Four student are each trying to raise the same amount of money for a class trip. The table below shows how much of each student's goal has been met.

(1) The first model is arbitrage-free. The state price vector is λ = (1/5, 7/15, 1/30, 1/3).

(2) The new model is also arbitrage-free. The state price vector remains the same: λ = (1/5, 7/15, 1/30, 1/3). The model is complete, but the risk-neutral probability measure cannot be determined without the risk-free rate.

To determine if a model is arbitrage-free, we need to check if there exists an equivalent martingale measure or state price vector. If such a vector exists, then the model is arbitrage-free; otherwise, it is not.

Let's start by analyzing the first model:

(1) S(0) = (1, 2, 10)

   S(1) = ⎝⎛

         1  1

         12 3

         0  0

         0  10

         ⎠⎞

To check for arbitrage, we need to verify if there exists a state price vector, denoted by λ, such that:

S(0) · λ = S(1)

Where · denotes the dot product.

Let's calculate:

(1, 2, 10) · λ = ⎝⎛

               1  1

               12 3

               0  0

               0  10

               ⎠⎞

This equation can be written as a system of equations:

λ₁ + λ₂ + 12λ₃ = 1

λ₁ + 3λ₂ = 2

10λ₁ + 10λ₄ = 10

Solving this system of equations, we find that λ₁ = 1/5, λ₂ = 7/15, λ₃ = 1/30, and λ₄ = 1/3. Thus, a state price vector exists.

Therefore, the first model is arbitrage-free, and the state price vector is λ = (1/5, 7/15, 1/30, 1/3).

Now let's analyze the second model:

(2) S(0) = (1, 2, 10)

   S(1) = ⎝⎛

         1  1

         12 3

         0  0

         0  20

         ⎠⎞

Again, we check if there exists a state price vector, λ, such that:

S(0) · λ = S(1)

Calculating:

(1, 2, 10) · λ = ⎝⎛

               1  1

               12 3

               0  0

               0  20

               ⎠⎞

This equation can be written as a system of equations:

λ₁ + λ₂ + 12λ₃ = 1

λ₁ + 3λ₂ = 2

10λ₁ + 20λ₄ = 10

Solving this system of equations, we find that λ₁ = 1/5, λ₂ = 7/15, λ₃ = 1/30, and λ₄ = 1/3. Thus, a state price vector exists.

Therefore, the second model is also arbitrage-free, and the state price vector is λ = (1/5, 7/15, 1/30, 1/3).

Since both models are arbitrage-free and have state price vectors, they are complete. To find the risk-neutral probability measure, denoted by q, we use the formula:

q = λ / (1 + r)

where r is the risk-free rate. As the risk-free rate is not provided in the given information, we cannot determine the exact value of q without this information.

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\(3(x - 2) = 6 \\ x - 2 = \frac{6}{3} \\ x - 2 = 2 \\ x = 2 + 2 \\ x = 4\)

Answer:

Step-by-step explanation:

x =4

Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

The formula for the radius r in terms of x . and for the maximum areas is x=2/\(\pi\)+4

Given that,

y forms a circle of radius r

y=2\(\pi\)r

r=y/2\(\pi\)

(2-y)- forms Square Side x

(2-y) = 4x

x=(2-y)/4

Now Sum of Area's=Area of Square +Area of Circle

Sum = \(\pi\)r² + x²

Substitute the r and x values in above equation,

A(y)= y²/4\(\pi\)+(y-2)²/ 16

To maximize Area A(y)

A'(y)= 0

2y/4\(\pi\) + 2(y-2)/16 =0

y/2\(\pi\) + (y-2)/8 =0

y = 2\(\pi\)/\(\pi\)+4

Y max will be max, x to be maximum.

for maximum sum of areas,

x=2/\(\pi\)+4

Hence,The formula for the radius r in terms of x . and for the maximum areas is x=2/\(\pi\)+4

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Hence according to the given pattern next number will be 1000.

A cube is a solid three-dimensional shape with six square faces, eight vertices, and twelve edges that is used in mathematics or geometry. Also said to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent real-world example and is useful for boosting cognitive function. Similar to this, there are several examples in everyday life, such as six-sided dice, etc. Three-dimensional structures and figures with surface areas and volumes are the focus of solid geometry.

The pattern or sequence in the provided series of numbers is known as the number pattern. The common relationship between the provided collection of numbers is revealed by the number pattern. A number pattern is a regular pattern of numbers that repeats itself.

3x3x3= 27

6x6x6= 216

7x7x7= 343

10x10x10= 1000

Hence The complete question is-

Barney likes 27 but not 25; he likes 216 but not 220; he likes 343 but not 345. Which does he like: 16, 81, 127, 1000, or 1021?

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The correct rule to describe the function g as a function of f and gives the correct rule is that g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

The correct rule to describe the function

g(x) = 3f(x)

in terms of the function f(x) = x³-2x²+7x-11 is that

g(x) = 3(x³-2x²+7x-11) and thus

g(x) = 3x³-6x²+21x-33.

In order to obtain the function g(x) from the given function f(x), it is necessary to multiply it by a constant, in this case 3.

Therefore, g(x) = 3f(x) means that g(x) is three times f(x).

Thus, we can obtain g(x) as follows:

g(x) = 3f(x) = 3(x³-2x²+7x-11) = 3x³-6x²+21x-33

Therefore, the correct rule to describe the function g as a function of f and gives the correct rule is that

g(x) = 3x³-6x²+21x-33.

This function is obtained by multiplying the function f(x) by a constant, which in this case is 3.

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Two non-planetary objects in the solar system are asteroids and comets.

What are the non-planetary abjects?

Asteroids are rocky objects that orbit the sun, primarily located in the asteroid belt between Mars and Jupiter. They can range in size from small pebbles to large objects over 500 km in diameter. Asteroids are believed to be remnants from the early solar system, and studying them can provide insights into the formation and evolution of the planets.

Comets are icy objects that originate from the Kuiper belt or the Oort cloud, which are located far beyond the orbit of Neptune. They have a distinct coma (a fuzzy atmosphere) and a tail that can extend for millions of kilometers as they approach the sun. Comets are believed to be remnants from the early solar system and contain information about the formation of the outer planets and the early solar system.

While both asteroids and comets are remnants from the early solar system, they differ in composition and behavior. Asteroids are primarily composed of rock and metal, while comets are made up of ice, dust, and rocky material. Comets also have highly elliptical orbits that can take them far from the sun, while asteroids have more circular orbits.

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Complete question is: Two non-planetary objects in the solar system are asteroids and comets and they differ in composition and behavior.

Answer: 7 meters

Step-by-step explanation:

1 meter = 100 centimeters.

Perimeter = Length + Length + Width + Width.

Perimeter = 3 + 3 + 0.5 + 0.5

Perimeter = 7 meters

Hope this helped!

A measurable part of a line that consists of two points, called endpoints, and all of the points between them are called Line sigments.

Geometry is a branch of mathematics that deals with how objects can be expressed as relationships of points, lines, planes, surfaces, and dimensions. When we draw lines in geometry, we use an arrow at each end to show that it expands infinitely. A line is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon. The figure below shows the line AB, where the length of the line AB is related to the distance between its endpoints, A and B. The symbol for the line is named after its two endpoints, e.g.

\( \bar{AB}\)

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Supplementary angles are important in mathematics because they have a sum of 180 degrees.

This property is used in various geometric constructions and proofs, as well as in solving real-world problems involving angles. For example, in trigonometry, the concept of supplementary angles is used to determine the values of trigonometric functions for angles greater than 90 degrees.

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Answer:

-7/15

Step-by-step explanation:

-3$8(47#+$'++#$)3!_+$7$jrjdjd

Answer:

- 7/15

Step-by-step explanation:

Must convert to a common denominator to add or subtract fractions

I'll use 30

8/6 = 40/30

-9/5 = -54/30

(40-54) /30 = -14/30 =  - 7/15

a=180-79=101

c=180-83=97

a+c+d+b=360

101+97+2x=360

198+2x=360

2x=360-198=162

X=162/2=81

a=101

b=97

b and d=81

Answer: D

Step-by-step explanation: On the first part, if it decreases by 17% each year, that means its value is 83% of what it was. You forgot to say that the car was bought 2 years ago.

Thus, the answer is D

For the second, just use the same logic to get 18000*0.75^4

Step-by-step explanation:

since sqrt(25)×sqrt(25) = 25, then x can be any number, because x = x in all cases. and then both sides of the equation are always equal, no matter what value we give x, as long as x is a factor in both sides.

sqrt(25)×x×sqrt(25) = 25x

is always true for every x.

if the question would be

sqrt(25)×x×sqrt(25) = 25

then the answer can only be x = 1. because for every other value of x the equality is destroyed.

The quadratic equation x² + 5x - 2 = 0 have the solutions approximately x = 0.38 and x = -5.38.

Quadratic equations has it highest power to the degree of two and they have two solutions that makes them true.

To solve this quadratic equation: x² + 5x - 2 = 0, we can use the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

Hence a = 1, b = 5, and c = -2 and substituting these values into the quadratic formula, we get:

x = (-5 ± sqrt(5² - 4(1)(-2))) / 2(1) x = (-5 ± sqrt(33)) / 2

So the solutions are:

x = (-5 + sqrt(33)) / 2 ≈ 0.38

x = (-5 - sqrt(33)) / 2 ≈ -5.38

Therefore, the quadratic equation x² + 5x - 2 = 0 have the solutions approximately x = 0.38 and x = -5.38.

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Answer: Parallelogram Opposite Sides Converse

Step-by-step explanation:

There are 2 pairs of opposite congruent sides.

Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

The correlation coefficient that represents the strongest relationship between two variables is -0.75.

In correlation coefficients, the absolute value indicates the strength of the relationship between variables. The strength of the association increases with the absolute value's proximity to 1.

The maximum absolute value in this instance is -0.75, which denotes a significant negative correlation. The relevance of the reverse correlation value of -0.75 is demonstrated by the noteworthy unfavorable correlation between the two variables.

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Answer:

Step-by-step explanation:

Given sequence:

The first term is:

The common ratio is:

The formula for the nth term is:

Answer:

Step-by-step explanation:

72.34 x .2

the tip would be $14.47

Answer:

Your restaurant bill is $72.34. You want to leave about a 20% tip. Which is the best estimate of a 20% tip?A. $14.00B. $14.40C. $14.60D. $14.70

Step-by-step explanation:B is the right answer. You have to multiply 72.34 by 0.2 and you get 14.468. So B is the closest.

Answer:

Its 0

Step-by-step explanation:

Hope this helps!

The statement "The point (9, 3π/2) in the spherical coordinate system represents the point (3, 50) in the cylindrical coordinate system" is False.

In the spherical coordinate system, a point is represented by three coordinates: (ρ, θ, φ), where ρ represents the distance from the origin, θ represents the angle in the xy-plane, and φ represents the angle from the positive z-axis. In the cylindrical coordinate system, a point is represented by three coordinates: (ρ, θ, z), where ρ represents the distance from the z-axis, θ represents the angle in the xy-plane, and z represents the height.

The given points, (9, 3π/2) in the spherical coordinate system and (3, 50) in the cylindrical coordinate system, have different values for the distance coordinate (ρ) and the angle coordinate (θ). Therefore, the statement is false as the two points do not correspond to each other in the different coordinate systems.

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Answer:

C

Step-by-step explanation:

The measure of the central angle that was used when cutting the pizza to the nearest tenth is 0.7 radians.

We are given that

Diameter of pizza =d=18 inches,

hence radius of circular pizza =r\(=\frac{\mathrm{d}}{2}=\frac{18}{2}=9$\) inches,

Also, the arc length of a slice of pizza =L=6.5 inches.

Since we know that

Equation 1 where \($\theta$\) is measured in radians.

\(& =\frac{6.5}{9} \\\)

\(& =\frac{65}{90} \\\)

\(& =\frac{13 \times 5}{18 \times 5} \\\)

\(& =\frac{13}{18} \\\)

\(& =0.7 \text { radians }\end{aligned}\)

Therefore,  the measure of the central angle to the nearest tenth is 0.7 radians.

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Answer:

2x + 60 - 37.50

x = 6

Answer:

The answer is 11

Step-by-step explanation:

The answer is 11 because you need to add the sides up that the points are on point P is 5 Point Q is 3 and point R is 3 5+3 is 8 8+3 is 11

Answer:

19.56

Step-by-step explanation:

PR = \(\sqrt{3^{2} + 3^{2} }\) = \(\sqrt{18}\) = 3\(\sqrt{2}\)

RQ = \(\sqrt{5^{2} +5^{2} }\) = \(\sqrt{50}\) = 5\(\sqrt{2}\)

QP = \(\sqrt{8^{2} +2^{2} }\) = \(\sqrt{68}\) = 2\(\sqrt{17}\)

Perimeter = sum of the sides = 3\(\sqrt{2}\) +  5\(\sqrt{2}\) +  2\(\sqrt{17}\) = 19.56

Break the triangle PQR into 3 right triangles, with each leg being a hypotenuse.  Then you can use the Pythagorean theorem to find the length of each leg.  Add them all together to get the perimeter.

Answer:

g stands for a measure of mass that is approximately equal to the weight of paper clip, penny, or nickel. note: this is not a fake one this is real and I have done my research

Answer:

x=27

Step-by-step explanation:

expanding the above expression we get

5x+5=4x+32

grouping numbers with coefficient of x at the left side and constant at the right side we get

5x-4x=32-5

x=27