A consumer's utility is described by U(x, y) = xy. Marginal utilities then are described as MUX = y and MUy=x. Suppose the price of x is 1 and the price of y is 2. Consumer's income is 40. Then price of y falls to 1. When graphing, make sure to put x on the horizontal axis, and y on the vertical axis.
(a) Calculate the optimal consumption choice before the price change. Illustrate that choice on a graph. Label that choice A
(b) Calculate the optimal consumption choice the consumer would buy at the new price of y, if they wanted to get the same amount of utility as before the price change. Mustrate that choice on the same graph. Label that choice B
(c) What is the substitution effect of the price change? Illustrate on the graph.
(d) What is the optimal consumption choice after the price change? Illustrate on the graph and label that choice C (e) What is the income effect of the price change? Illustrate on the graph.

Answer:

$35,000

Step-by-step explanation:

The amount that would be repaid = amount borrowed + interest earned on loan

interest earned on deposit can be determined by determining the simple interest

Simple interest = principal x time x interest rate

principal = the amount deposited = 20,000

Time = the duration of the deposit =5  

interest rate = the percentage on deposit that would be earned = 15

20,000 x 5 x 0.15 = $15,000

total = 20,000 + 15,000 = $35,000

Answer:B

Step-by-step explanation:

Answer:

11t -2

Step-by-step explanation:

3t - 5 + 8t + 3

Combine like terms

3t +8t- 5  + 3

11t -2

Start by changing the problem to 3t + -5 + 8t + 3.

Now combine like terms.

Combine like terms → your numbers

and your "t" terms.

So 3t + 8t is 11t and -5 + 3 is -2.

So the answer is 11t - 2.

The approximated value of f'(0) using the 2-point forward difference formula with h = 0.2 is -0.21385. So, first option is the correct answer.

To calculate an approximate value of f'(0) using the 2-point forward difference formula with h = 0.2, we can use the given function values:

f(-0.2) = -0.91736

f(0) = -1

f(0.2) = -1.04277

Using the 2-point forward difference formula, we have:

f'(0) ≈ (f(h) - f(0)) / h

Substituting the values:

f'(0) ≈ (f(0.2) - f(0)) / 0.2

f'(0) ≈ (-1.04277 - (-1)) / 0.2

f'(0) ≈ (-0.04277) / 0.2

f'(0) ≈ -0.21385

Therefore, the approximated value of f'(0) using the 2-point forward difference formula with h = 0.2 is -0.21385. Therefore, the correct answer is first option: f'(0) ≈ -0.21385.

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The equation of a line that is parallel to the line 2x - 5y = 10 and passes through the point (-5, 1) is B. 2x - 5y = -5.

To find the equation of a line that is parallel to the line 2x - 5y = 10, we need to determine the slope of the given line first. The equation is in the form of Ax + By = C, where A = 2, B = -5, and C = 10.

To find the slope, we can rearrange the equation into slope-intercept form (y = mx + b), where m represents the slope.

2x - 5y = 10

-5y = -2x + 10

y = (2/5)x - 2

From this equation, we can see that the slope of the given line is 2/5.

A line that is parallel to this line will have the same slope. Therefore, the equation of the parallel line can be determined using the point-slope form (y - y1 = m(x - x1)), where (x1, y1) represents the coordinates of the given point (-5, 1).

Using the slope of 2/5 and the point (-5, 1), we can now check the options to see which ones satisfy the conditions:

A. y = -x - 1: This equation has a slope of -1, not 2/5. It is not parallel to the given line.

B. 2x - 5y = -5: This equation has the same slope of 2/5 and passes through the point (-5, 1). It satisfies the conditions and is parallel to the given line.

C. y = -x - 3: This equation has a slope of -1, not 2/5. It is not parallel to the given line.

D. 2x - 5y = -15y: This equation has a slope of 2/20, which simplifies to 1/10. It is not parallel to the given line.

E. -1 = -(x - 5): This equation does not represent a line. It is not a valid option.

Therefore, the equation of a line that is parallel to the line 2x - 5y = 10 and passes through the point (-5, 1) is B. 2x - 5y = -5.

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The decimal number (25679)₁₀ is equivalent to the octal number (62117)₈. The base conversion method, also known as the radix conversion method, is a systematic approach to converting numbers from one base to another.

To convert the decimal expansion (25679)₁₀ to an octal expansion, we can use the base conversion method.

Step 1: Divide the decimal number by 8 and keep track of the remainders.

25679 ÷ 8 = 3209 remainder 7

3209 ÷ 8 = 401 remainder 1

401 ÷ 8 = 50 remainder 1

50 ÷ 8 = 6 remainder 2

6 ÷ 8 = 0 remainder 6

Step 2: The remainders from bottom to top form the octal expansion.

Therefore, (25679)₁₀ = (62117)₈.

Hence, the decimal number (25679)₁₀ is equivalent to the octal number (62117)₈.

The question should be:

Use base conversion method, convert the decimal expansion (25679)₁₀ to an Octal expansion.

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Using the inverse matrix, the solution to the system of equations is X₁ = -7/25 and X₂ = -2/25.

To solve the system of equations using the inverse matrix, we can represent the equations in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

The system of equations can be written as:

Equation 1: -3X₁ + 2X₂ = -3

Equation 2: 3X₁ + 5X₂ = 1

Equation 3: 3X₁ - 2X₂ = 4

Equation 4: -4X₁ + 3X₂ = -5

Rewriting the equations in matrix form, we have:

[tex]\left[\begin{array}{ccc}-3&2\\3 &5\\3 &-2\\-4 &3\end{array}\right] \left[\begin{array}{ccc}X1\\X2\end{array}\right]=\left[\begin{array}{ccc}-3\\1\\4\\-5\end{array}\right][/tex]

To find the solution, we need to calculate the inverse of the coefficient matrix A. Let's call it A^(-1).

[tex]A^{-1}=\left[\begin{array}{ccc}\frac{-11}{25}&\frac{2}{25}\\\frac{3}{25}&\frac{3}{25}\\\end{array}\right][/tex]

Now, we can solve for X by multiplying A^(-1) with B:

[tex]\left[\begin{array}{ccc}X1\\X2\end{array}\right]=\left[\begin{array}{ccc}\frac{-11}{25}&\frac{2}{25}\\\frac{3}{25}&\frac{3}{25}\\\end{array}\right]\left[\begin{array}{ccc}-3\\1\\4\\-5\end{array}\right][/tex]

Performing the matrix multiplication and Simplifying the results, we have:

X₁ = -7/25

X₂ = -2/25

Therefore, the solution to the system of equations is X₁ = -7/25 and X₂ = -2/25.

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Answer:

I am guessing it is 67 as for maybe the whole thing is 180 degrees. So 180 subtracted by 67 and 46 equals 67!!!

67+46+?=180

113+?=180

?=180-113

?=67

Answer:

Step-by-step explanation:

1. Write the question.

17 - 2x = -11

2. Subtract 17 from both sides

-17          -17

    - 2x = -28

3. Negatives cancel

      2x = 28

4. Divide both sides by 2

        /2     /2

        x = 14

5. Check the answer, write the equation.

17 - 2x = -11

6. Substitute x with the value

17 - 2(14) = -11

17 - 28 = -11

-11 = -11

The answer is correct!

Hope this helped,

Kavitha

Answer:

1.04 mill

Step-by-step explanation:

15 inches to mill = 381

[tex]365\sqrt{381}[/tex] = 1.04 ( rounded )

Answer:

D. A = 3n + 15

Step-by-step explanation:

3 should be beside the n variable because n represents each ride that was purchased.

As 15 represents the fee

The A variable represents the total amount spent

Therefore your answer is D.

Your Welcome.

Answer:

1 hour: $12.75

Step-by-step explanation:

Easy divide 38.25 by 3 which is 12.75

Step-by-step explanation:

[tex]90 = 4x - 6 \\ 96 = 4x \\ x = 24[/tex]

[tex]2x - 8 = \\ = 48 - 8 = \\ = 40[/tex]

a) The odds of surviving is 1/4

b) The odds of not surviving is 4.

c) You would receive a payout of $6.25 if you bet $25 on surviving and you successfully survive the zombie apocalypse.

a) The odds of surviving the zombie apocalypse can be calculated by taking the probability of survival (20%) and dividing it by the probability of not surviving

100% - 20% = 80%

So the odds of surviving would be,

20%/80% = 1/4

This means that for every one chance of surviving, there are four chances of not surviving.

b) The odds of not surviving the zombie apocalypse can be calculated by taking the probability of not surviving (80%) and dividing it by the probability of survival (20%).

So the odds of not surviving would be

80%/20% = 4/1

This means that for every four chances of not surviving, there is one chance of surviving.

c) If you bet $25 on surviving and you do survive, based on the odds of 1/4, you would win the bet. The payout can be calculated by multiplying the bet amount by the odds of surviving.

So the payout would be

$25 * 1/4 = $6.25

Therefore, based on the odds, you would receive a payout of $6.25 if you bet $25 on surviving and you successfully survive the zombie apocalypse.

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Step-by-step explanation:

The first composite shape is a combination of a rectangular prism and a pyramid. To find the volume of the entire shape you find the volume of each individual shape and add them together. The second figure consists of a cylinder and a hemisphere.

Hope that helps :)

Answer:

This theorem states that 'if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. ' This is kind of like the SAS, or side-angle-side postulate. But SAS requires you to know two sides and the included angle.

Step-by-step explanation:

Answer:

B because it does not contain an = sign

Answer:

12

Step-by-step explanation:

To determine the number of discs, divide the area of the metal sheet by the area of the discs

The metal sheets are in the shape of a rectangle, thus the area of a rectangle would be used to determine the area of the sheet

Area of a rectangle = length x breadth

56 x 33 = 1848 cm^2

The disc is in the shape of a circle.

area of a circle = πr²

π = 3.14

r = radius

3.14 x 7² = 153.86 cm²

Number of discs = 1848 /153.86 = 12

Answer:

The hikers are 5 miles apart.

Step-by-step explanation:

East + West = 3 miles apart (x-axis)

North + South = 4 miles apart (y-axis)

Then use the pythagorean theorem to find the distance between them.

sqrt(distance) = sqrt(3^2+4^2)

distance = sqrt(25)

distance = 5 miles

Answer:

a. -12n^3 + 8n^2 - 2n

b. n^4 - n/2

c. 6b^7 + 2b^6 - b^5

Step-by-step explanation:

btw photomath (the app) is really good for this type of stuff

Answer:

7.2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Distance "D" = rate × time

or d = r × t.

Tad and his buddies drove to the orange bowl(while going) -50mph

Tad and his buddies while returning from a trip -75mph

Total round trip = 12 hours

Distance while going = 50 x t

Distance while returning = 75 (12 - t)

50t = 75(12 -t)

50t = 900 -75t

50t + 75t = 900

125t = 900

t = 900/125

t= 7.2

The total number of hours it takes Tad and his buddies to drive to the orange bowl is 7.2 hours.

Answer:

x=0

I used phone math!!!!!!!!

The integrate is W = 12 ∫[0 to 1] (1 + 3t)^(3/2) dt + 27 ∫[0 to 1] (1 + 2t) √(1 + 3t) dt.

To find the work done by the force field F in moving an object from point A to point B, we can use the line integral of the force field along the path connecting A and B. The line integral is given by the formula:

W = ∫[C] F · dr

where C represents the curve connecting points A and B, F is the force field, dr is the differential displacement vector along the curve, and · denotes the dot product.

First, let's calculate the differential displacement vector dr. Since we are moving from point A(1, 1) to point B(3, 4), the differential displacement vector dr can be expressed as:

dr = dx i + dy j

Now, let's determine the curve C connecting A and B. The curve can be parametrized as follows:

x(t) = 1 + 2t

y(t) = 1 + 3t

where t varies from 0 to 1.

Differentiating these parametric equations, we obtain:

dx = 2 dt

dy = 3 dt

Substituting these values into the differential displacement vector dr, we have:

dr = 2 dt i + 3 dt j

Next, let's calculate the force field F at each point along the curve C. Given that F(x, y) = 6y^(3/2) i + 9x √y j, we can substitute the parametric equations for x and y into F:

F = 6(1 + 3t)^(3/2) i + 9(1 + 2t) √(1 + 3t) j

Now, let's evaluate the line integral by substituting the values of F and dr into the integral expression:

W = ∫[0 to 1] (6(1 + 3t)^(3/2) i + 9(1 + 2t) √(1 + 3t) j) · (2 dt i + 3 dt j)

Expanding the dot product, we have:

W = ∫[0 to 1] (12(1 + 3t)^(3/2) dt + 27(1 + 2t) √(1 + 3t) dt)

Now, we can simplify and integrate each term separately:

W = 12 ∫[0 to 1] (1 + 3t)^(3/2) dt + 27 ∫[0 to 1] (1 + 2t) √(1 + 3t) dt

To evaluate these integrals, we can use appropriate substitution or integration techniques. After integrating both terms, we will have the value of the work done by the force field F in moving the object from A to B along the curve C.

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Answer:

[tex]4 \sqrt{2 - 3 = 1[/tex]

Answer:

(-2,8), (-1,6), (0,4), (1,2), (2,0), (3,-2)

Step-by-step explanation:

Insert these points in graph and draw a line. You will get the answer. ^_^

sorry had to edit because of a blunder

Events A and B are considered independent if and only if the probability of their intersection (P(A ∩ B)) is equal to the product of their individual probabilities (P(A) * P(B)).

Independence: Two events A and B are independent if the occurrence or non-occurrence of one event does not affect the probability of the other event.

Joint Probability: The joint probability P(A ∩ B) represents the probability of both events A and B occurring together.

Multiplication Rule: According to the multiplication rule for independent events, if events A and B are independent, the probability of their intersection is equal to the product of their individual probabilities.

P(A ∩ B) = P(A) * P(B)

Interpretation: If the equation holds true, events A and B are considered independent since the probability of their intersection can be determined solely by multiplying their individual probabilities.

Dependence: If the equation does not hold true, it implies that the occurrence of one event affects the probability of the other event, indicating dependence between the two events.

In summary, the multiplication rule for independent events states that events A and B are independent if and only if P(A ∩ B) = P(A) * P(B).

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Answer:

Step-by-step explanation:

1/5 + 1/5 = 2/5

1/7 + 1/7 = 2/7

1/3 + 1/3 = 2/3

There are an infinite number of these fractions. They must be 1 and 1 in the numerator, and the denominator must be relatively prime  to 2. The examples I have picked are prime in the denominator, but the rule is not without many exceptions. For example

1/9 + 1/9 = 2/9

I don't think you can pick an even denominator because it will reduce when put with two.  Oh wait 2/18 + 2/18 = 4/18 = 2/9 But these could be reduced before adding. Still, it might count. It depends on who is marking the question.

What about an odd and even denominator?

1/9 + 1/18 = 3/18 = 1/6  There must be something that works, but I can't come up with an example.

Answer:

40

Step-by-step explanation:

This rhombus is divided into 4 triangles. UL= upper left LL= lower left UR= upper right LR= Lower Right

UL: ½bh = ½(5)(4)=10

LL: ½bh = ½(5)(4)=10

UR: ½bh = ½(5)(4)=10

LR: ½bh = ½(5)(4)=10

Add up all the areas of each individual triangle (10+10+10+10 =40) and that's your final answer.