which answer is right and please explain

The corresponding eigenvalues for the given matrix and vector pairs are:

1. Eigenvalue: λ = -2

2. Eigenvalue: λ = -2

3. Eigenvalue: λ = -3

4. Eigenvalue: λ = -10

5. Eigenvalue: λ = -5

1. Matrix: \(\left[\begin{array}{cc}-10&-8\\24&18\end{array}\right]\)

  Vector: \(\left[\begin{array}{cc}1\\-2\end{array}\right]\)

To check if [1; -2] is an eigenvector,

we need to solve the equation Av = λv:

                          \(\left[\begin{array}{cc}-10&-8\\24&18\end{array}\right]\)  \(\left[\begin{array}{cc}1\\-2\end{array}\right]\)

                            \(\left[\begin{array}{cc}-10&-8\\24&18\end{array}\right]\)  \(\left[\begin{array}{cc}1\\-2\end{array}\right]\)  = \(\left[\begin{array}{cc}\lambda\\-2\lambda\end{array}\right]\)

Solving this system of equations,  λ = -2.

2. Matrix: \(\left[\begin{array}{cc}12&-14\\1&-9\end{array}\right]\)

  Vector: \(\left[\begin{array}{cc}1\\1\end{array}\right]\)

To check if [1; 1] is an eigenvector, we need to solve the equation

Av = λv:

                         \(\left[\begin{array}{cc}12&-14\\1&-9\end{array}\right]\) \(\left[\begin{array}{cc}1\\1\end{array}\right]\) = \(\lambda \left[\begin{array}{cc}1\\1\end{array}\right]\)

This simplifies to:

                         \(\left[\begin{array}{cc}12&-14\\1&-9\end{array}\right]\) \(\left[\begin{array}{cc}1\\1\end{array}\right]\) = \(\left[\begin{array}{cc}\lambda\\\lambda\end{array}\right]\)  

Solving this system of equations, we find that λ = -2.

3. Matrix: \(\left[\begin{array}{cc}-5&-4\\8&7\end{array}\right]\)

  Vector: \(\left[\begin{array}{cc}1\\-2\end{array}\right]\)

  To check if [1; -2] is an eigenvector, we need to solve the equation Av = λv:

                                            \(\left[\begin{array}{cc}-5&-4\\8&7\end{array}\right]\) \(\left[\begin{array}{cc}1\\-2\end{array}\right]\) = λ \(\left[\begin{array}{cc}1\\-2\end{array}\right]\)

  This simplifies to:

                                                   \(\left[\begin{array}{cc}-5&-4\\8&7\end{array}\right]\) \(\left[\begin{array}{cc}1\\-2\end{array}\right]\) =  \(\left[\begin{array}{cc}\lambda\\-2\lambda\end{array}\right]\)

  Solving this system of equations, we find that λ = -3.

4. Matrix: \(\left[\begin{array}{cc}15&24\\-2&-5\end{array}\right]\)

  Vector: \(\left[\begin{array}{cc}1\\1\end{array}\right]\)  

  To check if [1; 1] is an eigenvector, we need to solve the equation Av = λv:

                                    \(\left[\begin{array}{cc}15&24\\-2&-5\end{array}\right]\) \(\left[\begin{array}{cc}1\\1\end{array}\right]\)  = λ \(\left[\begin{array}{cc}1\\1\end{array}\right]\)

  This simplifies to:

                                     \(\left[\begin{array}{cc}15&24\\-2&-5\end{array}\right]\) \(\left[\begin{array}{cc}1\\1\end{array}\right]\)  =  \(\left[\begin{array}{cc}\lambda\\\lambda\end{array}\right]\)

  Solving this system of equations, we find that λ = -10.

5. Matrix: \(\left[\begin{array}{cc}19&-7\\42&-16\end{array}\right]\)

  Vector: \(\left[\begin{array}{cc}3\\1\end{array}\right]\)

  To check if [3; 1] is an eigenvector, we need to solve the equation Av = λv:

                                        \(\left[\begin{array}{cc}19&-7\\42&-16\end{array}\right]\) \(\left[\begin{array}{cc}3\\1\end{array}\right]\) = λ \(\left[\begin{array}{cc}3\\1\end{array}\right]\)

This simplifies to:

                                       \(\left[\begin{array}{cc}19&-7\\42&-16\end{array}\right]\) \(\left[\begin{array}{cc}3\\1\end{array}\right]\) = λ \(\left[\begin{array}{cc}3\lambda\\\lambda\end{array}\right]\)

Solving this system of equations, we find that λ = -5.

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12 terms are in an arithmetic sequence.

What comprises an arithmetic series?

A group of integers that are arranged in a particular order and share a difference between each term is known as an arithmetic sequence.

            For instance, the common difference between the numbers 3, 9, 15, 21, and 27 in mathematics is 6. The term "arithmetic progression" can refer to an arithmetic sequence.

a = 6,

d = -3,

last term, l = -45

a + (n - 1)*d

45 = a + (n - 1)d

45 = 6 + (n -1)-3

45 - 6 = -3(n - 1)

39 = -3(n - 1)

-3(n - 1) = 39

n - 1 = -39/3

n - 1 = -13

n = -13 + 1

n = - 12

There are 12 terms.

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Answer:

x = -223/11 = -20.273

Step-by-step explanation:

Step  1  : Simplify:  11/5

Step 2: Simplify 33/5

Step  3  :

Adding fractions which have a common denominator

Step  4: Simplify: 1/2

Step  5  :  see below

Step  6  :  see below

Pulling out like terms/factors

Step  7 : Simplify: 51/2

Step 8:  Simplify: 22/5

Step 10: Simplify: 43/10

Step  9  :

Calculating the Least Common Multiple

Step  11  :

Adding fractions which have a common denominator

Done.

Hope this helps.

(a) To determine if the market is complete, we need to check if the rank of matrix A is equal to the number of basis assets. The rank of A is 2, but there are 3 basis assets. Therefore, the market in this model is incomplete.

(b) The return on the riskless asset can be calculated by finding the dot product of the price vector S and the riskless asset payoff vector. The riskless asset has a payoff vector of (1, 1, 2), so the return is given by:

Return = S · (1, 1, 2) = 1 (1) + 1 (1) + 2 (2) = 1 + 1 + 4 = 6

Therefore, the return on the riskless asset is 6.

(c) To find the state prices consistent with A and S, we need to solve the equation A' * p = S, where p is the vector of state prices. The transpose of matrix A, denoted as A', is:

A' =

[1, 0, 2; 0, 1, 2; 0, 2, 2]

Solving the equation A' * p = S, we get:

[1, 0, 2; 0, 1, 2; 0, 2, 2] * p = [1, 1, 2]

By solving this system of linear equations, we can find the state prices p. If there are no solutions to the system, then there are no consistent state prices, indicating the presence of arbitrage opportunities.

(d) If there are arbitrage opportunities, the type of arbitrage can be determined based on the sign of the state prices. If all state prices are non-negative, then there is no arbitrage. However, if any of the state prices are negative, it indicates the presence of arbitrage.

To find the arbitrage portfolio, we need to identify a portfolio of assets that has a non-negative initial value and positive future values in all states. The specific arbitrage portfolio would depend on the values of the state prices and the prices of the basis assets.

If there are no arbitrage opportunities (i.e., all state prices are non-negative), we can find the risk-neutral probabilities by normalizing the state prices. The risk-neutral probabilities represent the likelihood of each state occurring in a risk-neutral world.

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The domain of a function f(x) is the set of values of the variable x for which the function is defined (has a defined finite value).

In the case of rational functions like this one, the function becomes undefined when the denominator is 0, so we can write:

As the square root will only give positive values or zero, there is no value of x that will make the square root be equal to -5. Then, this condition does not give us any discontinuity for f(x).

We have now to consider that the square root of (20-x) will not accept negative arguments in order to be in the realm of real numbers. So then, we have the condition:

Then, f(x) will not be defined for x that do not satisfy this condition.

We can conclude that f(x) is defined for all values of x that are equal or less than 20.

Answer: The domain is {x: x<=20}

Then

Answer:

First, find the function of the line:

Therefore, the function is \(y=\frac{3}{4} x\).

Since it's the area under the graph that's shaded(not ≥ or >) and the graphed line is dotted(not ≤ or ≥), then the inequality would be \(y<\frac{3}{4} x\).

Answer:

x = 5

Step-by-step explanation:

The difference between consecutive terms will be equal , then

a₂ - a₁ = a₃ - a₂ , that is

x + 9 - (3x - 2) = 2x + 5 - (x + 9) ← distribute parenthesis on both sides

x + 9 - 3x + 2 = 2x + 5 - x - 9 , simplify both sides

- 2x + 11 = x - 4 ( subtract x from both sides )

- 3x + 11 = - 4 ( subtract 11 from both sides )

- 3x = - 15 ( divide both sides by - 3 )

x = 5

Answer:

x = 5

Step-by-step explanation:

Each new term is 1 greater than the previous term.  Therefore:

x + 9 = (3x - 2) + 1                   Equivalent to x + 9 = 3x - 2 + 1, or:

                                                                       9 + 2 - 1 = 2x, or 2x = 10

                                                Thus, x = 5

Check by substituting 5 for x as indicated:

3x - 2 becomes 13 (which means the next term must be 14)

x + 9 becomes 14, and

2x + 5 becomes 15

and these consecutive sequence terms are {13, 14, 15}

Answer:

1.2

Step-by-step explanation:

17 ÷ 20 + 7 ÷ 20

I hope this helps!

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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Answer:

Step-by-step explanation:

y=mx+b

your m is the slope and your b is the y-intercept

so for y=5x-3 your slope would be 5 and your y-intercept would be -3

The equation y = 5x - 3 represents a line with a slope of 5 and a y-intercept of -3.

The equation of a graph can be expressed as y = mx + b, which is in the slope-intercept form. This means that:

m is the slope

b is the y-intercept of the graph.

The line described by the equation y = 5x - 3 has a slope of 5, meaning that as x increases by 1, y increases by 5. The y-intercept, represented by the constant term -3, indicates that the line intersects the y-axis at the point (0, -3).

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Answer:

$141.30

Step-by-step explanation:

180 - 38.70 = 141.30

Answer:

So to get the midpoint we need to get the x's add them and divide by 2 and do the same for y. So we have -1 and 7, add them and we get 6/2 = 3. The x's midpoint is 3. Now we need to do for y.  2+3 = 5. 5/2 is y. So answer is

brainliest?

Answer:

She will save 1.24

Step-by-step explanation:

2.65 x 4 10 .60 plus .53 x 4 equals 12.72

6.48 x 2 equals 13.96

Answer:

r=1

Step-by-step explanation:

-5r+2r=-3r

-3r=-3

Divide by -3 on both sides

r=1

Answer:

The answer is 0.02

Step-by-step explanation:

1/50=0.02

Answer:

The meal cost 80 dollars

The inequality is 3,080 + w <= 4500. and we have explained the possible weights of the fourth horse.

What is inequality?

Inequality is a mathematical statement that compares two values or expressions and shows the relationship between them. It is used to express that one value is either greater than, less than, greater than or equal to, or less than or equal to another value. Inequalities can be represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), ≠ (not equal to).

We know that Mr. Thornton has already loaded three horses into his trailer with the following weights: 890 pounds, 1250 pounds, and 940 pounds. To load a fourth horse, we need to know the total weight of the trailer and the horses.

Total weight of the trailer = 890 + 1250 + 940 = 3,080 pounds

The trailer can support no more than 4500 pounds, so we need to make sure that the total weight of the trailer and the fourth horse does not exceed 4500 pounds.

Therefore, we can write the inequality:

3,080 + w <= 4500

This inequality tells us that the total weight of the trailer and the fourth horse (3,080 + w) must be less than or equal to 4500 pounds.

To graph the solutions of this inequality on a number line, we can start by plotting point 4500 on the number line. Since the inequality contains the "less than or equal to" sign, we need to shade everything to the left of 4500, including 4500.

The solutions to this inequality are all possible weights of the fourth horse that would not cause the total weight of the trailer and the horses to exceed 4500 pounds. The solutions are all real numbers between 0 and 420.

It's worth mentioning that the solution set is an interval [0,420] and it includes 0, but not 420. It means that the horse can weight 0 pounds (which is not possible) but it can't weight 420 pounds since it would exceed the maximum weight that the trailer can support.

Hence, the inequality is 3,080 + w <= 4500. and we have explained the possible weights of the fourth horse.

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The height of the building will be;

⇒ 21.6 feet

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

Ethel uses a mirror to measure the height of a building.

The triangles in the diagram are similar.

Now,

Since, The triangles in the diagram are similar.

Let the height of the building = x

Hence, By definition of proportion we get;

⇒ 6 / 10 = x / 36

Solve for x as;

⇒ 6 × 36 / 10 = x

⇒ x = 21.6 feet

Thus, The height of the building = 21.6 feet

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The probability that there are no more than 3 cars in the system is 0.50

Probability:

In math, the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes is referred as probability.

Given,

Because of limited space availability and a desire to provide an acceptable level of service, the bank manager would like to have no more than three cars in the system at any time.

Here we need to find the probability that there are no more than 3 cars in the system.

Here we know that the present level of service for three or fewer cars is the probability that there are 0, 1, 2, or 3 cars in the system.

As per the Model 1, Exhibit 8A.8, the probability of having more than three cars in the system is 1.0 minus the probability of three or fewer cars => 1.0 − 0.685 = 31.5 percent

And the 95 percent service level of three or fewer cars, this states that

=> P0 + P1 + P2 + P3 = 95 percent.

When we can solve this by trial and error for values of λ/μ.

Therefore, the value of λ/μ = 0.50

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Answer:

Ans is x<3

Step-by-step explanation:

➜-2x<-6

➜2x<6

➜2x/2<6/2

➜x<3

The οnly sοlutiοn is sinθ = 0, θ = kπ, where k is any integer.

Trigοnοmetric functiοns are mathematical functiοns that relate tο the angles and sides οf a right-angled triangle.  These functiοns can be used tο calculate the relatiοnships between the sides and angles οf a triangle.

1a) Using inverse tangent functiοn,

θ = tan^{-1}(-2/3) ≈ -0.93 + kπ οr 2.21 + kπ, where k is any integer.

1b) Using cοsine functiοn,

\(2cos^{2}\theta - 1 = 0\)

\(cos^{2}\theta= 1/2\)

cοsθ = ±√(1/2) = ±1/√2

Sο, θ = π/4 + kπ/2 οr 3π/4 + kπ/2, where k is any integer.

1c) Rearranging the equatiοn, we get

\(sin^{2}\theta - 6sin\theta- 7 = 0\)

Using the quadratic fοrmula,

sinθ = [6 ± √(36 + 28)]/2 = 3 ± √19

Since -1 ≤ sinθ ≤ 1, the οnly sοlutiοn is

sinθ = 3 - √19

\(θ = sin^{(-1)(3 - \sqrt{19})} \approx 0.47 + 2k\pi\) οr π - 0.47 + 2kπ, where k is any integer.

1d) Factοring οut sinθ frοm the equatiοn, we get

sinθ(cοsθ - 7) = 0

Sο, either sinθ = 0 οr cοsθ = 7. Since -1 ≤ sinθ, cοsθ ≤ 1, the οnly sοlutiοn is

cοsθ = 7 has nο real sοlutiοn, sο the οnly sοlutiοn is

sinθ = 0

θ = kπ, where k is any integer.

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Answer:

16 meters

Step-by-step explanation:

r=8m

8*2=16

d=16m

Answer:

16

Step-by-step explanation:

The diameter is the radius times 2.

Answer:

14 1/3

Step-by-step explanation:

You have to divide 86 by 6, which gives you 14 with a remainder of 2. This would result in 14 2/6, or simplified: 14 1/3

Answer:

14 2/6

Step-by-step explanation:

We want to transform 86/6 into a mixed number. We can achieve this by following these steps:

Step 1: Divide the numerator (86) by the denominator (6):

86 / 6 = 14 remainder 2

Step 2: Build your answer using the quotient (14) as the whole number and the remainder (2) as the numerator, keeping the same denominator (6). Thus,

The improper fraction 86/6

is equivalent to 14 2/6

simplest form is 14 1/3

A z-score that is used for hypothesis testing is also called test statistic. The correct option is a. test statistic.

A z-score, also known as a standard score, is a statistical measure that represents the number of standard deviations an observation or data point is from the mean of a distribution.

In hypothesis testing, the z-score is commonly used as a test statistic.

A test statistic is a numerical value calculated from the sample data and is used to assess the likelihood of observing the obtained results under the null hypothesis.

It serves as a basis for making decisions about the null hypothesis, such as determining statistical significance or comparing it to critical values.

On the other hand, a critical value is a specific value or values that define the boundaries of a critical region or rejection region in a hypothesis test.

It is used to determine whether to reject or fail to reject the null hypothesis.

The level of significance refers to the predetermined threshold or probability at which the null hypothesis is rejected. It is denoted by alpha (α) and represents the probability of making a Type I error in hypothesis testing.

The critical region is the range of values in which the test statistic must fall for the null hypothesis to be rejected. It is determined based on the critical values or cutoffs associated with the chosen level of significance.

Therefore, the z-score used in hypothesis testing is commonly referred to as a test statistic.

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The constant of proportionality of the graph is k = 3/2.

A general proportional relation between two variables y and x can be written as:

y = k*x

Were k is the constant of proportionality.

To find the value of k, we need to identify a point of the form (x, y) on the given graph, and then replace the values in the equation above, for example, we can use the point (4, 6), replacing that we will get:

6 = k*4

6/4 = k

3/2 = k

That is the constant of proportionality.

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Answer:

A. 1206 cm³

Step-by-step explanation:

We have a cone and are asked to find the approximate volume of it.

Keep in mind we are using π for 3.14

The forumla of a cone is V = πr²\(\frac{h}{3}\)

We know the radius = 12

and the height = 8

Substitute :

V = π12²\(\frac{8}{3}\)

Since these are multiplied with each other, we can first start off with multiplying the fraction, including with factoring 12²:

V = \(\frac{2^4*3^2*8\pi }{3}\)

Cancel the common factor - 3 :

V = \(2^4 * 8 * 3\pi\)

Multiply 8 and 3π :

V = \(2^4 * 24\pi\)

Solve the exponent :

V = \(16 * 24\pi\)

Multiply :

V = \(384\pi\)

Multiply for the final answer :

1205.76 cm³

which can be rounded up to

A. 1206 cm³

Answer:

-104 is the answer .....

Answer:

p ≤49

p+14 ≤50

Step-by-step explanation:

Take the total you can pick and subtract the ones you have already picked

75 - 26 =49

you can pick up to 49 more

p ≤49

Take the total you can pick and subtract the ones you have already picked

50 - 14 =36

you can pick up to 36 more

p+14 ≤50

p≤36

Answer: P>49

P+14<50

Step-by-step explanation:

I think