15 points help please and will give you brainlist!!!

Given that a consumer with u(x,y)=x^3 y^2 pays

px=3,

py =4. Utility is maximized when

y=2We have to determine the consumer's income.

Let I be the income of the consumer. Then the consumer's budget constraint can be represented aspx x+py y=I, where px=3 and

py=4. Hence we have3x+4y

=I ................

(1)From the utility function, the consumer's marginal rate of substitution is given byMRS = (∂u/∂x)/(∂u/∂y)

= 2x^2/3y^2Setting this equal to the price ratio py/px

= 4/3, we get2x^2/3y^2

= 4/3or x^2/y^2

= 2Substituting y

=2 (since utility is maximized when y

=2), we getx^2/4

= 2or x^2

= 8Hence, x

= ±2√2.

Substituting this in equation (1), we get3(±2√2)+4(2) = Ior I

= 14 ± 6√2Since I is the income, it cannot be negative. Hence the income is given byI

= 14 + 6√2.

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Answer:

it should be 4.5

Step-by-step explanation:

Answer:

Width of screen =57.44 cm

Step-by-step explanation:

Please refer to the attached image:

The TV screen is usually in the form of a rectangle.

The diagonal of the TV is termed as the screen size.

Size is given to be 70 cm

Height = 40 cm

As per the attached image:

BC = 40 cm

BD = 70 cm

Pythagoras theorem is given as:

\(\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Height}^{2}\)

Using pythagoras theorem in \(\triangle BDC\):

\(BD^{2}= BC^{2}+ CD^{2}\)

\(70^{2}= 40^{2}+ CD^{2}\\\Rightarrow CD^{2} =4900 - 1600\\\Rightarrow CD^{2} =3300\\\Rightarrow CD =57.44 cm\)

Hence, width of screen, CD =57.44 cm

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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Side a is 2.5 inches long, side b is 5 inches long and side c is 6.5 inches long. Therefore, option C is the correct answer.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, scale factor =2:1

Scale drawing to object the scale factor is 2:1.

Now,

a=1/2 *5 =2.5 inches

b= 1/2 *10 = 5 inches

c= 1/2 * 13 = 6.5 inches

Therefore, option C is the correct answer.

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Maclaurin series of `f(x)` is given by:f(x) = `f(0)` + `f'(0)x` + `(f''(0)/2!) x²` + `(f'''(0)/3!) x³` + `(f⁴(0)/4!) x⁴` + `(f⁵(0)/5!) x⁵` + `(f⁶(0)/6!) x⁶` = `0 + 0x + 0x² + 0x³ + 0x⁴ + 0x⁵ + (7200/6!)x⁶` = `10x⁶`

Answer: `10x⁶`.

The given function is `f(x) = x⁶ sin(10x⁵)`. We need to find the Taylor series of `f` centered at `0` (Maclaurin series of `f`).

Formula used: The Maclaurin series for `f(x)` is given by `f(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + ...... + (f^n(0)/n!)x^n`.

Here, `f(0) = 0` because `sin(0) = 0`.

Differentiating `f(x)` and its derivatives at `x = 0`:`f(x) = x⁶ sin(10x⁵)`

First derivative: `f'(x) = 6x⁵ sin(10x⁵) + 50x¹⁰ cos(10x⁵)`

Differentiate `f'(x)`

Second derivative: `f''(x) = 30x⁴ sin(10x⁵) + 200x⁹ cos(10x⁵) - 250x¹⁰ sin(10x⁵)`

Differentiate `f''(x)`

Third derivative: `f'''(x) = 120x³ sin(10x⁵) + 1800x⁸ cos(10x⁵) - 2500x⁹ sin(10x⁵) - 5000x²⁰ cos(10x⁵)`

Differentiate `f'''(x)`

Fourth derivative: `f⁴(x) = 360x² sin(10x⁵) + 7200x⁷ cos(10x⁵) - 22500x⁸ sin(10x⁵) - 100000x¹⁹ cos(10x⁵) + 100000x²⁰ sin(10x⁵)`

Differentiate `f⁴(x)`

Fifth derivative: `f⁵(x) = 720x sin(10x⁵) + 36000x⁶ cos(10x⁵) - 112500x⁷ sin(10x⁵) - 1900000x¹⁸ cos(10x⁵) + 2000000x¹⁹ sin(10x⁵)`

Differentiate `f⁵(x)`

Sixth derivative: `f⁶(x) = 7200 cos(10x⁵) - 562500x⁶ cos(10x⁵) + 13300000x¹⁷ sin(10x⁵)`

Evaluate at `x = 0`:

The derivatives of `f(x)` evaluated at `x = 0` are:f(0) = 0f'(0) = 0f''(0) = 0f'''(0) = 0f⁴(0) = 0f⁵(0) = 0f⁶(0) = 7200

Maclaurin series of `f(x)` is given by:f(x) = `f(0)` + `f'(0)x` + `(f''(0)/2!) x²` + `(f'''(0)/3!) x³` + `(f⁴(0)/4!) x⁴` + `(f⁵(0)/5!) x⁵` + `(f⁶(0)/6!) x⁶` = `0 + 0x + 0x² + 0x³ + 0x⁴ + 0x⁵ + (7200/6!)x⁶` = `10x⁶`

Answer: `10x⁶`.

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Answer: 51

Step-by-step explanation: 24^2+45^2=C

24*24=576

45*45=2025

576+2025=2601

Square root of 2601 is 51

The equation that shows the product of a square matrix A and its identity matrix as A is A * I = A.

In matrix multiplication, when a matrix is multiplied by an identity matrix, the resulting matrix is the same as the original matrix. An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. The size of the identity matrix is determined by the size of the original matrix.

By multiplying a square matrix A by the identity matrix I, each element of A is multiplied by the corresponding element of I, which is 1 if the positions are on the diagonal and 0 otherwise. Since multiplying any number by 1 gives the same number, the resulting matrix will be equal to the original matrix A. Therefore, the equation A * I = A expresses this relationship.


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Answer:

247 horses

Explanation:

Key Info: 225 horses this year and this is 22 horses fewer than last year

We know that fewer means it is subtraction, but since we don't know how many horses were there last year we do the opposite which is addition.

In this case the inverse or opposite equation is 225 + 22 = h.

After adding this up you should get 247 horses were there last year.

There are 247 horse counts last year.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

A rancher counted 225 horses on the range, which is 22 fewer than last

year.

let h be number of horses counted last year.

Then, the number of horses count

h - 22 = 225

add 22 on both side

h -22 + 22= 225 + 22

h = 247

Hence, there are 247 horse counts last year.

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The given null hypothesis statement a. true, statement b. true and finally statement c. true.

a. False. Rejection of the null hypothesis using ANOVA only tells us that at least one group mean is different from the others, but it doesn't necessarily mean that all means are different from each other. Additional post-hoc tests, such as Tukey's HSD or Bonferroni, are needed to identify which specific means are different from each other.

b. True. If the null hypothesis is rejected using ANOVA, it means that there is significant variability between the groups. This variability is measured by the F-statistic, which is the ratio of between-group variability to within-group variability. A high F-statistic indicates that the standardized variability between groups is higher than the standardized variability within groups.

c. True. If the null hypothesis is rejected using ANOVA, it means that there is at least one significant difference between the means of the groups. Pairwise comparisons can be conducted using post-hoc tests to identify which specific pairs of means are significantly different. However, it's important to adjust the significance level for multiple comparisons to avoid making Type I errors.

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Answer:

200.96

Step-by-step explanation:

So, we have to find the area of both.

The area for the mat is

(pi)12^2=3.14x144. However, since it is HALF a circle, we divide it by two.

So, 226.08

Next, the water bowl.

(3.14)4^2=50.24.

226.08-25.12=200.96

I may be wrong!

The matches between the angles of rotation and the resulting vector matrices are:

1. 45 degrees: [7√2, 7√2]

2. 90 degrees: [2, -2]

3. 180 degrees: [-6, 2]

To determine the resulting vector matrices after rotating the vector [6, -2] at different angles, we need to apply rotation matrices. The rotation matrix for a given angle θ is:

R(θ) = [cos(θ), -sin(θ)]

[sin(θ), cos(θ)]

Now, let's match the angles of rotation with the corresponding vector matrices:

1. 45 degrees:

R(45°) = [√2/2, -√2/2]

[√2/2, √2/2]

The resulting vector matrix after rotating [6, -2] by 45 degrees is:

[√2/2 * 6 + -√2/2 * -2, √2/2 * -2 + √2/2 * 6] = [7√2, 7√2]

2. 90 degrees:

R(90°) = [0, -1]

[1, 0]

The resulting vector matrix after rotating [6, -2] by 90 degrees is:

[0 * 6 + -1 * -2, 1 * -2 + 0 * 6] = [2, -2]

3.180 degrees:

R(180°) = [-1, 0]

[0, -1]

The resulting vector matrix after rotating [6, -2] by 180 degrees is:

[-1 * 6 + 0 * -2, 0 * -2 + -1 * 6] = [-6, 2]

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Answer:

$ 7,299.92

Step-by-step explanation:

A = $ 7,299.92

A = P + I where

P (principal) = $ 6,000.00

I (interest) = $ 1,299.92

Answer:

80y-24z

Step-by-step explanation:

Thomas has 10 pound of meat. He used 0.14 pound of meat to make one hamburger, he can make 71 hamburger with the meat he has.

Thomas has in total 10 pounds of meat

In making one hamburger 0.14 pound of meat is used,

So the amount of hamburger made with the remaining meat is

10 - 0.14 = 9.86 pound

So, 9.86/0.14 = 70.42 ≈ 70.

So in total of 70 Hamburgers can be made with the meat Thomas has.

An object or event's attributes are quantified through measurement so that they can be compared to those of other things or occurrences. Measurement, then, is the process of establishing how big or little a physical quantity is in relation to a fundamental reference quantity of the same kind.

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The average productivity of this production process is approximately 1.96 units per labor hour.

The average productivity, in terms of the average number of units per labor hour, for a production process can be determined using the expected value approach. In this case, the random variable X represents the number of units produced each week, with corresponding probabilities. The average production, or expected value, can be calculated by summing each production value multiplied by its probability. Finally, the productivity can be obtained by dividing the average production by the number of labor hours needed.

In this scenario, the production values are 99, 104, and 116, with corresponding probabilities of 0.1, 0.7, and 0.2, respectively. To find the average production, we multiply each production value by its probability and sum the results:

Average production = (99 * 0.1) + (104 * 0.7) + (116 * 0.2) = 9.9 + 72.8 + 23.2 = 105.9

Given that the number of labor hours needed is 54 units per labor hour, we can calculate the average productivity:

Productivity = Average production / Labor hours = 105.9 / 54 ≈ 1.96

The average productivity of this production process is approximately 1.96 units per labor hour.

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Answer: They look right to me

Step-by-step explanation:

Division is one of the four fundamental arithmetic operations. The number of machines that will be needed to produce 1,984 printers in a day is 32 machines.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that 20 machines produce 1,240 printers in a day. Therefore, the rate of production for a single machine can be written as,

Rate of production for a day = 1240/20 = 62 printer per machine

Now, the number of machines that will be needed to produce 1,984 printers in a day is,

Rate of production for a day = 1,984 / Number of machine

62 = 1984 / Number of machine

Number of machines = 32 machines

Hence, the number of machines that will be needed to produce 1,984 printers in a day is 32 machines.

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1. The base pay Carter makes regardless of computer sales is $100

2. The linear relationship that shows the sales will be P = 100 + 10x

From the information given, Carter is a salesperson who sells computers at an electronics store and he makes a base pay amount each day and then is paid a commission for every computer sale he makes.

The starting salary is $100. This is the base pay.

The commission given is $10 per good sold. Therefore, the expression will be:

= 100 + 10x

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Using the Bisector Theorem, the length of DE is 4y + 13 if we bisect (Line Over DE) at point R, DR = 2y + 9, and RE = 3y – 1.

Since l bisects DE at point R, we can use the segment bisector theorem, which states that the ratio of the lengths of the two segments is equal to the ratio of the lengths of the two other segments:

DR/RE = DE/ER

Substituting DR = 2y + 9 and RE = 3y - 1, we get:

(2y + 9)/(3y - 1) = DE/ER

Since R is the midpoint of DE, we have ER = DR = 2y + 9. Substituting this into the equation above, we get:

(2y + 9)/(3y - 1) = DE/(2y + 9)

Cross-multiplying, we get:

DE = (2y + 9)²/(3y - 1)

Expanding the numerator, we get:

DE = (4y² + 36y + 81)/(3y - 1)

Simplifying the expression, we get:

DE = 4y + 13

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Answer:

d

Step-by-step explanation:

The number of terms required to give a sum of 960 is 40.

The given problem involves an arithmetic progression. An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, the arithmetic progression consists of positive integer terms.

The sum of the first 10 terms of the arithmetic progression is equal to the sum of the 20th, 21st, and 22nd terms.
We need to find out how many terms are required to give a sum of 960, considering that the term is less than 20.

To solve this problem, we can use the formula for the sum of an arithmetic progression:

Sn = (n/2) * (a + l)
Where:
- Sn represents the sum of the first n terms
- n represents the number of terms
- a represents the first term
- l represents the last term

First, let's find the common difference (d) of the arithmetic progression. Since the terms are positive integers, the common difference is a positive integer as well.

To find the common difference, we can use the given information that the sum of the first 10 terms is equal to the sum of the 20th, 21st, and 22nd terms.

Let's assume the first term of the arithmetic progression is a, and the common difference is d.

The sum of the first 10 terms can be expressed as:
S10 = (10/2) * (a + (a + 9d)) = 10a + 45d

The sum of the 20th, 21st, and 22nd terms can be expressed as:
S20 + S21 + S22 = [(20/2) * (2a + (20 - 1)d)] + [(21/2) * (2a + (21 - 1)d)] + [(22/2) * (2a + (22 - 1)d)] = 63a + 63d

According to the given information, S10 is equal to S20 + S21 + S22:
10a + 45d = 63a + 63d

Simplifying the equation:
53d = 53a

We can conclude that the common difference (d) is equal to the first term (a).

Now, let's find out how many terms are required to give a sum of 960.

Using the formula for the sum of an arithmetic progression, we can rearrange the equation to solve for n:
Sn = (n/2) * (a + l)
960 = (n/2) * (a + (a + (n-1)d))
960 = (n/2) * (2a + (n-1)a)
960 = (n/2) * (2 + (n-1))
960 = (n/2) * (n + 1)

Simplifying the equation, we have a quadratic equation:
n^2 + n - 1920 = 0

We can solve this equation using factoring, completing the square, or using the quadratic formula. Factoring the equation, we get:
(n + 48)(n - 40) = 0

Setting each factor equal to zero, we have:
n + 48 = 0 or n - 40 = 0
n = -48 or n = 40

Since we are considering positive integer terms, we can ignore the negative value for n. Therefore, the number of terms required to give a sum of 960 is 40.

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The given equation is sometimes true.

First, we have to simplify the expressions on both sides of the equal sign:

2x + 3(x - 4) = 2(2x - 6) + x2x + 3x - 12 = 4x - 12 + x

Simplifying: 5x - 12 = 5x - 12

Now, we have the equation: 5x - 12 = 5x - 12Here, the expression on the left side of the equation is equal to the right side of the equation. Therefore, the given equation is always true.

However, it should be noted that if we tried to solve this equation to find the value of x, we would end up with an equation where 0 = 0. This means that there is no single value of x that can make this equation true.So, the given equation is always true when it is written in its simplified form, but it has no solution.

Therefore, we can say that the given equation is sometimes true.

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Answer:

this a answer nogufyoias5 oFos

Answer:

I need this answer as well

Step-by-step explanation:

Step-by-step explanation:

We know that if (h,k) is the center of any circle and whose radius is = r then its equation is :

\( {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \)

Given, the equation of circle

\( {(x + 2)}^{2} + (y - 3) ^{2} = 25 = {5}^{2} \)

By comparing, we will get,

h = -2

k = 3

So, center of the circle is ( -2,3)

\(\large \green{ \: \: \: \: \boxed{\boxed{\begin{array}{cc} \bf\:Mark\\\bf\:me\:as\\\bf brainliest \end{array}}}} \\ \)

Answer:

-2;3

Step-by-step explanation:

we have a formular

(x-a)^2 +(y-b)^2=c

the center of the cirlce is (a;b)

so in this case it's (-2;3)

The method that he chooses to select his sample is Stratified Sampling.

In Stratified, the population is divided into subpopulations and then the same sampling is applied to each region or subpopulation.

The ability to obtain a sample population that most accurately represents the overall population being investigated while ensuring that each subgroup of interest is represented makes stratified random sampling one popular technique employed by researchers. Researchers use stratified sampling to ensure that specific subgroups are represented in the sample. It also helps in the precise evaluation of each group's characteristics. This technique is often used in surveys to better understand disparities between subpopulations.

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