1) = \dfrac{\sqrt{357} }{29}\)

Step-by-step explanation:

The parameters of the angle θ₁ are;

The location of θ₁ = Quadrant II

cos(θ₁) = -22/29

We note the following;

1) The sine of an angle in quadrant II is positive

2) The cosine of an angle in quadrant II is negative,

2) The cos of an angle = The adjacent leg length to the reference angle divided by the hypotenuse length of a right triangle

3) With regards to the right triangle for finding cos(θ₁)

The adjacent leg length = -22 (The x-axis is negative in quadrant II)

The hypotenuse length = 29

The negative sign is obtained from the value of cosine in the quadrant

Therefore, by Pythagoras' theorem, for a right triangle, we have;

The opposite leg length to 'θ₁' = √(29² - 22²) = √(357)

\(sin\angle X = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length}\)

Therefore, we have;

\(sin(\theta_1) = \dfrac{\sqrt{357} }{29}\).

The ratio of the cooling time of Earth to the cooling time of the exoplanet is 16,777,216.

An exoplanet, also known as an extrasolar planet, is a planet that orbits a star other than the Sun, which is part of our solar system. An exoplanet is one of many planets that might exist in the universe outside of our solar system.

The ratio of the cooling time of Earth to the cooling time of the exoplanet can be determined using Stefan-Boltzmann's Law and Wien's Law.

We first need to use the Stefan-Boltzmann Law in order to calculate the cooling time.

σT⁴ = L/(16πR²)

σ(5780)⁴ = (3.846 × 10²⁶ W)/(16π(6.3781 × 10⁶)² m²)

Ratio of the exoplanet's radius to the Earth's radius:

re/rE = 8.00

Ratio of the exoplanet's mass to the Earth's mass:

me/mE = (re/re)³ = 8³ = 512 (since density is assumed to be the same for both planets)

Ratio of the exoplanet's luminosity to the Earth's luminosity:

Le/LE = (me/mE)(re/rE)² = 512(8)² = 32768

Ratio of the exoplanet's temperature to the Earth's temperature:

Te/TE = (Le/LE)¹∕⁴ = 32768¹∕⁴ = 32.0

The Wien Law can now be used to determine the ratio of the cooling times of the two planets.

(T/wavelength max)E = 2.898 × 10⁻³ m K(5780 K) = 1.68 × 10⁻⁸ m (using Earth as the comparison planet)

(T/wavelength max)e = 2.898 × 10⁻³ m K(Te)(8.00) = wavelength max (using the exoplanet)

Ratio of the wavelengths:

wavelength max,e/wavelength max,E = (Te/TE)(re/rE) = 32.0 × 8.00 = 256

Ratio of the cooling times:

cooling time,e/cooling time,E = (wavelength max,e/wavelength max,E)³ = 256³ = 16,777,216

Hence, the ratio of Earth's cooling time to the exoplanet's cooling time is 16,777,216.

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Answer:

Honestly, I have no idea what you are talking about.  I'm assuming you are just spamming the website, which you really shouldn't do.

Step-by-step explanation:

:(

Answer:

222 girls

185 boys.

Step-by-step explanation:

For every 11 pupils there are 6 girls and 5 boys.

That is 5/11 are boys and 6/11 are girls.

So number of girls in the school

= 407 * 6/11

= 2442/11

= 222 girls.

Number of boys = 407 * 5/11

= 2035/11

= 185. boys.

Check these values:

222+ 185 = 407

- correct.

The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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The formula for the volume of a square prism is given as V = s^2 * h. V = s^2 * h = 1.5^2 * 8 = 2.25 * 8 = 18 cm^3 So the volume of the square prism is 18 cubic centimeters.

this is what weegy answered

Answer:196

Step-by-step explanation:

Answer:

196

Step-by-step explanation:

Exponential expressions are just a way to write powers in short form. The exponent indicates the number of times the base is used as a factor. So in the case of 32, it can be written as 2 × 2 × 2 × 2 × 2=25, where 2 is the “base” and 5 is the “exponent”. We read this expression as “two to the fifth power”.

Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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Answer:2:15 minutes is how long he hiked

Step-by-step explanation:

Answer: 2 hours and 15 minutes

Step-by-step explanation:

Answer:

The population will be 896 turtles 6 years later ⇒ B

Step-by-step explanation:

The exponential increasing formula is y = a\((1+r)^{x}\), where

∵ There are 300 turtles

∴ a = 300

∵ The population of the turtles exponentially increases 20% each year

∴ r = 20%

→ Divide it by 100 to change it to decimal

∵ 20% = 20 ÷ 100 = 0.2

∴ r = 0.2

∵ The time is 6 years

∴ x = 6

→ Substitute these values in the exponential formula above

∵ y = 300\((1+0.2)^{6}\)

∴ y = 300\((1.2)^{6}\)

∴ y = 895.7952

→ Round it to the nearest whole number

∴ y = 896

∴ The population will be 896 turtles 6 years later

Answer:

The answer is

Step-by-step explanation:

To find an equation of a line when given the slope and a point we use the formula

\(y - y_1 = m(x - x_1)\)

From the question we have

\(y - 8 = 0(x - 4) \\ y - 8 = 0 \\\)

We have the final answer as

Hope this helps you

Answer:

9.57 moles

Step-by-step explanation:

There is 1.1  mole per liter....

1.1 M/ l * 8.7 L = 9.57 moles

Hi there!

For a line to be PARALLEL, it must contain the same slope.

The given line has a slope of 4, so we can use the point-slope formula to solve:

\(\large\boxed{y - y_1 = m(x - x_1)}\)

y1 = y-coordinate of given point

x1 = x-coordinate of given point

m = slope

Plug in the values:

\(y - 1 = 4(x - (-2))\\\\y - 1 = 4(x + 2)\)

Simplify:

\(y - 1 = 4x + 8\\\\\boxed{y = 4x + 9}\)