explain why a 2 x 2 matrix can have at most two distinct eigenvalues. explain why an n x n matrix can have at most n distinct eigenvalues

Answer:

b

Step-by-step explanation:

The Particular Integral is,$$y_p = -\frac{512}{6301}sin(8t)+\frac{343}{6301}cos(8t)$$

The given differential equation is:$$\frac{d^2}{dy^2}+49y = 4.5sin(8t)$$For finding the Particular Integral, the initial steps are: Finding the characteristic equation of the homogeneous equation.$$m^2+49=0$$$$\Rightarrow m = 7i, -7i$$Let us assume the Particular Integral of the form,$$y_p = A sin(8t)+Bcos(8t)$$ Differentiating the Particular Integral to get,$$\frac{d}{dt}y_p = 8Acos(8t)-8Bsin(8t)$$$$\frac{d^2}{dy^2}y_p = -64Asin(8t)-64Bcos(8t)$$ Substituting these in the differential equation, we get$$(-64Asin(8t)-64Bcos(8t))+49(Asin(8t)+Bcos(8t)) = 4.5sin(8t)$$S implifying the equation, we get,$$(49A-64B)cos(8t)+(49B+64A)sin(8t)=4.5sin(8t)$$Comparing the coefficients, we get$$49A-64B=0$$$$49B+64A=4.5$$Solving these equations, we get,$$A = -\frac{512}{6301}$$$$B = \frac{343}{6301}$$

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Answer:

3,992

Step-by-step explanation:

1/10 = 0.1

399.2/0.1 = 3,992

Answer:

3990

Step-by-step explanation:

Place the decimal to a fraction:

399.2 = 399 2/10

Simplify =  399 1/5

Put in improper fraction = 1995/5

Simplify more = 399/1 or 399

So:

399 divided by 1/10 = 3990

Answer:

Each term in the second sequence is double the corresponding term in the first sequence.

Step-by-step explanation:

pls mark as brainliest

The correct statement that describe the two sequences is:

Each term in the second sequence is 10 times the corresponding term in the first sequence.

This is a type of sequence which have common difference between each term. It is represent mathematically as:

Tₙ = a + (n – 1)d

Where

Tₙ is the nth term

a is the first term

n is the number of terms

d is the common difference

Relationship = sequence 2 / sequence 1

Relationship = sequence 2 / sequence 1

Sequence 2 / sequence 1 = 10 / 1

Cross multiply

Sequence 2 = 10 × sequence 1

Relationship = sequence 2 / sequence 1

Sequence 2 / sequence 1 = 20 / 2

Sequence 2 / sequence 1 = 10 / 1

Cross multiply

Sequence 2 = 10 × sequence 1

If we continue with the pattern above, we'll discovered that

Sequence 2 = 10 × sequence 1

Thus, we can conclude that:

Each term in the second sequence is 10 times the corresponding term in the first sequence.

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Answer:

(7.5, 3)

Step-by-step explanation:

(5,5) and (10, 1)

Midpoint:

[tex](\frac{x1 + x2}{2} ,\frac{y1+y2}{2} )\\\\(\frac{5 + 10}{2} ,\frac{5+1}{2} )\\\\(\frac{15}{2} ,\frac{6}{2} )\\\\(7.5,3)[/tex]

Answer:

it should be (7.5,11.25)

Step-by-step explanation:

Answer: (I am really not sure the answer if it is wrong I am so sorry)

h=3, k=2

Horizontal: up, 2 units

Vertical: up, 3 units

2x^2 = 72

Divide both sides by 2:

X^2 = 36

Take the square root of both sides

X = 6

Answer:

4.0731 cm

Step-by-step explanation:

Use pythagorean Theorem which is a^2 + b^2 = c^2 where a and b are the sides of the triangle and c is the hypotenuse, in other words the longest side.

Since x is in line with the center of the circle and is perpendicular with line that measures 15.6 cm we know that one side of the triangle is half of 15.6 or 7.8.

So then we input our known values into the formula and solve for the missing one. The formula looks like this

7.8^2 + b^2 = 8.8^2

solve for b and you get about 4.07431

your very welcome

Answer:

X= 4.1

Step-by-step explanation:

Other answer wasn't rounded.

X= 4.1 cm

The values of all sub-parts have been obtained.

(a). There are three varieties were in the experiment.

(b). ANOVA condition has been obtained.

(c). Pooled standard deviation is 9.7742.

What is ANOVA?

To examine how different means differ from one another, analysis of variance is a collection of statistical models and the corresponding estimate techniques. Ronald Fisher, a statistician, created the ANOVA.

(a). Suppose that there are 1 variety or group in the study.

given df (between) = 2 and df (between) = (l - 1).

Therefore,

l = df (between) + 1

l = 2 + 1

l = 3.

(b). In the given ANOVA the p-value (prob = 0.6801) is large enough to accept the null hypothesis thus there is sufficient evidence to conclude that the always yield (bu/acre) of different verities of oats in three groups in same.

(c) Evaluate the pooled standard deviation:

Given MS (with in) = 95.3342 pooled standard deviation is,

Spooled = √(MS (with in))

Spooled = √95.3342

Spooled = 9.7742.

Hence, the values of all sub-parts have been obtained.

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The 99% confidence interval for the mean monthly rent of all families with a monthly income of $2500 is given as follows:

(5.96, 22.38)

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 12 - 1 = 11 df, is t = 3.1058.

The parameters are given as follows:

[tex]\overline{x} = 14.17, s = 9.16, n = 12[/tex]

The lower bound of the interval is given as follows:

[tex]14.17 - 3.1058 \times \frac{9.16}{\sqrt{12}} = 5.96[/tex]

The upper bound of the interval is given as follows:

[tex]14.17 + 3.1058 \times \frac{9.16}{\sqrt{12}} = 22.38[/tex]

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Answer:

it's 3.12 it's super easy it is 3.12 trust me you won't get it wrong

Answer:

1:3 red to blue

Step-by-step explanation:

you have x shirts. Let's call the number of red shirts r and the number of blue shirts b.

r = x * 1/4

b = x - r = x - (x * 1/4) = x * 3/4

r:b = (x * 1/4):(x * 3/4) = (1/4):(3/4) = 1:3

The Durbin-Watson test is an important tool for determining autocorrelation.

The steps involved in testing autocorrelation theory using the Durbin-Watson (DW) test are as follows:

a. Develop the hypothesis to be tested.

In this case, the hypothesis is that the model residuals are autocorrelated

b. Estimate the original model, and obtain the residuals .

c. The residuals should be arranged in order of time.

d. The formula for Durbin-Watson is applied to the residuals.

e. The Durbin-Watson statistic value is interpreted in the context of the hypothesis to determine whether to accept or reject the null hypothesis.

If the Durbin-Watson statistic is greater than two but less than or equal to four, the residuals are said to be uncorrelated.

On the other hand, if the Durbin-Watson statistic is less than two, positive autocorrelation exists.

Similarly, if the Durbin-Watson statistic is greater than four, negative autocorrelation exists.

Now, considering the values given in part 2 of the question, we have;

60 quarterly observations3 explanatory variables (plus a constant term)Durbin-Watson statistic of 0.95The calculation of DW statistic can be done as follows:

DW = 2.0 - 2(r)where, r is the sample autocorrelation coefficient of the residuals. To test the hypothesis, we need to perform the following actions;

Calculate the critical value of DW at 1% level of significance and for the given degrees of freedom.

Decide the conclusion by comparing the calculated value of DW with the critical value.

If the calculated value is less than the lower critical value, we reject the null hypothesis; otherwise, we accept the null hypothesis. Therefore, The null hypothesis H0:

No first-order autocorrelation versus alternative hypothesis Ha:

first-order autocorrelation exists can be tested with a DW test. The test statistic (DW) is 0.95, which is greater than the lower critical value (dL) of 1.28.

Therefore, the null hypothesis H0 is not rejected, and it can be concluded that there is no first-order autocorrelation in the regression model residuals.

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Answer:

1335.18

Step-by-step explanation:

V=π(d/2)2h

Answer:

1335.18

Step-by-step explanation:

V=π(d/2)2h

this is 3rd grade math? jesus..

Answer:

that poor 3rd grader O.O that is hard

Step-by-step explanation:

online

Step-by-step explanation:

y-intercept=when x is 0

So just set 0 for x in all equations

2(3^0)

2(1)=2

(0,2)

-5(.5)^0

-5(1)

-5=y

(0,-5)

6(3)^0

6(1)=6

(0,6)

Hope that helps :)

Answer:

2

6

9

Step-by-step explanation:

Because if you pay attention to our teacher he told us how to respond it!

Answer:

A. 20.2 ft.

Step-by-step explanation:

Use the pythagorean theorem to find the missing side length.

a^2+b^2=c^2

11^2+17^2=c^2

Answer:

no

Step-by-step explanation:

no because its equal to 2x+10

Answer:

47 degrees

Step-by-step explanation:

A triangle’s degrees add up to 180, so we can use that theorem

102 + 31 + x = 180

133 + x = 180

x = 47 degrees

The number of different simple random samples of size 5 that can be obtained from a population of size 35 is 324,632.

To calculate the number of different simple random samples of size 5 that can be obtained from a population of size 35, we can use the combination formula. The formula for combination is given by:

C(n, r) = n! / (r! * (n-r)!)

where n is the population size and r is the sample size.

In this case, we have n = 35 (population size) and r = 5 (sample size). Plugging in these values into the formula:

C(35, 5) = 35! / (5! * (35-5)!)

Simplifying this expression:

C(35, 5) = 35! / (5! * 30!)

Calculating the factorial values:

C(35, 5) = 35 * 34 * 33 * 32 * 31 / (5 * 4 * 3 * 2 * 1)

C(35, 5) = 324,632

Therefore, the number of different simple random samples of size 5 that can be obtained from a population of size 35 is 324,632.

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The center of mass can be determined by dividing the moment of the solid with respect to each coordinate axis by the total mass.

In cylindrical coordinates, the paraboloid and the plane can be represented as z = 12r^2 and z = a, respectively. To find the mass, we integrate the density function k over the region of the solid, which is bounded by z = 12r^2, z = a, and the region in the xy-plane where the paraboloid intersects the plane z = a. The integral becomes M = k * ∭ρ dV, where ρ is the density function.

To find the center of mass, we calculate the moments of the solid with respect to each coordinate axis. The x-coordinate of the center of mass can be obtained by dividing the moment about the x-axis by the total mass. Similarly, the y-coordinate and z-coordinate of the center of mass can be calculated by dividing the moments about the y-axis and z-axis, respectively, by the total mass.

By evaluating the triple integral and performing the necessary calculations, we can determine the mass and center of mass of the given solid in cylindrical coordinates.

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Answer:

a = 42 and B = 50

Step-by-step explanation:

6 x 5 = 30

6 x 7 = 42

B

7 x 10

5 x 10

Answer:

Monkey A ate 42 vegtables and monkey B ate 50 fruits

Step-by-step explanation:

There are 5 blocks of fruits and 7 of vegtables.

Monkey A ate 30 fruits; 30/5 = 6. So that means each block is worth 6 peices of food. And 6x7 = 42.

Monkey B ate 70 vegtables; 70/7 = 10. So that means each block is worth 10 peices of food. And 10x5 = 50

-----------------------------------------------------------------------------------------------------------------

Missing values

Vegtables: 42

Fruit: 50

The members chosen to participate in the upcoming moral doction can be determined through a random selection process.

One way to generate a random number is to use a random number generator (RNG). In this case, the list of members includes names like Cena, Prece, Thompson, Noon, Cooper, Zen, OG, Man, Loche, Dan, Zana, DE, Wine, and Tale. To select four members randomly, you can use the RNG to generate four random numbers within the range of the list indexes. The corresponding names at those indexes would be the chosen members.

In order to select four random members from the list of names including Cena, Prece, Thompson, Noon, Cooper, Zen, OG, Man, Loche, Dan, Zana, DE, Wine, and Tale, you can use an RNG. The RNG generates random numbers within a specified range. In this case, the range would be the number of elements in the list, which is 14.

Let's assume the RNG generates the following numbers: 21, 15, 23, and 23. Using these numbers as indexes, you would select the corresponding names in the list: Thompson, Noon, Dan, and Dan. Therefore, the four randomly selected members would be Thompson, Noon, Dan, and Dan.

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Answer:

The type of television program viewed

Step-by-step explanation:

The Independent variable may be explained as those variables which determines the outcome or output of an experiment or analysis. The output is the dependent variable. Hence, the independent variable determines the predicted variable.

In the scenario described above, the type of television program viewed, either violent or nonviolent is the independent or predictor variable. This determines the level or incidence of aggressive behavior exhibited by the subject, this incidence of aggressive behavior is the dependent or predicted variable.