If f(1) = T and f(n) = 4f(n − 1) then find the value of f(5).

Answer:

Bill is 36

Step-by-step explanation:

Bill, Paul, and Milo are represented as b, p, m

b = 15+p; p = 1/2m + 7; b + p + m = 85

b = 36, m = 28, p = 21

Therefore Bill is 36 y/o

Answer:

Step-by-step explanation:

Let Milo's age = x

\(Paul's \ age =\dfrac{1}{2}x+7\\\\\\Bill's \ age = \dfrac{1}{2}x + 7 +15 =\dfrac{1}{2}x+22\)

Sum of all three ages = 85

\(x +\dfrac{1}{2}x+7 +\dfrac{1}{2}x+22 = 85\\x +\dfrac{1}{2}x+\dfrac{1}{2}x+7+22 =85\\2x+29=85\\ 2x = 85-29\\\\ 2x = 56\\\\ x = \dfrac{56}{2}\\\\x =28 \ years\\\\\\Bill's \ age =\dfrac{1}{2}x+22 =\dfrac{1}{2}*28+22\\\\\\= 14+22\\\)

Bill's age = 36 years

a) E = UΣV^T, b) Generate a vector of independent standard normal random variables, z = (z1, z2)^T, c) x1 = μ + E^(1/2)z1, x2 = μ + E^(1/2)z2, d) the factor loading is the square root of 1.586 multiplied by the vector (0.924, -0.383), e) 1 - (0.924^2 * 1.586), f) X1 = μ1 + (factor loading for X1) * F1, X2 = μ2 + (factor loading for X2) * F2.

(a) The singular value decomposition (SVD) expression for the covariance matrix E can be written as: E = UΣV^T, where U is an orthogonal matrix consisting of the eigenvectors of E, Σ is a diagonal matrix with the square roots of the eigenvalues of E on the diagonal, and V^T denotes the transpose of the matrix V.

(b) To generate random vectors from the multivariate normal distribution N(0, E), where a = (0, 0)^T and E is given, you can follow these steps:

1. Compute the matrix square root of E, denoted as E^(1/2), by performing the eigenvalue decomposition of E: E = QΛQ^T, where Q is a matrix of the eigenvectors of E and Λ is a diagonal matrix with the eigenvalues of E on the diagonal.

2. Generate a vector of independent standard normal random variables, z = (z1, z2)^T.

3. Compute the random vector x = μ + E^(1/2)z, where μ is the mean vector (0, 0)^T.

(c) Using the provided N(0, 1) random numbers (-0.626, 0.184, -0.836, 1.5), and assuming these correspond to z1, z2, z3, and z4 respectively:

1. Take the first two values (-0.626 and 0.184) as z1 and z2, and compute the random vector x1 = μ + E^(1/2)z1.

2. Take the next two values (-0.836 and 1.5) as z3 and z4, and compute the random vector x2 = μ + E^(1/2)z2.

(d) When using only the second eigenvalue and eigenvector (A2 and e2) for factor analysis, the factor loadings can be calculated as the square root of the eigenvalue multiplied by the corresponding eigenvector. In this case, the factor loading is the square root of 1.586 multiplied by the vector (0.924, -0.383).

(e) The specific variances for the two random variables can be obtained by subtracting the squared factor loadings from their respective eigenvalues. For the first random variable (X1), the specific variance is 4 - (0.383^2 * 1.586). For the second random variable (X2), the specific variance is 1 - (0.924^2 * 1.586).

(f) The random variables X1 and X2 can be expressed in terms of the obtained factor loadings as:

X1 = μ1 + (factor loading for X1) * F1,

X2 = μ2 + (factor loading for X2) * F2,

where μ1 and μ2 are the means of X1 and X2 respectively, and F1 and F2 are the latent factors associated with X1 and X2, respectively.

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Answer:

He has 7

Step-by-step explanation:

5 plus 2 equals 7

Answer:

7 apples

Step-by-step explanation:

5 + 2 = 7

The maximum value of g is,

⇒ (- 3, 1)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The graph of quadratic function g is shown on the grid. the coordinates of the x-intercepts, the y-intercept, and the vertex are integers.

Now, The maximum value of g is the vertex of the parabola.

Hence, by graph;

The maximum value of g is,

⇒ (- 3, 1)

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Answer:

1- line of symmetry

2- line symmetry

3- rotational symmetry

Step-by-step explanation:

im pretty sure because i just did this unit :]

Answer:

b

Step-by-step explanation:

42.75+4=6

The standard equation of a hyperbola with a vertical transverse axis, centered at the origin, and values of a = 9 and b = 4 is y^2/81 - x^2/16 = 1.

The standard equation of a hyperbola centered at the origin with a vertical transverse axis is given by (y^2/a^2) - (x^2/b^2) = 1. In this case, we are given that a = 9 and b = 4, so substituting these values into the equation, we get:

(y^2/81) - (x^2/16) = 1

This is the standard equation of the hyperbola in question. It tells us that the center of the hyperbola is at the origin (0,0), the transverse axis is vertical (parallel to the y-axis), and the distance from the center to the vertices is 9 units (which is the value of a).

The distance from the center to the foci is given by c = sqrt (a^2 + b^2), which in this case is sqrt (81 + 16) = sqrt (97). The asymptotes of the hyperbola are the lines y = (a/b) x and y = -(a/b) x, which in this case are y = (3/4) x and y = -(3/4) x.

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Given triangle LMN with two vertices L(2, 6), M(6, 2), and a centroid at C(4, 5). The missing vertex of triangle LMN has the coordinates N (4, 6).

To determine the coordinates of the missing vertex, we can use the properties of the centroid of a triangle.

Given the coordinates of the vertices L(2, 6), M(6, 2), and the centroid C(4, 5), we can calculate the coordinates of the missing vertex N.

The centroid of a triangle is the point of intersection of its medians. A median is a line segment connecting a vertex to the midpoint of the opposite side.

To find the coordinates of the missing vertex N, we can use the midpoint formula and the fact that the centroid divides each median in a 2:1 ratio.

Let's find the coordinates of the midpoint of LM. The x-coordinate of the midpoint is (2 + 6) / 2 = 8 / 2 = 4, and the y-coordinate is (6 + 2) / 2 = 8 / 2 = 4. Therefore, the midpoint of LM is (4, 4).

Since the centroid C divides the median LM in a 2:1 ratio, we can find the coordinates of N by using the following formula:

x-coordinate of N = 2 * x-coordinate of C - x-coordinate of midpoint

= 2 * 4 - 4

= 8 - 4

= 4.

y-coordinate of N = 2 * y-coordinate of C - y-coordinate of midpoint

= 2 * 5 - 4

= 10 - 4

= 6.

Therefore, the missing vertex N has the coordinates (4, 6).

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Multiple regression analysis is  is applied when analyzing the relationship between  b) A dependent variable and several independent variables .

In a multiple regression analysis, several regression equations are used to predict the value of the dependent variable based on the values of the independent variables. These equations are derived using data from a single sample.

Multiple regression analysis is especially useful in situations where the relationship between variables is complex and cannot be accurately captured by simple linear regression. By considering multiple factors simultaneously, researchers can better identify the true effects of each independent variable on the dependent variable .

In summary, multiple regression analysis involves using several regression equations and a single sample to examine the relationship between one dependent variable and multiple independent variables.

This technique helps researchers better understand the complex relationships between variables and make more accurate predictions based on the combined influence of all factors. The correct answer is b).

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Answer:

14 m/s²

Step-by-step explanation:

From the question

a ∝ F/m.............. Equation 1

Where a = aceleration, m = mass, F = force

make F the subject of the equation

F = ma............ equation 2

Given: m = 7 kg, a = 4 m/s²

Therefore,

F = 7(4)

F = 28 N

For another object whose mass is 2 kg,

Make a the subject of equation 2

a = F/m

a = 28/2

a = 14 m/s²

Answer:

give me the answer of the man age or woman

Lynda previous best time was 52.9 second.

Given that, Lynda runs the 400 meter for her school's track team.

She beat her best time by 3.6 seconds in the meet today with a time of 49.3 seconds.

It means that, previous best time of Lynda was 3.6 second more than as compared to todays time.

So that,

Previous best time is, \(=49.3+3.6=52.9seconds\)

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To find a particular solution to the given differential equation, we can assume a constant value for y and solve for it.

The given differential equation is y′′ + 3y = -9. To find a particular solution, we assume y = k, where k is a constant. Substituting this assumption into the differential equation, we get k'' + 3k = -9. Since k is a constant, its second derivative is zero, so the equation simplifies to 3k = -9. Solving for k, we find k = -3.

Therefore, a particular solution to the given differential equation is y = -3. This means that for this particular value of y, the second derivative of y is zero, and when we substitute it into the differential equation, it satisfies the equation.

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The correct option A, "None of the associations listed are correct," is the appropriate response.To determine the association suggested by the two-way table, we need to calculate the relative frequency of the data.

The table provides information about whether individuals have a brother and a sister.

Based on the options given, let's calculate the relative frequencies to see which association is suggested:

Calculate the relative frequency for individuals who have a brother and a sister:Relative frequency = (Number of individuals with both a brother and a sister) / (Total number of individuals)

Calculate the relative frequency for individuals who have a brother but no sister:Relative frequency = (Number of individuals with a brother but no sister) / (Total number of individuals)

Calculate the relative frequency for individuals who have a sister but no brother:Relative frequency = (Number of individuals with a sister but no brother) / (Total number of individuals)

Calculate the relative frequency for individuals who have neither a brother nor a sister:Relative frequency = (Number of individuals with neither a brother nor a sister) / (Total number of individuals)

By comparing the relative frequencies, we can determine which association is suggested by the data.Unfortunately, the given two-way table is missing, so we cannot perform the necessary calculations to determine the association.

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Answer:

Acceleration = 3 units

Time = 35s

Initial velocity = 0 units

Using s=ut+0.5a(t^2)

So,

Distance

=0.5*a*t*t (Because u=0)

=0.5*3*35*35=0.5*3*1225=1837.5 meters =1.8375 km

"From a table of integrals, we know that for \(\(a \neq 0\)\) and \(\(b \neq 0\):\)

\(\[\int \cos(at) \, dt = \frac{1}{a} \cdot \cos(at) + \frac{1}{b} \cdot \sin(bt) + C\]\)

and

\(\[\int e^a t \cos(bt) \, dt = \frac{e^{at}}{a} \cdot \cos(bt) + \frac{b}{a^2 + b^2} \cdot \sin(bt) + C\]\)

Use this antiderivative to compute the following improper integral:

\(\[\int_{-\infty}^{0} \cos(3t) \, dt = \lim_{{T \to \infty}} \int_{0}^{T} e^t \cos(3t) \, e^{-st} \, dt = \lim_{{T \to \infty}} \text{ if } s \neq 1, \, \text{ or } \lim_{{T \to \infty}} \text{ if } s = 1.\]\)

For which values of \(\(s\)\) do the limits above exist? In other words, what is the domain of the Laplace transform of \(\(\frac{1}{\cos(3)} \cdot e^t \cos(3t)\)\)?

Evaluate the existing limit to compute the Laplace transform of  on the domain you determined in the previous part:

\(\[L\{e^t \cos(3t)\\).

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Answer:

a pi = 3.14

Step-by-step explanation:

The symbol which compares the two angles is "< ".

What is an angle?

Angles around a point define the sum of angles that can be arranged together so that they construct a full arch. Angles around a point add to 360 °.

π/3 =180/3 = 60 degree

π/3 > 45 degree

45 degree <  π/3

Therefore, the correct answer is option A. <.

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Answer:

2

Step-by-step explanation:

when the value is below 2

a situation in which no identifiable relationship exists between the values of the error term.

The value of Durbin–Watsons statistic indicates no autocorrelation is present is 2.

The output of a regression model is tested for autocorrelation using the Durbin-Watson statistic. Zero autocorrelation is indicated by a value of 2.0 in the DW statistic, which has a range of zero to four. Positive autocorrelation is indicated by values below 2.0, and negative autocorrelation is shown by values over 2.0.

As, The range of the Durbin-Watson statistic is 0–4. There is no first-order autocorrelation when the number is 2 or close to 2.

The range of 1.50 to 2.50 is suitable.

A number between 0 and 4 will always be assigned to the Durbin-Watson statistic.

A value of 2.0 means that no autocorrelation in the sample was found. Positive autocorrelation is shown by values between 0 and less than 2 whereas negative autocorrelation is indicated by values between 2 and 4.

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Answer:

I say A or B but in favor A

Step-by-step explanation:

Answer: 22

Step-by-step explanation: Divide the total by pi or 3.14 and the diameter is 22 and the radius is 11

Step-by-step explanation:

First of all, let us lay down the clues;

●There is a 20% discount on the mobile set.

●The price after the discount is Rs 13 920

●We need to find the original price.ie.(100% stands for original price)

Now let's start;As there is a 20% Discount on the m.Set, we need to find the exact percentage decrease.

So,

100%-20%= 80%

Now let's do Direct Proportion,

80%= Rs 13 920

1%= 13 920/80

100%= 13 920/80*100=Rs 17 400

RS 17 400

Answer:

3.167

Step-by-step explanation:

Mean = Sum of the number of boxes/ sum of the number of months

Mean number of boxes sold last year = (435+428+437+398+447+426)/6= 428.5

Mean number of boxes sold this year=

(440+416+445+423+420+446)/6 = 431.667

Difference = 431.667-428.5

≈ 3.167

Answer:

  (a)  {x| –4 < x ≤ 4}

Step-by-step explanation:

The domain is the horizontal extent of the graph.

Your problem statement tells you the left end is an open circle at x=-4, and the right end is a closed circle at x=4. The domain is ...

  -4 < x ≤ 4

Answer:A

Step-by-step explanation:

Answer:

14.91

Step-by-step explanation:

Have a good day :)

Answer:

The answer is 14.91

Step-by-step explanation:

To find the answer we must first see how many times 5 can go into 74.55.  Since 5 x 14.91 = 74.55, then it means that our answer is 14.91.  

Answer:

B= 21

Step-by-step explanation:

A^2 + B^2 = C^2

72^2 + B^2 = 75^2

Solve for B

B = 21

Yes , rotating is  a congruence transformation.

What is a congruence transformation?

A transformation that changes the position of the figure while not dynamical its size or form is termed a congruity transformation.

Main body:

A congruity transformation is that the movement or locating of a form specified it produces a form that is congruent to the initial.

Translations, reflections, and rotations are the three types of congruence transformations. That is, the pre-image and the image are always congruent.

Hence ,rotating is  a congruence transformation.

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We have the equation of a line:

\(y=-\dfrac{5}{4}x-1\)

The formula of a slope of a line passes through points A, B:

\(A(x_A,\ y_A),\ B(x_B,\ y_B)\\\\m=\dfrac{y_B-y_A}{x_B-x_A}\)

Complete the table:

Put the values of x to the equation of a line and calculate the value of y:

\(x=0\\\\y=-\dfrac{5}{4}\cdot0-1\\\\y=-1\\\\\\x=4\\\\y=-\dfrac{5}{4}\cdot4-1\\\\y=-6\)

Substitute to the formula of a slope:

\(m=\dfrac{-6-(-1)}{4-0}\\\\m=\dfrac{-6+1}{4}\\\\\huge\boxed{m=-\dfrac{5}{4}}\)