the system of equations below.
6x + 3y = 9
Y = -2x +3
Choices:
0
(0,0)
(9,9)
no solution
infinitely many solutions

The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.

The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:

(a) Local non-satiation:

This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.

(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:

MU1 = α * xi^(α−1) * x2^(β)

The marginal utility of x2 can be obtained as:

MU2 = β * xi^(α) * x2^(β−1)

Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.

(c) Quasi-concavity:

The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.

(d) Homotheticity:

The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.

In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.

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Answer:

1.

Step-by-step explanation:

262 2. 360 is the best a

answer I can give you ooo

Answer:

A is the correct answer

Hope this helps :)

Answer:

Step-by-step explanation:

This is because you have to substitute numbers.

So,

f(x) = 4 * 2^x

f(1) = 4 * 2^1 = 8

f(2) = 4 * 2^2 = 16

f(3) = 4 * 2^3 = 32

This shows exponential growth. Hope this helped!

Hope this helps,

Kavitha

We would expect the central 95% of autos to be found in the interval from 20 to 40 mpg.

The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, approximately 68% of the observations fall within one standard deviation of the mean, approximately 95% of the observations fall within two standard deviations of the mean, and approximately 99.7% of the observations fall within three standard deviations of the mean.

Assuming that the distribution of autos' miles per gallon (mpg) is approximately normal, we can use the empirical rule to estimate the interval in which we would expect the central 95% of autos to be found.

Then, according to the empirical rule, approximately 95% of autos should be found within 2 standard deviations of the mean. We can write:

μ - 2σ ≤ x ≤ μ + 2σ

where x represents the mpg of an individual auto.

For example, if we take a random sample of 100 autos and find that the mean mpg is 30 and the standard deviation is 5, then we can estimate the interval in which we would expect the central 95% of autos to be found as:

30 - 2(5) ≤ x ≤ 30 + 2(5)

20 ≤ x ≤ 40

Therefore, we would expect the central 95% of autos to be found in the interval from 20 to 40 mpg.

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Answer:

110.25π \(in^{3}\)

Step-by-step explanation:

The can is a circular cylinder and has the formula for the volume to be

V = \(\pi r^{2} h\)

r = 3.5 and h = 11

Since the paint is now 2 in. from the top of the can, then there are 9 in. left in the can, which means there is 9/11 of the total volume in the can.

Therefore,  \(V = (9/11)\pi (3.5^{2} )(11)\)

 we get V = (9/11)(12.25)(11)π

                 =  110.25π \(in^{3}\)

Answer:

83.8

Step-by-step explanation:

use the z-score formula:

z = (X - μ) / σ

where X is the test statistic (the grade we're trying to find in this case), μ is the mean, σ is the standard deviation.

z = (X - μ) / σ

1.6 = (X - 71) / 8

8(1.6) = X - 71

12.8 = X - 71

X = 12.8 + 71

= 83.8.

z-score of 1.6 (A grade) is grade of 83.8

Answer:

Equation Form

x = \(\frac{5}{2}\)    

y = \(-\frac{3}{2}\)

Point Form= ( \(\frac{5}{2}\) ,  \(-\frac{3}{2}\))

Explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer:

To women, it was a steed upon which they rode into a new world. All this triggered a backlash from many (male) doctors and onlookers, who cited all sorts of reasons to dissuade women from riding bikes. It would lead to not only bicycle face, but also exhaustion, insomnia, heart palpitations, headaches, and depression. During the late 19th and early 20th centuries, women began to escape some of their restrictions by riding bycicles. Despite strong opposition from men, women cycled on, and the bicycle became an instrument of change that subverted the status quo and became a powerful symbol of women's emancipation.

Step-by-step explanation:

Based on the given data, we can calculate the control limits using 3-sigma for the diameter of the auto pistons.

a) The value of x is 155.56 mm (rounded to two decimal places).

b) The value of R is 4.44 mm (rounded to two decimal places).

c) Using 3-sigma, the Upper Control Limit (UCL) for the diameter is calculated as:

UCL = x + 3R = 155.56 + 34.44 = 156.93 mm (rounded to two decimal places)

The Lower Control Limit (LCL) for the diameter is calculated as:

LCL = x - 3R = 155.56 - 34.44 = 154.19 mm (rounded to two decimal places)

d) Using 3-sigma, the Upper Control Limit for the Range (UCLR) is calculated as:

UCLR = D4 * R = 2.115 * 4.44 = 7.89 mm (rounded to two decimal places)

The Lower Control Limit for the Range (LCLR) is always 0 in this case since negative ranges are not possible.

e) If the true diameter mean should be 155 mm, the new centerline (nominal line) would be 155 mm. In this case, the UCL and LCL would be calculated using 3-sigma as follows:

UCL = Nominal + 3R = 155 + 34.44 = 156.37 mm (rounded to two decimal places)

LCL = Nominal - 3R = 155 - 34.44 = 153.63 mm (rounded to two decimal places)

Please note that the control limits calculated using 3-sigma assume a normal distribution and the data follows the same pattern in the future.

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The complete question is:

What is the value of x? = x= 155.56 mm (round your response to two decimal places). b) What is the value of R? R= 4.44 mm (round your response to two decimal places). c) What are the UCL, and LCL; using 3-sigma? Upper Control Limit (UCL) = 156.93 mm (round your response to two decimal places). Lower Control Limit (LCL) = 154.19 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCLR)= 7.89 mm (round your response to two decimal places). Lower Control Limit (LCLR)= 0.99 mm (round your response to two decimal places). e) If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCL and LCL? Upper Control Limit (UCL)= 156.37 mm (round your response to two decimal places). Lower Control Limit (LCL;)= 153.63 mm (round your response to two decimal places). Refer to Table 56.1-Factors for Computing Control Chart Limits (3 sigma) for this problem Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day 1 2 3 4 5 Mean x (mm) 150.9 153.2 153.6 153.5 154.6 Range R (mm) 4.0 4.8 4.1 4.8 4.5

Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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Answer:

Not sure sorry!

Wish that I could help!

Step-by-step explanation:

Answer:

Wait do we actually have to answer it? XD

Step-by-step explanation:

The value of quadratic function is,

⇒ y = 9x² + 54x - 63

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The equation is,

⇒ y = 9 (x - 1) (x + 7)

Now, We can find the quadratic equation as;

⇒ y = 9 (x - 1) (x + 7)

⇒ y = 9 (x² + 7x - x - 7)

⇒ y = 9 (x² + 6x - 7)

⇒ y = 9x² + 54x - 63

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The value of m<2 = 107

Given:

m<SOX = 160

m<1 = x+14

m<2 = 3x - 10

x + 14 + 3x - 10 = 160

4x + 14 - 10 = 160

4x + 4 = 160

4x = 160 - 4

4x = 156

divide by 4 on both sides

4x/4 = 156/4

x = 39

m<2  = 3*39 - 10

= 117 - 10

= 107

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Answer:

4,500 hope this help

Step-by-step explanation:

Answer: 60

8x15 / 2

Step-by-step explanation:

Answer:

40 units

Step-by-step explanation:

Using Pythagoras Theorem to find the hypotenuse:

\( \sqrt{ {15}^{2} + {8}^{2} } \)

\( = \sqrt{289} \)

= 17 units

The perimeter

= 15+8+17

= 40 units

Answer:

=6x3+15x2y−46x2−115xy+80x+200y

Step-by-step explanation:

Answer: $460

Step-by-step explanation:

It cost $180/per week. The family will have the car for 2 weeks, so:

($180)(2)= 360

Additionally, it is $0.25 per mile. The family traveled 400 miles, so:

($0.25)(400)= 100

In total:

$360 + $100 = $460

answer:

\({ \tt{ \cos(100x) + \frac{4}{3} = 0}} \\ { \tt{ \cos(100x) = - \frac{4}{3} }} \\ { \tt{100x = { \cos }^{ - 1} ( - \frac{4}{3} )}} \\ { \tt{invalid \: answer}}\)

To determine if all the colors are equally likely, compare the expected probabilities with the observed probabilities. If they are close, then the colors are likely equally likely.

To determine if all the colors in a bag of M&Ms are equally likely based on the probabilities, you need to compare the observed probabilities with the expected probabilities.

First, calculate the expected probability for each color by dividing the total number of M&Ms of that color by the total number of M&Ms in the bag. For example, if there are 10 red M&Ms out of 50 total M&Ms, the expected probability for red would be 10/50 = 1/5.

Next, compare the expected probabilities with the observed probabilities. If the observed probabilities are close to the expected probabilities for all the colors, then it suggests that the colors are equally likely. However, if there is a significant difference between the observed and expected probabilities, it indicates that the colors are not equally likely.

For example, if the observed probability for red is 1/10 instead of 1/5, it suggests that red is less likely compared to what would be expected if the colors were equally likely.

In summary, to determine if all the colors are equally likely, compare the expected probabilities with the observed probabilities. If they are close, then the colors are likely equally likely.

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The possible solution set for the system is (- 1, 4) and (4, - 1).

Given are the equations as -

x + y = 3

x² + y² = 17

Refer to the graph of the function attached. The points of intersection represents the possible solution set.

Therefore, the possible solution set for the system is (- 1, 4) and (4, - 1).

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Answer:

the perimeter of a rectangle

p= 2L + 2W

Answer:

Similar-AA

Step-by-step explanation:

If you know 2 angles of the triangle you automatically know the third. If all the corresponding angles of two triangles are the same, they are similar.

(p.s. This sign ~ means similar)

Answer:

the first one is correct.

Step-by-step explanation:

a function is where a x value only has ONE y value. In the last one the x value 6 had more than one y value and in the second one -2 had more than one y value

Answer:

A = length * width

A = 5 (x+2)

A = 5x+10

I'm SO SORRY

Answer:

y=-3x-3      I think

Step-by-step explanation:

To determine the constant amount that can be withdrawn each year for 20 years, we need to calculate the annuity payment using the present value of an annuity formula.

Inherited amount: RM300,000

Interest rate: 7% per year

Number of years: 20

Using the present value of an annuity formula:

PV = P * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present value (inherited amount)

P = Annuity payment (constant amount to be withdrawn each year)

r = Interest rate per period (7% or 0.07)

n = Number of periods (20 years)

Plugging in the values:

300,000 = P * [(1 - (1 + 0.07)^(-20)) / 0.07]

Solving this equation, we find that the constant amount that can be withdrawn each year is approximately RM15,000.

Therefore, the correct answer is A. RM15,000.

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Raquel might submit an application for finance or a loan, purchase a reconditioned or used computer, or borrow one from a friend or relative. Making a budget and carefully weighing her alternatives can help her save money for a computer.

If Raquel needs to buy a computer for her new job and doesn't have any cash to pay for it, there are a few options she could consider.

The first option would be to apply for a loan or financing. Many electronics retailers offer financing options with little or no interest, allowing Raquel to make payments over time without having to pay a large amount upfront.

Another option is to look for a used or refurbished computer. This could be a cheaper alternative to buying a brand new computer, and it may be possible to find one that is still in good condition. Raquel could try checking online marketplaces like Craigslist or eBay, or local secondhand shops or computer repair stores. However, she should make sure to do her research and buy from a reputable seller.

Lastly, Raquel could consider borrowing a computer from a friend or family member. This could be a temporary solution until she is able to save up enough money to buy her own computer.

Overall, it's important for Raquel to carefully consider her options and choose the one that works best for her situation. It may be helpful for her to make a budget and prioritize her expenses to see where she can cut back in order to save money for a computer.

Summary: Raquel could apply for a loan or financing, buy a used or refurbished computer, or borrow one from a friend or family member. She should carefully consider her options and make a budget to save money for a computer.

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Answer:

540

Step-by-step explanation:

If you divide 540 by 100 (100%) you get 5.4 then multiply it by 10 (10%) to get 54 again. THIS WAS TO CHECK TO GET: 10% or 100% is 10 so multiply 54•10=540

Hope this helps! ;-)

Answer:

Disagree.

If you rotate the octagon 90° it will look the same.

good luck, i hope this helps :)

Answer:

Disagree

Step-by-step explanation:

If you have any shape and you rotate it 90 degrees, it moves down and to the right, not onto itself.