Tianna has $4200 in an account that pays her monthly rent of $600 while she is attending college for the school year. She occasionally reviews her account to determine the amount left in the account.

i)  The Cobb-Douglas production function y = \(Ax^1h^1x^2b^2\) is negatively sloped and convex to the origin. ii) These positive signs ensure that the partial derivatives and second-order partial derivatives are positive or non-negative. iii) This equation represents the isocline defined by RTS = 1 for the given Cobb-Douglas production function.

i) To prove that the Cobb-Douglas production function y = Ax^1h^1x^2b^2 is negatively sloped and convex to the origin, we need to show that the partial derivatives with respect to x1 and x2 are positive, and the second-order partial derivatives are non-negative.

Partial derivatives:

∂y/∂x1 = A *\((1 * x^1 * h^1 * x^2b^2) / x1 = A * h^1 * x^2b^2\)

∂y/∂x2 = A *\((1 * x^1 * h^1 * x^2b^2) / x2 = A * x^1 * h^1 * b^2 * x2(b^2-1)\)

The partial derivatives are positive since A, h^1, and x^1 are assumed to be positive parameters.

Second-order partial derivatives:

∂^2y/∂x\(1^2\) = \(A * h^1 * x^2b^2 > 0\)

∂^2y/∂x\(2^2\) = \(A * x^1 * h^1 * b^2 * (b^2-1) * x2(b^2-2) > 0\)

The second-order partial derivatives are non-negative since A, \(h^1,\) and \(b^2\) are assumed to be positive parameters.

Therefore, the Cobb-Douglas production function y = \(Ax^1h^1x^2b^2\) is negatively sloped and convex to the origin.

ii) For the function to be well-behaved, the parameters A, \(h^1,\) and \(b^2\) should have the following signs:

- A should be positive, as it represents the overall productivity level of the production function.

-\(h^1\) should be positive, as it represents the elasticity of output with respect to the input factor x1.

- \(b^2\) should be positive, as it represents the elasticity of output with respect to the input factor x2.

These positive signs ensure that the partial derivatives and second-order partial derivatives are positive or non-negative, leading to a well-behaved and meaningful production function.

iii) The marginal rate of technical substitution (RTS) for a Cobb-Douglas production function is defined as the ratio of the marginal product of one input to the marginal product of the other input:

RTS = (∂y/∂x1) / (∂y/∂x2)

From the partial derivatives calculated earlier, we have:

RTS = \((A * h^1 * x^2b^2) / (A * x^1 * h^1 * b^2 * x2(b^2-1))\)

    =\((x^2b^2) / (x^1 * b^2 * x2(b^2-1))\)

    = \((x^2b^2) / (x^1 * x2(b^2-1))\)

To find the isocline defined by RTS = 1, we set RTS equal to 1:

1 =\((x^2b^2) / (x^1 * x2(b^2-1))\)

Simplifying, we get:

\(x2(b^2-1) = x^1 * x^2b^2\)

This equation represents the isocline defined by RTS = 1 for the given Cobb-Douglas production function.

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Answer:

0.875

Step-by-step explanation:

to convert the fraction 7/8 to decimal

therefore 7 divided 8 = 0.875

The expression is equivalent to "\(z^4 * (z + 6)^2 + (z + 6)\)".

To clarify, I understand the expression as: "z * (z + 6) * z * (z + 6) * z + (z + 6)". Let's break down the expression and simplify it step by step:

Distribute the multiplication:

z * (z + 6) * z * (z + 6) * z + (z + 6)

becomes

z * z * z * (z + 6) * (z + 6) * z + (z + 6)

Combine like terms:

z * z * z simplifies to \(z^3\)

(z + 6) * (z + 6) simplifies to (z + 6)^2

The expression now becomes:

\(z^3 * (z + 6)^2 * z + (z + 6)\)

Multiply \(z^3\) and z:

 \(z^3 * z\) simplifies to \(z^4\)

The expression becomes:

  \(z^4 * (z + 6)^2 + (z + 6)\)

So, an equivalent expression to "z (z + 6)z (z + 6)z + (z + 6)" is "\(z^4 * (z + 6)^2 + (z + 6)\)".

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Answer:

Lana gets $66

Step-by-step explanation:

Wendy has $200.

Jake gets 27% of $200 that is 27% x $200 = $54

Karl gets 2/5 of $200 that is 2/5 x $200 = $80

Lana gets the rest = 200 - 54 - 80 = $66

Answer:

$\($44.33\)

Step-by-step explanation:

Since Danny eats \(^{1}/_3\) of the food we can make an equation

\(133\)\(\cdot^1/_3\) = $\(44.33\)

Keyword- \((of)\) means multiplication

brainliest please :)

The number of ounces of pasta that Jada cooked is \(5\frac{1}{3}\) ounces of pasta.

Given the following data:

To determine how many ounces of pasta Jada cooked:

In this exercise, you're required to calculate the number of ounces of pasta that was cooked by Jada.

Therefore, we would determine the fraction that Jada cooked by multiplying it by the total number of pasta as follows:

\(Jada = \frac{2}{3} \times 8\\\\Jada = \frac{16}{3}\\\\Jada = 5\frac{1}{3}\)

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In analyzing the performance of implementing the given methods over Singly Linked List and Doubly Linked List data structures, we consider the Big-O notation, which provides insight into the time complexity of these operations as the size of the list increases.

Add to Start of List:

Singly Linked List: O(1)

Doubly Linked List: O(1)

Both Singly Linked List and Doubly Linked List offer constant time complexity, O(1), for adding an element to the start of the list.

This is because the operation only involves updating the head pointer (for the Singly Linked List) or the head and previous pointers (for the Doubly Linked List). It does not require traversing the entire list, regardless of its size.

Add to End of List:

Singly Linked List: O(n)

Doubly Linked List: O(1)

Adding an element to the end of a Singly Linked List has a time complexity of O(n), where n is the number of elements in the list. This is because we need to traverse the entire list to reach the end before adding the new element.

In contrast, a Doubly Linked List offers a constant time complexity of O(1) for adding an element to the end.

This is possible because the list maintains a reference to both the tail and the previous node, allowing efficient insertion.

Add at Given Index:

Singly Linked List: O(n)

Doubly Linked List: O(n)

Adding an element at a given index in both Singly Linked List and Doubly Linked List has a time complexity of O(n), where n is the number of elements in the list.

This is because, in both cases, we need to traverse the list to the desired index, which takes linear time.

Additionally, for a Doubly Linked List, we need to update the previous and next pointers of the surrounding nodes to accommodate the new element.

In summary, Singly Linked List has a constant time complexity of O(1) for adding to the start and a linear time complexity of O(n) for adding to the end or at a given index.

On the other hand, Doubly Linked List offers constant time complexity of O(1) for adding to both the start and the end, but still requires linear time complexity of O(n) for adding at a given index due to the need for traversal.

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Answer:

The answer is 80

Step-by-step explanation:

56 / 7= 8

8x10 =80

Answer:

60°

Step-by-step explanation:

90° = 6x

15° = x

60° = 4x

Answer:

60

Step-by-step explanation:

We know that LMO = 90

2x+4x = 90

6x = 90

Divide by 6

6x/6 = 90/6

x = 15

We want to find LMN = 4x = 4*15 = 60

Let us suppose that the farmer buys x cows, y pigs and z sheep. The total cost of cows, pigs, and sheep bought by the farmer is

10x + 3y + 0.5z.

The total number of cows, pigs, and sheep bought by the farmer is

x + y + z.

Given that the farmer spent exactly 100 and bought exactly 100 animals, we can write two equations as follows.

:\($10x + $3y + $0.5z = $100 ---(1)x + y + z = 100 ---(2).\)

Multiplying equation (2) by 10 on both sides, we get

:10x + 10y + 10z = 1000

Subtracting this equation from equation (1), we get

:7y + 9.5z = 500

The LHS of the equation

7y + 9.5z = 500

is an odd number. This means that either y or z has to be odd and the other even. If y is even, then z has to be odd and vice versa. However, both

3y and 0.5z

are integers.

The solutions are:

x =

52,

y = 8,

z = 40 ---(Option A)

or = 48,

y = 16,

z = 36

x = 44,

y = 24,

z = 32x

= 40,

y = 32

z = 28

The farmer buys 52 cows, 8 pigs, and 40 sheep.

Hence,

the answer is 52 cows, 8 pigs, and 40 sheep.

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Answer:

0.6376785714275 is the average degrees celcius in the city.

Step-by-step explanation:

In order to find the average, I must add the numbers and divide them by 4.

2.34 + -2/7 + -0.45 + 3/8 = 2.55071428571

2.55071428571/4 = 0.6376785714275

I AM 100% SURE

Can I have Brainliest?

Answer: 0.024

Step-by-step explanation:

percents are out of 100 so 2.4% divided by 100 = the decimal. 2.4/100 = 0.024

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Answer:

23.6

Step-by-step explanation:

A=1/2abSinC

A=1/2*6*8*Sin80

= 24 * Sin 80

=23.635

Not sure if this is 100% correct Sowwie

Answer:

7 u

Step-by-step explanation:

To Find :-

Solution :-

Using Distance Formula , we have ,

→ D = √{ (x - x')² + ( y - y')² }

→ D = √{ ( 4+3)² + (5-5)² }

→ D = √{7²}

→ D = 7 units

The time complexity of this dynamic programming approach is \( O(n) \) as we iterate through each point on the segment.

The problem of traveling from the west-most point \( s \) to the east-most point \( t \) of a 1-dimensional segment with \( n \) teleporters can be approached using dynamic programming. Let's consider the subproblem of reaching each point \( x \) on the segment and compute the minimum cost to reach \( x \).

Let's define an array \( dp \) of size \( n+2 \), where \( dp[x] \) represents the minimum cost to reach point \( x \). We initialize all elements of \( dp \) with a large value (infinity) except for \( dp[s] \) which is set to 0, as the cost to reach the starting point is 0.

We can then iterate through each point \( x \) on the segment and update \( dp[x] \) by considering all possible teleporters. For each teleporter at position \( p \), we can teleport from \( p \) to \( x \) with a cost of \( c \). We update \( dp[x] \) by taking the minimum of the current value of \( dp[x] \) and \( dp[p] + c \).

Finally, the minimum cost to reach the east-most point \( t \) will be stored in \( dp[t] \).

The time complexity of this dynamic programming approach is \( O(n) \) as we iterate through each point on the segment.

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The value of c in the quadratic equation given is 32.

Given a quadratic equation of the form 3x² + bx + c = 0 has roots of 6 plus or minus square root of 2, we know that the quadratic equation can be written as:

3(x - (6 + √2))(x - (6 - √2)) = 0

Expanding this product gives:

3[(x - 6 - √2)(x - 6 + √2)] = 0

Using the difference of squares, we can simplify this expression to:

3[(x - 6)² - (√2)²] = 0

3(x - 6)² - 6 = 0

Multiplying out the squared term, we get:

3x² - 36x + 102 - 6 = 0

Simplifying, we get:

3x² - 36x + 96 = 0

Dividing both sides by 3, we get:

x² - 12x + 32 = 0

Therefore, the value of c is 32.

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Answer:

The last option:  \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Step-by-step explanation:

Main concepts:

Concept 1. Parts of a Radical

Concept 2. Radicals as exponents

Concept 3. Exponent properties

Concept 4. How to simplify a radical

Concept 1. Parts of a Radical

Radicals have a few parts:

If the index isn't shown, it is the default index of "2".  This default index for a radical represents a square root, which is why people sometimes erroneously call the radical symbol a square root even when the index is not 2.

In this situation, the radical's index is 4, and the radicand is 81 x^18 y^6.

Concept 2. Radicals as exponents

For any radical, the entire radical expression can be rewritten equivalently as the radicand raised to the power of the reciprocal of the index of the radical.  In equation form:

\(\sqrt[n]{x} =x^{^{\frac{1}{n}}}\)

So, the original expression can be rewritten as follows:

\(\sqrt[4]{81x^{18}y^{6}}\)

\((81x^{18}y^{6})^{^{\frac{1}{4}}}\)

Concept 3. Exponent properties

There are a number of properties of exponents:

Continuing with our expression, \((81x^{18}y^{6})^{^{\frac{1}{4}}}\), we can apply the "distributive" property since all of the parts are multiplied to each other...

\((81)^{^{\frac{1}{4}}}(x^{18})^{^{\frac{1}{4}}}(y^{6})^{^{\frac{1}{4}}}\)

Applying the "Bases raised to powers, raised again to another power, multiplies powers" rule for the parts with x and y...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{18}{4}}})(y^{^{\frac{6}{4}}})\)

Reducing those fractions, (both the numerators and denominators have a factor of 2)...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{9}{2}}})(y^{^{\frac{3}{2}}})\)

Rewriting the exponent of the "81" back as a radical...

\(\sqrt[4]{81} x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Concept 4. How to simplify a radical

For any radical with index "n", the result is the number (or expression) that when multiplied together "n" times gives the radicand.

In our case, the index is 4.  So, we're looking for a number that when multiplied together four times, gives a result of 81.

One method of simplifying radicals is to completely factor the radicand into prime factors, and forms groups (each containing an "n" number of matching items).

Note that 81 factors into 9*9, which further factors into 3*3*3*3

This is a group of 4 matching items, and since the index of the radical is 4, we have found a group that can be factored out of the radical completely:

\(\sqrt[4]{81} =\sqrt[4]{(3*3*3*3)}=3\)

So, our original expression, simplifies finally to \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

This is the last option for the multiple choice.

Answer:

5t

Step-by-step explanation:

Step 1:

- 5( t^5)²/ - 5t^9      Equation

Step 2:

- 5t^10 / - 5t^9        Multiply

Answer:

5t         Subtract and Divide

Hope This Helps :)

Answer:

5t remember sumbtract and divide braine

Step-by-step explanation:

Step 1:

- 5( t^5)²/ - 5t^9      Equation

Step 2:

- 5t^10 / - 5t^9        Multiply

Answer:

\(Area = 18\)

Step-by-step explanation:

Given;

\(a = 2\\ h = 4\\ b=7\)

See attachment for trapezium

Required

The area

From the attachment, the formula is:

\(Area = \frac{1}{2} * (a + b) * h\)

\(Area = \frac{1}{2} * (2 + 7) * 4\)

\(Area = \frac{1}{2} * 9 * 4\)

\(Area = 18\)

Graphically, the two lines will appear as two distinct lines running parallel to each other, never intersecting.

Mathematical statements known as algebraic rules connect two variables and are expressed as equations. One of the algebraic constants is area = length x width. As a result of a set of factors, you can also develop your own rule.

To solve the system of equations:

3x - 2y = 8

6x - 4y = 12

We can simplify the second equation by dividing both sides by 2:

3x - 2y = 8

3x - 2y = 6

Now we can see that the two equations represent two parallel lines with the same slope (-3/2) and different y-intercepts (4 and 3).

Since the two lines are parallel, they will never intersect and therefore there is no solution to the system of equations.

Graphically, the two lines will appear as two distinct lines running parallel to each other, never intersecting.

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Identify the coordinates of the points A and B on the graph:

The attached graph will be used to identify the cordinates

Each point can be identified by an ordered pair of numbers; that is, a number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate. Ordered pairs are written in parentheses (x-coordinate, y-coordinate)

points A = (x,y)

points B = (x,y)

Therefore the coordinates of point A and B are

The series Σ(k = 1) cos(17)^k is convergent because |cos(17)| < 1. As k approaches infinity, the terms approach zero, indicating convergence.

To determine the convergence or divergence of the series [infinity] Σ(k = 1) cos(17)^k, we need to examine the behavior of the terms.

Let's analyze the individual terms of the series:

a_k = cos(17)^k

As k approaches infinity, the behavior of cos(17)^k depends on the value of cos(17).

If |cos(17)| < 1, then as k increases, the term cos(17)^k approaches zero. In this case, the series will converge.

However, if |cos(17)| ≥ 1, then the terms cos(17)^k will not converge to zero as k increases. In this case, the series will diverge.

Now, let's evaluate |cos(17)|:

|cos(17)| ≈ 0.951

Since |cos(17)| is less than 1, the terms cos(17)^k approach zero as k approaches infinity. Therefore, the series [infinity] Σ(k = 1) cos(17)^k is convergent.

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Answer:

x=0.333

Step-by-step explanation:

12(3x)=12

36x=12

/36 on both sides

x=0.333

Answer:

10 miles

Step-by-step explanation:

3600 ÷ 90 is 40 then 40÷4 is 10

Answer: 1/6mile

Step-by-step explanation:

¼mile in 1½hr

In 1½hr He biked ¼mile

in 1hr He biked ¼ ÷ 1½

¼ ÷ 1½

¼ ÷ 3/2

¼ × ⅔ = 2/12 = ⅙mile

Answer:

see below

Step-by-step explanation:

A rectangle is a parallelogram with four right angles, so all rectangles are also parallelograms and quadrilaterals. On the other hand, not all quadrilaterals and parallelograms are rectangles.

A rhombus is a parallelogram with four congruent sides.

A square can be defined as a rhombus which is also a rectangle – in other words, a parallelogram with four congruent sides and four right angles.

A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Answer:

38

Step-by-step explanation:

Make a chart

20 =  4850

?   = 9215

9215 / 4850 = 1.9

20 x 1.9 = 38

I don't know it this is right but I hope it helps

Answer:

Equation: 20 / 4850 = x / 9215  Answer: 37.99 minutes

Step-by-step explanation:

(The backslashes are representing a divide symbol, not a fraction)

I don't know what kind of equation you need but the equation I wrote is the one I used to solve this. You must divide the amount of time it took to run the distance which is 20 minutes by the yards jogged which is 4850. That will give you the amount of time it took the athlete to jog one yard which you should then multiply by 9215 yards to find out how much time would be needed to cover that distance. In the equation, if you replace the "x" with the answer (37.99), the equations should be equal.

(I'm really sorry if this doesn't make sense or it's confusing but I hope it helped)

Answer:

Step-by-step explanation:

A is the answer

Answer:

Option A. f(x) = 4(3)x

is the answer.

Step-by-step explanation:

Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86