Which is a correct first step in solving 5 - 2x < 8x - 3?
5 < 6x-3
3x < 8x-3
5 < 10x - 3
2 - 2x < 8x

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:

F(2x+3) = 12/(2x+3) +1/2

Step-by-step explanation:

Put the argument of the function where the variable is. You can simplify if you want, but the original function definition is not simplified, so we assume it is not required.

F(x) = 12/x + 1/2

Put (2x+3) where x is:

F(2x+3) = 12/(2x+3) + 1/2

12/k+1/2

24/a+1/2

12/x-1+1/2

12/2x+3+1/2

Answers should be correct, respectively (to the order of ur questions)

Answer:

n = -27

Step-by-step explanation:

"n" is the number we want to find and we can find it using the equation, n/9 + 7 = 4

Solving for n gives us n = -27

Answer: C. 85°

Step-by-step explanation:

Answer:

I look lik dis almost dreads and then them types of braces and my eye brows look like that and I got a tattoo on my face but my eyes are blue and I have contacts so no more glasses

Answer:

(x+4)+(2x)

Step-by-step explanation:

Answer

\(168in^{2}\)

Step-by-step explanation:

SA=2(wl+hl+hw)

2·(6·2+9·2+9·6)

=168

Answer:

C

because it looks right

Answer:

1/36

Step-by-step explanation:

On the first cube, there is a 1/6 probability to roll a 1. On the second cube, theres is a 1/6 probability to roll a 6

Multiply the two fractions and it would equal 1/36

There would be a 1/36 probability.

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

We can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

A 95% confidence interval for the population mean can be constructed using the t-distribution when the sample size is small (<30) or the population standard deviation is unknown.

In this case, we have a random sample of 46 people with a mean body mass index (BMI) of 27.2 and a standard deviation of 6.0.

Thus, we need to use the t-distribution to construct the confidence interval.

The formula for the confidence interval is as follows:

Upper limit of the confidence interval:27.2 + (2.013) (6.0/√46) = 29.032Lower limit of the confidence interval:27.2 - (2.013) (6.0/√46) = 25.368

Therefore, the 95% confidence interval for the population mean BMI is (25.368, 29.032).

This means that we can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

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Discrete-data is a category of quantitative information that has countable or finite values.

This indicates that there are no intermediate values between the precise numerical values that can be used to convey the data; only those values can be used. The number of siblings a person has, the number of pets a home has, and the number of individuals in a room are all examples of discrete data.

Numerous statistical methods, such as measures of central tendency like the mean, median, and mode, as well as measures of dispersion like range and standard deviation, can be used to analyse discrete data. Additionally, discrete data can be displayed graphically using tools like bar charts and frequency histograms.

A discrete data set is the number of stories in a skyscraper in Manhattan. A continuous data set, on the other hand, can be divided into ever-smaller pieces and can take on any value within a range. Therefore (b), "A discrete data set because the possible values can be counted."

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The area of the regular pentagon is 252.7m²

The formula that is used for calculating the area of a regular pentagon is expressed with the equation;

A = 5/2 x s x a

where the parameters are;

Apothem is the line from the center of the pentagon to a side, intersecting the side at 90 degrees right angle.

apothem,a = s/2 tan (180/n)

Substitute the values

Apothem, a = 7.6/2 tan 16

a = 7.6/0.57 = 13.3m

Substitute the values, we get;

Area = 5/2 × 7.6 × 13.3

Multiply the values, we have;

Area = 505. 4/2

Divide the values, we get;

Area = 252.7 m²

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Answer:  Press this link to get your answer -)

Step-by-step explanation:

The ratio is simply the fractional representation of two values in their simplest form. The ratio of Cell A to Cell B is 20 which means that the size of Cell A is 20 times the size of Cell B.

Given that :

Cell size A = \(Cell A = 0.0005\times 10^{-5}\\\\Cell B = 0.0025\times10^{-7} \\\\Ratio = \frac{Cell A }{Cell B} \\\\Ratio = \frac{0.0005 \times 10^-5}{0.0025 \times 10^-7}\)

\(Ratio = 20\)

Therefore, the ratio of the size of Cell A to the size of Cell B is 20 : 1, which can be interpreted to mean that cell A is 20 times larger than cell B.

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Answer:

\(\Huge \boxed{\mathrm{d}}\)

Step-by-step explanation:

y is equal to $1.67 per pounds of peanuts

pounds of peanuts = x

y is equal to $1.67 per x

per is for each

y = $1.67 × x

The equation that correctly describes this relation is option d.

Answer:

The answer is B.

Step-by-step explanation:

Answer:

The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.

The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115

Step-by-step explanation:

The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.

The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.

The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.

The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115

a)  [T] =

|3 0 1|

|-2 1 0|

|-1 2 4|

b)  Since T is both injective and surjective, it is invertible. Moreover, we know that its inverse is given by T^(-1)(a,b,c) = A^(-1)(a,b,c), where A^(-1) is the inverse of the matrix [T] found in part (a).

a) To find [T], we need to apply T to each of the standard basis vectors e1 = (1,0,0), e2 = (0,1,0), and e3 = (0,0,1), and write the resulting vectors as columns of a matrix. We have:

T(e1) = (3(1) + 0, -2(1) + 0, -(1) + 2(0) + 4(0)) = (3,-2,-1)

T(e2) = (3(0) + 0, -2(0) + 1, -(0) + 2(1) + 4(0)) = (0,1,2)

T(e3) = (3(0) + 1, -2(0) + 0, -(0) + 2(0) + 4(1)) = (1,0,4)

Therefore, [T] =

|3 0 1|

|-2 1 0|

|-1 2 4|

b) To show that T is invertible, we need to show that it is both injective (one-to-one) and surjective (onto).

Injectivity: Suppose that T(x,y,z) = T(x',y',z') for some vectors (x,y,z) and (x',y',z'). Then we have:

(3x+z, -2x+y, -x+2y+4z) = (3x'+z', -2x'+y', -x'+2y'+4z')

This leads to the following system of linear equations:

3x + z = 3x' + z'

-2x + y = -2x' + y'

-x + 2y + 4z = -x' + 2y' + 4z'

We can rewrite this system in matrix form as Ax = B, where

A =

|3 0 1|

|-2 1 0|

|-1 2 4|

x =

|x|

|y|

|z|

and

B =

|3x' + z'|

|-2x' + y'|

|-x' + 2y' + 4z'|

The coefficient matrix A is the same as [T], and we know that it is invertible (since its determinant is nonzero, as we will see shortly). Therefore, we can write x = A^(-1)B. This gives:

|x|     | 2x' + z'|

|y|  =  |-x' + y' |

|z|     | x'      |

Since x', y', and z' are arbitrary, we have shown that T(x,y,z) = T(x',y',z') implies (x,y,z) = (x',y',z'). Thus, T is injective.

Surjectivity: To show that T is surjective, we need to prove that for any vector (a,b,c) in R^3, there exists a vector (x,y,z) in R^3 such that T(x,y,z) = (a,b,c). In other words, we need to find solutions to the system of linear equations

3x + z = a

-2x + y = b

-x + 2y + 4z = c

We can write this system in matrix form as Ax = B, where

A =

|3 0 1|

|-2 1 0|

|-1 2 4|

x =

|x|

|y|

|z|

and

B =

|a|

|b|

|c|

We want to show that there exists a solution for any choice of a, b, and c. This is equivalent to showing that the augmented matrix [A|B] has full rank, which in turn is equivalent to showing that det([A|B]) is nonzero.

Using row reduction, we can find that

det([A|B]) = 17a - 4b + c

Since this expression is a linear combination of a, b, and c with nonzero coefficients, it is nonzero for any choice of (a,b,c). Therefore, [A|B] has full rank, and we can find a unique solution x = A^(-1)B for any (a,b,c). This shows that T is surjective.

Since T is both injective and surjective, it is invertible. Moreover, we know that its inverse is given by T^(-1)(a,b,c) = A^(-1)(a,b,c), where A^(-1) is the inverse of the matrix [T] found in part (a).

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Answer:

7

Step-by-step explanation:

\(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

\(\sqrt{((-1)-6)^{2} +(8-8)^{2} }\)

simplify to get 7 as answer

The distance between (6,8) and (-1,8) is 7.

It is required to find the distance between each points.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

By the use the distance formula to find the distance between (6,8) and (-1,8).

∵The distance between two points is given by

=\(\sqrt{(x_{2}-x_{1} )^{2}+ (y_{2}-y_{1} )^{2} } \\\\\)

Distance between the point (6,8) and origin(-1,8) =

\(\sqrt{(-1-6 )^{2}+ (8-8 )^{2} } \\\\=\sqrt{(-7 )^{2}+ (0 )^{2} }\\\\=7\)

Hence, the distance between (6,8) and (-1,8) is 7.

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Answer:

x = 65

Step-by-step explanation:

The opposite angles of a cyclic quadrilateral sum to 180° , then

x + 115 = 180 ( subtract 115 from both sides )

x = 65

Answer:

given,triangle EFG is congruent to triangle HIJ,THEIR corresponding sides are equal,

so, 10x=x+45

10x_x=45

or,9x=45

therefore , x=5

again,

3y = y+14

or, 3y_y=14

or, y=14/2

therefore the value of y is 7.

so the value of x is 5 and y is 7.

hope its helpful to uh...

900 miles

1) Since when we talk about linear scale drawings, Then we must consider the following ratio:

2) So let's pug into that the given data:

3) So the actual distance from Denver to Chicago is 900 miles

Answer: 128 hours

Step-by-step explanation:

The probability that an integer in the set is divisible by 2 and not divisible by 3 is (d) 1/2.

The set { 1 , 2 , 3 , … , 100 } contains integers from 1 to 100, inclusive. To find the probability that an integer is divisible by 2 and not divisible by 3, we need to determine the number of integers that meet this condition and divide it by the total number of integers in the set.

The integers divisible by 2 are {2, 4, 6, ..., 100}. The total number of integers divisible by 2 is 50, as every other number is divisible by 2.

The integers divisible by 3 are {3, 6, 9, ..., 99}. The total number of integers divisible by 3 is 33.

To find the integers that are divisible by 2 and not divisible by 3, we can find the set difference between the two sets: {2, 4, 6, ..., 100} - {3, 6, 9, ..., 99}. This set is {2, 4, 8, ..., 98, 100}.

The total number of integers in this set is 50, the same as the number of integers divisible by 2.

Therefore, the probability that an integer in the set is divisible by 2 and not divisible by 3 is 50/100 = 1/2, which can be expressed as the fraction (d) 1/2.

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The closest that the family will come to the waterfall while on the road is 5.6 miles.

To solve this problem, we can use the law of cosines. Let x be the distance that the family travels from the point where the bearing is S71E to the point where the bearing is S35E, and let d be the distance from the family's starting point to the waterfall.
We have:
cos(71) = d/x
cos(35) = d/(x+8)
Multiplying both sides of the first equation by x and both sides of the second equation by (x+8), we get:
d = x cos(71)
d = (x+8) cos(35)
Setting the right-hand sides of these equations equal to each other and solving for x, we get:
x cos(71) = (x+8) cos(35)
x = 8 cos(35)/(cos(71)-cos(35))
Plugging this into the first equation above, we get:
d = x cos(71) = 8 cos(35) cos(71)/(cos(71)-cos(35))
This gives us the distance from the family's starting point to the waterfall. To find the closest distance that the family will come to the waterfall while on the road, we need to subtract the radius of the waterfall from this distance. Let's assume that the radius of the waterfall is 50 feet.
The closest distance that the family will come to the waterfall while on the road is:
d - 50 = 8 cos(35) cos(71)/(cos(71)-cos(35)) - 50
This is approximately equal to 5.6 miles. Therefore, the closest that the family will come to the waterfall while on the road is 5.6 miles.

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Answer:

x=-5

Step-by-step explanation:

-2x-41=5x-6

-35=7x

-5=x

Hello there!

-2x - 41 = 5x - 6

Move the 41 over by adding 41 to both sides.

-2x = 5x + 35

Move the 5x by subtracting it from both sides.

-7x = 35

Divide by -7 to get x.

-7/-7 = 35/-7

x = -5  

Therefore, x would equal -5.

Answer:

The sale price is $107.25

Answer:

[See Below]

Step-by-step explanation:

✦ Formula = √area

  ✧ √484 = 22

✦ Check: 22 x 22 = 484

So the side length is 22.

~Hope this helps Mate. If you need anything feel free to message me.

Answer:

C 120

Step-by-step explanation:

Answer:

\(60\)

Step-by-step explanation:

\(Let\ the\ constant\ of\ proportionality\ between\ the\ angles\ be\ x\\Hence,\\\angle 1=3x\\\angle 2=4x\\\angle 3=5x\\\angle 4=6x\\Hence,\\We\ know\ through\ the\ Angle\ Sum\ Property\ Of\ A\ Quadrilateral\ that\ \\'The\ Sum\ Of\ All\ The\ Interior\ Angles\ Of\ A\ Quadrilateral\ is\ 360'.\\Hence,\\\angle 1+\angle 2+\angle 3+\angle4=360\\Hence,\\3x+4x+5x+6x=360\\7x+11x=360\\18x=360\\x=360/18\\x=20\\Now,\\From\ the\ observations\ we\ know\ that,\\\)

\(\angle4\ with\ a\ measure\ of\ 6x\ is\ the\ largest\ angle.\\While, \angle1\ with\ a\ measure\ of\ 3x\ is\ the\ smallest.\\Hence,\\6x-3x\\=3x\\As\ x=20,\\3x=3*20=60\)

Answer:

300kg

Step-by-step explanation:

240(25/100)

240(.25) = 60

25% of 240 = 60, so add that 60 to get an extra 25% for this month

240 + 60 = 300

The x-coordinate of P is 5 and the y-coordinate of P is 3.333.

To find the x- and y-coordinates of point P on the directed line segment from point A to point B, such that P is two-thirds the length of the line segment from A to B, we can use the following formula:

P = A + (2/3)(B-A)

Where A and B are the coordinates of the starting and ending points of the line segment, and P is the point we are trying to find the coordinates for.

For example, if the coordinates of A are (3,4) and the coordinates of B are (6,8), then the coordinates of P would be:

P = (3,4) + (2/3)((6,8) - (3,4)) = (3,4) + (2/3)((3,4)) = (3,4) + (2/3)(3,4) = (3,4) + (2,8/3) = (3,4) + (2,8/3) = (5,10/3) = (5,3.333)

So the x-coordinate of P is 5 and the y-coordinate of P is 3.333.

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A researcher will pose all of these related to sampling. So, the correct answer is all of the questions

The first question is related to the applicability of the findings of study which are typically beyond the data sources that are selected for study

The second question is related to the fact that sample of participants selected for the study reflects the diversity of the actual population to which extent

The third question relates to identifying the individuals which will be available for the study and it will consider different factors such as their experiences

The fourth question is not that much relevant as it as related with depth and the precision of the findings of the study

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