Sharon is 3 times older than her brother and half her sister's age who is 24. How old is Sharon’s brother PLEASE HELP RN FAST

The point estimate of the proportion of women who trust recommendations made on Pinterest is 0.78.

The point estimate of the proportion of men who trust recommendations made on Pinterest is 0.60

A 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on Pinterest is (0.809, 0.2791).

The point estimate of the proportion of women who trust recommendations made on Pinterest is:

= 117 / 150

= 0.78.

The point estimate of the proportion of men who trust recommendations made on Pinterest is:

= 102 / 170

= 0.60

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The missing justification in the proof of the angle bisector construction is "AAS Congruence".

As per the question, we have shown that BMP and NBP are congruent and adjacent, which means that angle MBP is congruent to angle NBP, angle BMP is congruent to angle BNP, and segment BP is shared by both triangles.

Therefore, we can apply AAS congruence to conclude that triangles BMP and NBP are congruent.

Since corresponding parts of congruent triangles are congruent, we can then conclude that angle ABC is bisected by BP. This is because angles MBA and NBP are congruent (by construction), and angles MBP and NBA are congruent (by the fact that triangles BMP and NBP are congruent).

Therefore, by the definition of an angle bisector, BP bisects angle ABC.

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Answer:

APEX

D. reflexive property

Nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the sierra Nevada mountains.

Early snowfall prevented the Central Pacific from starting construction on Tunnel No. 6, or the Summit Tunnel, in August 1865. It was built using a variety of engineering and construction methods and was located more than seven thousand feet above sea level.

When the workmen finally broke through, they discovered that they were only two inches off from the calculations that were used to locate its end points and central shaft. The length of the tunnel that was built through the Sierra Nevada mountains is therefore given as nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the Sierra Nevada mountains.

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The sample data and regression analysis to gain insights into the relationship between purchase costs and purchase revenues.

The assumption of a constant contribution margin per customer would be justified if the cost structure of the business remained constant and if the company did not offer discounts or promotions that would affect the contribution margin. In other words, the assumption would hold if the company's revenues and costs remained relatively stable over time.
It is difficult to determine if these conditions would hold without additional information about the business. However, we can analyze the sample data to see if there is a relationship between purchase costs and purchase revenues. By doing a scatter plot of the sample data, we can visually see if there is a correlation between the two variables. After plotting the data, we can use the sample data to run a regression of purchase costs on purchase revenues. The regression results can provide insights into the relationship between the two variables and can help us determine if the assumption of a constant contribution margin per customer is likely to hold. The intercept term of the regression results represents the fixed cost of the business. This is the cost that the business incurs regardless of how many units they sell. The slope of the regression line represents the variable cost per unit. By analyzing the regression results, we can determine if the variable cost per unit remains constant as the number of units sold increases. In conclusion, while it is difficult to determine this analysis can help us determine if the assumption is likely to hold and can provide valuable information for the business. if the conditions necessary for the assumption of a constant contribution margin per customer would hold without additional information about the business, we can use sample data and regression analysis to gain insights into the relationship between purchase costs and purchase revenues.

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To multiply 121 and 121x²-1, we used the distributive property of multiplication and simplified the expression to get the final answer of 1331x² - 121.

To multiply 121 and 121x²-1, we need to use the distributive property of multiplication. We can break up 121 as 11 * 11 and write as

121 * (121x²-1) = (11 * 11) * (121x²-1)

Using the distributive property here, we can then write

= 11 * 11 * 121x² - 11 * 11 * 1

Simplifying the expression, we get

= 1331x² - 121

So the multiplication of 121 and 121x²-1 is 1331x² - 121.

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--The given question is incomplete, the complete question is given

" Multiply 121 * 121x²-1 "--

When using the permutation approach to assess the difference in cell phone bills between in-state and out-of-state students, you are essentially testing the null hypothesis that there is no significant difference between the two groups. To do this, you would perform the following steps:

1. Calculate the observed difference in sample means (-7 in this case).
2. Combine the two groups (in-state and out-of-state) into a single dataset.
3. Randomly shuffle (permute) the dataset and create 10,000 new pairs of groups, each with the same number of observations as the original groups.
4. For each permutation, calculate the difference in means between the permuted groups.
5. Compare the observed difference in means (-7) to the distribution of permuted differences to determine the proportion of permuted differences that are equal to or more extreme than the observed difference. This proportion represents the p-value, which helps assess the likelihood of observing such a difference by chance alone.

If the p-value is below a pre-determined significance level (e.g., 0.05), you would reject the null hypothesis and conclude that there is a significant difference between the amounts spent on cell phone bills by in-state and out-of-state students. Otherwise, you would fail to reject the null hypothesis, suggesting no significant difference between the groups.

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When a single, standard number cube (with 6 sides) is tossed, the probability of getting a number other than 6 is 5/6 (option C), because there are 5 favorable outcomes (1, 2, 3, 4, and 5) out of the 6 possible outcomes (1 through 6).

The probability of getting a specific number on a standard number cube is 1/6, since there are six possible outcomes (1, 2, 3, 4, 5, or 6) and each is equally likely.

To find the probability of getting a number other than 6, we can count the number of outcomes that satisfy this condition.

There are five numbers (1, 2, 3, 4, or 5) that are not 6, so the probability of getting one of these numbers is 5/6. Therefore, the answer is C. 5÷6.

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The dependent variable in this study is the incidence of aggressive behavior displayed by the children during the period of free play.

The dependent variable is the outcome that is being measured and observed based on the independent variable, which in this scenario is the type of television program watched (violent or nonviolent). By observing and recording the incidence of aggressive behavior in each group, the researcher can determine if exposure to violent television programs has an effect on children's behavior. In this study, the dependent variable is essential to determining if there is a significant difference between the groups, and it allows for the researcher to draw conclusions about the relationship between exposure to violent television and aggressive behavior in children. In this scenario, the dependent variable is the incidence of aggressive behavior observed in the children during the period of free play. The dependent variable is the outcome or response that is measured in a study, and it is influenced by the independent variable(s). In this case, the independent variables are the type of television program (violent or nonviolent) and the gender of the participants (boys and girls). The researcher is investigating the relationship between exposure to violent or nonviolent television content and the occurrence of aggressive behavior among boys and girls.

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The solution to the system of equations are x= 849/14, y= 221/7 and z=-59/14.

We can write the Equation from the matrix as

2x - y + 8z = 56

x+ 8y + z = 30

9x + y + z = 88

Solving the above equations we get

2x - y + 8z = 56

2x + 16y + 2z = 60

_____________

       -17y + 6z = -4

and, 9x + 72y + 9z = 270

        9x + y +     z    =  88

    __________________

               71y + 8z = 182

So, x= 849/14, y= 221/7 and z=-59/14

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To find the first derivative of f(x), we need to integrate the second derivative with respect to x once.

f'(x) = ∫ f''(x) dx = ∫ x(x-a)(x-b)^2 dx

f'(x) = ∫ (x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2) dx

f'(x) = 1/5 x^5 - 1/4(a+b)x^4 + 1/3(a^2+3ab+b^2)x^3 - 1/2ab(a+b)x^2 + 1/3ab^2x + C

where C is the constant of integration.

To find the second derivative of f(x), we need to differentiate f'(x) with respect to x.

f''(x) = d/dx [1/5 x^5 - 1/4(a+b)x^4 + 1/3(a^2+3ab+b^2)x^3 - 1/2ab(a+b)x^2 + 1/3ab^2x + C]

f''(x) = 1 x^4 - 1(a+b)x^3 + 1(a^2+3ab+b^2)x^2 - 1ab(a+b)x + 1ab^2

f''(x) = x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2

Therefore, the second derivative of f is given by f''(x) = x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2.

a. The coordinate is located on the fourth quadrant.

b. The radius is given as follows: 17 units.

c. The sine of the angle is given as follows: sin(x) = -15/17.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

The coordinates of the point in this problem are given as follows:

(8, -15).

Hence the point is located on the fourth quadrant, as it has a positive x-coordinate and a negative y-coordinate.

The radius is equivalent to the hypotenuse of the right triangle, hence it is obtained applying the Pythagorean Theorem as follows:

r = 8² + (-15)²

r = sqrt(8² + (-15)²)

r = 17 units.

The sine of the angle is given by the y-coordinate divided by the radius, hence:

sin(x) = -15/17.

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Based on the given information, when x equals 9, the regression line predicts that log(y) will equal 3.992. To find the predicted value of y when x is 9, you will need to apply the inverse transformation to the logarithmic value.  

The inverse transformation of log(y) is achieved by using the exponential function. Specifically, you can use the formula:

y = 10^(log(y))

In this case, since log(y) = 3.992, you can plug this value into the formula:

y = 10^(3.992)

When you calculate this, you will find that y ≈ 9762.97. Rounded to the nearest whole number, the regression line predicts that y will equal 9763 when x equals 9.

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A.  9 is the mean and 2.12 is standard deviation for the number of correct answers for such students.

B. The probability of getting 16 or more correct answers by chance is less than 0.001%, which means it would be highly unusual for a student to pass by guessing and getting at least 16 correct answers.

A. If the students are guessing on 18 true/false questions, the probability of getting any single question correct is 0.5. Therefore, the mean number of correct answers for the students is expected to be 9 (18 x 0.5). The standard deviation can be calculated using the formula: √(npq), where n is the number of questions (18), p is the probability of success (0.5), and q is the probability of failure (0.5). So, the standard deviation is √(18 x 0.5 x 0.5) = 2.12.

B. To pass the test, a student would need to get at least 9 correct answers. Getting 16 correct answers would be highly unusual if the students are just guessing, as the probability of getting 16 or more correct answers by chance is very low. The probability of getting exactly 9 correct answers is about 20%, and the probability of getting 10 or more correct answers is about 13%.

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The correct option is d. one-sample t-test. The VAR statement in the PROC TTEST step specifies the mean we want to analyze.

The PROC TTEST step is used in SAS software to perform hypothesis testing for means. When only a VAR statement and RUN statement are used in the PROC TTEST step, SAS will perform a one-sample t-test.

In a one-sample t-test, we compare the mean of a single sample to a known or hypothesized value. We use this test when we want to determine whether the sample mean is significantly different from a population mean or a hypothesized value.

For example, if we have a sample of students and we want to determine whether their mean test score is significantly different from a passing score of 70%, we would use a one-sample t-test. The VAR statement in the PROC TTEST step specifies the variable we want to analyze.

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The solution to the differential equation with the initial condition x(0) = -2 is: x(t) = -3/4 ln|t| / (1-t^2)^(3/2) - 2.

First, we need to separate the variables x and t, which means we want to get all the x's on one side and all the t's on the other side of the equation. We start by adding 1 to both sides: 4x(sqrt(1-t^2)) dx/dt = 1 Next, we can divide both sides by 4x(sqrt(1-t^2)) to get: dx/dt = 1 / [4x(sqrt(1-t^2))]

Now we can separate the variables by multiplying both sides by dt and dividing both sides by the expression in brackets: [4x(sqrt(1-t^2))] dx = dt To integrate both sides, we need to use a substitution.

Let u = 1-t^2, then du/dt = -2t. We can solve for dt to get dt = -du / (2t). Substituting this into the equation gives: [4x(sqrt(u))] dx = -du / (2t) Integrating both sides: ∫ [4x(sqrt(u))] dx = -∫ du / (2t)

Simplifying the left side: 2/3 x (1-t^2)^(3/2) + C1 = -1/2 ln|t| + C2 Where C1 and C2 are constants of integration. Using the initial condition x(0) = -2, we can find C1: 2/3 x (1-0^2)^(3/2) + C1 = -1/2 ln|0| + C2 -4/3 + C1 = C2

Now we have the general solution: 2/3 x (1-t^2)^(3/2) = -1/2 ln|t| + C Where C = C2 - 4/3. We can solve for x(t) by multiplying both sides by 3/2 and dividing by (1-t^2)^(3/2): x(t) = -3/4 ln|t| / (1-t^2)^(3/2) + D Where D = 2/3 C. Finally, using the initial condition x(0) = -2, we can solve for D: x(0) = -3/4 ln|0| / (1-0^2)^(3/2) + D -2 = D

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If rank(ST) < n, then by proving the contrapositive, it can be shown that rank(TS) < n. If 0 is an eigenvalue of ST, then 0 is also an eigenvalue of TS, as shown by analyzing the eigenvectors of ST and T.

(a) To prove the contrapositive, assume that rank(TS) = n. Then, by the rank-nullity theorem, the nullity of TS is 0. Therefore, the nullity of ST is also 0, since the nullity of TS and ST are equal. This means that the only vector in the kernel of ST is the zero vector.

Now, by the rank-nullity theorem again, we have that rank(ST) = n, since the dimension of the range of ST plus the nullity of ST equals the dimension of V, which is n. Hence, if rank(ST) < n, then rank(TS) < n.

(b) Suppose that 0 is an eigenvalue of ST, and let v be a corresponding eigenvector. Then, we have that ST(v) = 0, which implies that T(S(v)) = 0. Therefore, S(v) is in the null space of T, which is a subspace of V. Now, either S(v) = 0 or S(v) is an eigenvector of T with eigenvalue 0.

If S(v) = 0, then v is in the null space of S, which is also a subspace of V. Otherwise, S(v) is a nonzero eigenvector of T with eigenvalue 0, which means that it is in the null space of T.

In either case, we have shown that v is in the null space of TS, which means that 0 is an eigenvalue of TS. Hence, if 0 is an eigenvalue of ST, then 0 is an eigenvalue of TS.

In summary, if rank(ST) < n, then rank(TS) < n, and if 0 is an eigenvalue of ST, then 0 is an eigenvalue of TS.

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The weighted average cost of capital WACC = (0.375 x 0.165) + (0.125 x 0.12) + (0.5 x 0.12) x (1 - 0.28)

= 0.120 or 12.0%

To calculate the cost of capital for Brozierz Ltd, we need to calculate the cost of each component of their capital structure and weight them according to their proportion in the overall capital structure.

First, let's calculate the cost of equity using the Capital Asset Pricing Model (CAPM):

Cost of equity = risk-free rate + beta x (return on market - risk-free rate)

= 0.06 + 1.4 x (0.15 - 0.06)

= 0.165 or 16.5%

Next, let's calculate the cost of preference shares:

Cost of preference shares = (fixed dividend rate / market price of preference shares) + flotation costs

= (0.1 x 3 / 2.5) + 0

= 0.12 or 12%

The cost of debt is simply the interest rate on the bank loan, which is 12% per annum.

Now, we can calculate the weighted average cost of capital (WACC) using the formula:

WACC = (proportion of equity x cost of equity) + (proportion of preference shares x cost of preference shares) + (proportion of debt x cost of debt) x (1 - tax rate)

Let's calculate the proportion of each component:

Proportion of equity = 300,000 x 2.40 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.375

Proportion of preference shares = 100,000 x 2.50 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.125

Proportion of debt = 500,000 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.5

Therefore, the WACC is:

WACC = (0.375 x 0.165) + (0.125 x 0.12) + (0.5 x 0.12) x (1 - 0.28)

= 0.120 or 12.0%

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Given DC is tangent to circle N at point C: m∠DCN < m∠BAN and BE is tangent to Circle N at point A, is True

(1) From the diagram, we can see that angles ∠DCN and ∠BAN are vertical angles, so they are equal in measure. Since DC is tangent to Circle N at point C, we know that m∠DCN is a right angle. Therefore, m∠DCN = 90° and m∠BAN = 90° - m∠DCN. Since m∠DCN is positive, we have m∠BAN < 90°, which implies that m∠DCN < m∠BAN. So, statement (1) is true.

(2) Since DC is tangent to Circle N at point C, we know that angle ∠CBE is a right angle, and hence BE is perpendicular to CE. Also, we know that CE is the radius of Circle N, so it is perpendicular to NB. Therefore, BE is tangent to Circle N at point A. So, statement (2) is true.

(3) The length of NB cannot be determined from the given information. We only know that CE = 6, but we do not know the radius of Circle N or the position of point B along the circle. Therefore, we cannot determine the length of NB. So, statement (3) cannot be determined.

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Complete question:

Given DC is tangent to circle N at point C, which statements are true?

- m∠DCN < m∠BAN

- BE is tangent to Circle N at point A.

- NB ≈ 6.1

The surface area of the prism is 108 cm²

A prism is a solid shape that is bound on all its sides by plane faces.

The total surface area of the prism can be found by adding all the the area of the surfaces together.

area of surface 1 = 1/2 bh

= 1/2 ×4× 3

= 6cm²

area of surface 2 = area of surface 1

= 6cm²

area of surface 3 = l×w

= 8×3 = 24 cm²

area of surface 4 = 8×4 = 32cm²

area of surface 5 = 5× 8 = 40cm²

The total surface area = 6+6+24+32+40

= 108 cm²

therefore the surface area of the prism is 108cm²

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The mean percentage error (MAPE) for this data is 6.35%. MAPE is a measure of the accuracy of a forecasting model. A higher MAPE indicates that the model is less accurate, while a lower MAPE indicates that the model is more accurate.

In this case, the MAPE is relatively low, indicating that the forecasting model used is reasonably accurate. However, it's also important to consider other factors, such as the size and significance of the errors, before making any decisions based on the forecast.

To calculate the mean percentage error (MAPE) for this data, we need to first calculate the percentage error for each period. The percentage error is calculated as follows:

(Actual - Forecast) / Actual x 100

Using the data provided, we can calculate the percentage error for each period:

Period 1: (68 - 65) / 68 x 100 = 4.41%
Period 2: (65 - 64) / 65 x 100 = 1.54%
Period 3: (74 - 63) / 74 x 100 = 14.86%
Period 4: (64 - 68) / 64 x 100 = -6.25%
Period 5: (70 - 72) / 70 x 100 = -2.86%
Period 6: (72 - 73) / 72 x 100 = -1.39%

Next, we need to find the average of the absolute values of the percentage errors, which is known as the mean absolute percentage error (MAPE). To do this, we add up the absolute values of the percentage errors and divide by the number of periods:

(4.41 + 1.54 + 14.86 + 6.25 + 2.86 + 1.39) / 6 = 6.35%

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The line integral of [tex]xyz^2[/tex] ds over the curve C is equal to 2√6.

To evaluate the line integral ∫[tex]_C xyz^2[/tex] ds, where C is the line segment from (-1, 4, 0) to (1, 5, 1), we need to parameterize the curve and then evaluate the integral using the parameterization.

We can parameterize the curve C as r(t) = (-1 + 2t, 4 + t, t), for t between 0 and 1.

Then, the line integral becomes:

∫[tex]_C xyz^2[/tex] ds = ∫[tex]_0^1 (-1 + 2t)(4 + t)t^2[/tex] ||r'(t)|| dt

To compute the magnitude of the derivative r'(t), we differentiate each component of r with respect to t and then take the magnitude:

r'(t) = (2, 1, 1)

||r'(t)|| = √[tex](2^2 + 1^2 + 1^2)[/tex] = √6

Substituting this into the integral and simplifying, we get:

∫[tex]_C xyz^2[/tex] ds = ∫[tex]_0^1 (-4t^5 + 2t^4 + 4t^3 - 2t^2)[/tex] √6 dt

Evaluating this integral using the power rule and simplifying, we get:

∫[tex]_C xyz^2[/tex] ds = [tex][-t^6 + 2/3 t^5 + 2t^4 - 2/3 t^3]_0^1[/tex] * √6

∫[tex]_C xyz^2[/tex] ds = (4/3 - 2/3) * √6 = 2√6

Therefore, the line integral of [tex]xyz^2[/tex] ds over the curve C is 2√6.

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The correct answer is:

(a) No, because the column space of a 4 x 7 matrix is a subspace of R^4. There is a pivot in each row, so the column space is 4-dimensional. Since any 4-dimensional subspace of R^4 is R^4, Col A = R^4.

Explanation:

The column space of a matrix represents all possible linear combinations of its column vectors. In this case, since there are four pivot columns in the matrix A, it means that there are four linearly independent columns.

Therefore, the column space of A, Col A, is a subspace of R^4, and specifically, it is 4-dimensional. Thus, the correct answer is option B: Yes, because the column space of a 4 x 7 matrix is a subspace of R^4. There is a pivot in each row, so the column space is 4-dimensional. Since any 4-dimensional subspace of R^4 is R^4, Col A = R^4.

For the question about Nul A (null space), the information is not provided in the question, so we cannot determine its dimension or relationship to R^3.

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The sample space S for this experiment is S = {(yellow, yellow), (yellow, blue), (yellow, red), (blue, yellow), (blue, blue), (blue, red), (red, yellow), (red, blue), (red, red)}

Suppose we have three marbles of different colors - yellow, blue, and red. We draw one marble at random and then replace it before drawing another marble. The sample space of this experiment is the set of all possible outcomes or combinations of marbles that can be drawn.

Since we are drawing marbles with replacement, the possible outcomes for the first draw are yellow, blue, and red. Each of these outcomes can occur with equal probability of 1/3. After replacing the first marble, the same three colors are available for the second draw, resulting in nine possible outcomes for the pair of draws. We can represent the sample space as a set of ordered pairs (x,y), where x and y are the colors of the first and second draws, respectively.

In this sample space, each outcome is equally likely to occur with a probability of 1/9. We can use the sample space to calculate the probability of specific events, such as drawing two marbles of the same color or drawing at least one blue marble.

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The surface area of the regular pyramid is 178.3 mm² if the area of the base is 43.3 mm².

The surface area of a regular pyramid can be calculated using the following formula

Surface Area = Base Area + (1/2) x Perimeter of Base x Slant Height

Base area = 43.3 mm²

Perimeter of base = 10 + 10 + 10 = 30 mm

Slant height = 9 mm

Substitute the values in the formula, we get the surface area

= 43.3 + 1/2 x 30 x 9

= 43.3 + 15 x 9

= 43.3 + 135

= 178.3 mm²

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-- The given question is incomplete, the complete question is given below

"Use the net to find the surface area of the regular pyramid."

Answer:

Step-by-step explanation:

A particular solution of the differential equation y" -8y' +17y = 8e^6t is y_p = (8/5)e^(6t) obtained using the method of undetermined coefficients.

To find a particular solution of the non-homogeneous differential equation:

[tex]y" - 8y' + 17y = 8e^(6t)[/tex]

using the method of undetermined coefficients, we assume that the particular solution has the form:

[tex]y_p = Ae^(6t)[/tex]

where A is a constant to be determined.

We then take the first and second derivatives of y_p:

[tex]y'_p = 6Ae^(6t)[/tex]

[tex]y"_p = 36Ae^(6t)[/tex]

Substituting these expressions into the differential equation, we have:

[tex]y" - 8y' + 17y = 8e^(6t)[/tex]

[tex]36Ae^(6t) - 48Ae^(6t) + 17Ae^(6t) = 8e^(6t)[/tex]

Simplifying the left-hand side, we get:

[tex]5Ae^(6t) = 8e^(6t)[/tex]

Therefore, A = 8/5.

Hence, the particular solution is:

[tex]y_p = (8/5)e^(6t)[/tex]

Therefore, a particular solution of the differential equation y" -8y' +17y = 8e^6t is y_p = (8/5)e^(6t) obtained using the method of undetermined coefficients.

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The property of vectors that is incorrect is "Oa· (b + c) = a · b + a.c = (a + b ) + c = a +(b + c)". The correct property is "Oa· (b + c) = Oa·b + Oa·c".

The incorrect property of vectors among the given options is:

Oa·b = axb

This property is incorrect because the dot product (a·b) and cross product (axb) of two vectors are different operations with different results. The dot product is a scalar value, while the cross product is another vector that is orthogonal to the given vectors. The correct properties of vectors in your question are:

1. a x b = -b x a (cross product)
2. a · (b + c) = a · b + a · c (dot product distributive property)
3. (a + b) + c = a + (b + c) (vector addition associativity)

to learn more about distributive property click here:

brainly.com/question/13818728

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