onsider the following initial-value problem. f ′
(x)=6x 2
−12x,f(3)=6 Integrate the function f ′
(x). (Remember the constant of integration.) ∫f ′
(x)dx=2x 3
−6x 2
+C Excellent! Find the value of C using the condition f(3)=6. C= State the function f(x) found by solving the given initial-value problem. f(x)= Find the indefinite integral. (Remember the constant of integration.) ∫x 4
(5x 5
+4) 6
dx Find the indefinite integral. (Remember the constant of integration. Remember to use absolute values where appropriate.) ∫ x 7
−1
x 6

dx

Answers

Answer 1

1. Integrate the function C = f(3) − 2(33) + 6(32)

= 6 − 54 + 54

= 6.

2.  (1/25)[(5x5 + 4)-4/5]+C.

1. Integrate the function f′(x). (Remember the constant of integration.)

∫f′(x)dx

=2x3−6x2+C

Integrating f′(x) gives f(x).

f(x) = ∫f′(x)dx

= ∫6x2−12xdx

=2x3−6x2+C

Therefore,

f(3) = 2(33) − 6(32) + C

= 6.

Therefore, solving for C gives:

C = f(3) − 2(33) + 6(32)

= 6 − 54 + 54

= 6.

2. Find the indefinite integral. (Remember the constant of integration. Remember to use absolute values where appropriate.)

∫x45x5+4dx

To solve this problem, let

u = 5x5 + 4.

Therefore,

du/dx = 25x4

and

dx = du/25x4.

Substituting this into the integral gives:

∫x45x5+4dx

=1/5∫u-4/5du

=1/25u-4/5+C

Implying

∫x45x5+4dx

= (1/25)(5x5 + 4)-4/5+C

= (1/25)[(5x5 + 4)-4/5]+C.

To know more about function visit:

https://brainly.com/question/30721594

#SPJ11


Related Questions

A manufacturer wishes to make a cereal box in the shape of a golden rectangle, based on the theory that this shape is the most pleasing to the average customer. If the front of the box has an area of 135 in2, what should the dimensions be? Round to the nearest inch.
a. 16 x 8.
b.9 x 15
c.10 x 14
d.11 x 13
its B!!

Answers

The correct option is B. The dimensions of the cereal box as 9 inches by 15 inches.

Golden rectangle: The golden rectangle is a rectangle with proportions that follow the golden ratio, a ratio that has fascinated mathematicians, scientists, and artists for centuries.

The golden ratio is approximately 1:1.61803398875 and is frequently seen in nature and art.

A rectangle whose length is 1.618 times its width is known as a golden rectangle.

These dimensions are said to be aesthetically pleasing to the eye.

A manufacturer wishes to make a cereal box in the shape of a golden rectangle, based on the theory that this shape is the most pleasing to the average customer.

If the front of the box has an area of 135 in2, Round to the nearest inch.

The given area of the front of the box is 135 square inches.

To find the dimensions, we need to use the golden ratio.

Let the width of the cereal box be "w" inches.

Then, the length of the cereal box will be "lw" inches, where l is the golden ratio (l = 1.618).

Now, the area of the front of the cereal box is given as 135 square inches.

So we have:(w)(l w) = 135l w² = 135w² = 135 / l ≈ 83.5259w ≈ √(83.5259)w ≈ 9.1372

Therefore, the width of the cereal box ≈ 9.1372 inches.

Then, the length of the cereal box = l w ≈ 9.1372 × 1.618 ≈ 14.7636 inches.

Rounding to the nearest inch, we have the dimensions of the cereal box as 9 inches by 15 inches, so the correct option is (B).

For more questions on dimensions

https://brainly.com/question/28107004

#SPJ8

The following table shows the magnitude of earthquakes on the Richter scale, x, and the corresponding depth of the earthquakes (in kilometers) below the surface at the epicenter of the earthquake. Find the correlation coefficient of the following pairs of data: x = earthquake magnitude 2.9 4.2 3.3 4.5 2.6 3.2 3.4 y = depth of earthquake (in km) 5 10 11.2 10 7.9 3.9 5.5
A. 0.425 B. 0.491 C. 0.511 D. 0.526

Answers

The correlation coefficient for the given pairs of data, x = earthquake magnitude and y = depth of earthquake, is approximately 0.491.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. To calculate the correlation coefficient, we can use the formula:

r = Σ((xi - xbar)(yi - ybar)) / √(Σ(xi - xbar)² * Σ(yi - ybar)²)

Where xi and yi are the values of the two variables, xbar and ybar are their respective means, and Σ represents the sum of the values.

Using the provided data, we calculate the means: xbar = 3.5 and ybar = 7.2571. Then we compute the individual components of the formula and sum them:

Σ((xi - xbar)(yi - ȳ)) = (2.9 - 3.5)(5 - 7.2571) + (4.2 - 3.5)(10 - 7.2571) + (3.3 - 3.5)(11.2 - 7.2571) + (4.5 - 3.5)(10 - 7.2571) + (2.6 - 3.5)(7.9 - 7.2571) + (3.2 - 3.5)(3.9 - 7.2571) + (3.4 - 3.5)(5.5 - 7.2571) = -4.5678

Σ(xi - xbar)² = (2.9 - 3.5)² + (4.2 - 3.5)² + (3.3 - 3.5)² + (4.5 - 3.5)² + (2.6 - 3.5)² + (3.2 - 3.5)² + (3.4 - 3.5)² = 1.77

Σ(yi - ybar)² = (5 - 7.2571)² + (10 - 7.2571)² + (11.2 - 7.2571)² + (10 - 7.2571)² + (7.9 - 7.2571)² + (3.9 - 7.2571)² + (5.5 - 7.2571)² = 18.174

Substituting these values into the formula, we get:

r = -4.5678 / √(1.77 * 18.174) ≈ 0.491

Therefore, the correlation coefficient for the given data is approximately 0.491, which indicates a moderate positive linear relationship between earthquake magnitude and depth.

Learn more about correlation coefficient here:

https://brainly.com/question/29978658

#SPJ11

A steam radiator with the enveloping radiating surface 1.5 m long, 0.6 m high and 0.31 m deep is supporting itself on the floor of a large room. The radiator surface has been painted with a lacquer containing 10% aluminum (= 0.55). If the radiator and the surface are at 370 K and 300 K respectively, estimate the rate of heat interchange between thein.

Answers

The estimated rate of heat interchange between the steam radiator and the surrounding surface is approximately 293,000 watts or 293 kilowatts.

To estimate the rate of heat interchange between the steam radiator and the surrounding surface, we can use the equation for heat transfer by radiation:

Q = σ * A * (Th⁴ - Ts⁴)

Where:

Q is the rate of heat transfer (in watts)

σ is the Stefan-Boltzmann constant (5.67 x 10⁻⁸ W/m²K⁴)

A is the surface area of the radiator (in square meters)

Th is the temperature of the radiator (in kelvin)

Ts is the temperature of the surface (in kelvin)

Given:

Length of the radiator (L) = 1.5 m

Height of the radiator (H) = 0.6 m

Depth of the radiator (D) = 0.31 m

Temperature of the radiator (Th) = 370 K

Temperature of the surface (Ts) = 300 K

First, calculate the surface area of the radiator:

A = 2 * (L * H + L * D + H * D)

Substituting the given values:

A = 2 * (1.5 * 0.6 + 1.5 * 0.31 + 0.6 * 0.31) = 2.78 m²

Now, calculate the rate of heat interchange:

Q = 5.67 x 10⁻⁸ * 2.78 * (370⁴ - 300⁴)

Calculating the expression inside the brackets:

Q = 5.67 x 10⁻⁸ * 2.78 * (20665680000 - 810000000) = 2.93 x 10⁵ W

Therefore, the estimated rate of heat interchange between the steam radiator and the surrounding surface is approximately 293,000 watts or 293 kilowatts.

To know more about kilowatts:

https://brainly.com/question/28570701


#SPJ4

Interpretation of an ANCOVA is more problematic when: The IV has more than two levels Assignment to groups is not random The covariate is a random variable The covariate is a pre-treatment measure of

Answers

Interpretation of an ANCOVA is more problematic when the independent variable has more than two levels and the assignment to groups is not random.

ANCOVA (Analysis of Covariance) is a statistical method used to examine whether there are significant differences between groups on a dependent variable after controlling for the influence of one or more continuous variables, called covariates. The interpretation of ANCOVA can be more problematic under certain conditions.

Firstly, if the independent variable (IV) has more than two levels, then the interpretation can be more difficult. This is because when the IV has more than two levels, there are more means to compare and this can complicate the interpretation of the results. In such cases, it is important to use post hoc tests to determine which specific means are significantly different from each other.

Secondly, the assignment to groups is not random. If assignment to groups is not random, then the groups may differ on other variables apart from the IV, which can lead to confounding. This can make it difficult to determine whether any observed differences between groups are due to the IV or some other variable. Random assignment to groups is important because it helps to ensure that the groups are equivalent on other variables and that any observed differences between groups are likely due to the IV.

Thirdly, the interpretation can be problematic if the covariate is a random variable. This is because a random variable can add noise to the data, making it more difficult to detect any significant differences between groups. Lastly, if the covariate is a pre-treatment measure, then the interpretation can be problematic because pre-treatment measures are often highly correlated with the dependent variable. This can lead to multicollinearity, which can make it difficult to determine the unique contribution of the IV to the dependent variable.

In conclusion, the interpretation of ANCOVA can be more problematic under certain conditions such as when the IV has more than two levels, the assignment to groups is not random, the covariate is a random variable, or the covariate is a pre-treatment measure. It is important to be aware of these conditions and to take appropriate steps to address them when conducting ANCOVA.

To know more about ANCOVA refer here:

https://brainly.com/question/32216741

#SPJ11

87 87 suppose that Σ ai = -12 and Σ b; = -1. Compute the sum. i=1 i=1 87 Σ (19a. i=1 18b;)

Answers

Given: Σai = -12 and

Σbi = -1To find:

The value of 87

Σ(19ai - 18bi)

Formula used:

Σ(19ai - 18bi)

= 19 Σai - 18 Σbi Calculation:

Σai = -12

Σbi = -187 Σ(19ai - 18bi)

= 19 Σai - 18

Σbi = 19(-12) - 18(-1)

= -228 + 18 = -210

Hence, the value of 87 Σ(19ai - 18bi) is -210.

To know more about value visit:

https://brainly.com/question/30145972

#SPJ11

"The given equation has one real solution. Approximate it by
Newton’s Method. You will have to be correct to within four decimal
places, so it may be necessary to iterate the process several
times."

Answers

The approximate solution by Newton's Method is 1.6.

Newton’s method is a popular numerical technique for locating the roots of a function with one variable.

Let's take an example of how Newton's method can be used to estimate the real solution of an equation that we will call f(x) in this question.

Consider the equation f(x) = 0, which we must solve to find the roots of the equation.
We can express the Newton-Raphson formula as follows:
xn+1 = xn - (f(xn)/f'(xn))
Given the above formula, we will calculate the derivative of the function in this equation as f(x) = 2x - 3.

Let's calculate the value of x0 and use the formula to find the approximate value of x after a few iterations.
Let's consider a first guess of x0 = 1.
At n = 0, we'll estimate x1 as follows:
x1 = x0 - f(x0)/f'(x0)
= 1 - f(1)/f'(1)
= 1 - (2(1) - 3)/(2)
= 1.5
At n = 1, we'll estimate x2 as follows:
x2 = x1 - f(x1)/f'(x1)
= 1.5 - f(1.5)/f'(1.5)
= 1.6667
At n = 2, we'll estimate x3 as follows:
x3 = x2 - f(x2)/f'(x2)
= 1.6667 - f(1.6667)/f'(1.6667)
= 1.6
We will continue to iterate the formula until we reach the desired accuracy of 4 decimal places.

To know more about Newton's visit:

https://brainly.com/question/4128948

#SPJ11

Ron Graham is a prolific author of mathematical papers. His friend, Don Knuth, reads all of Ron's papers and realizes that, on average, there are 4 typos for every 100 page of writing. (a) (5 pts) Ron writes a new paper, that is 20 pages long. Don, before reading the actual paper, would like to anticipate the probability that the first half of the paper has no typos, using an exponential random variable. Which exponential r.v. would Don use? What is the probability Don calculates?

Answers

Don Knuth needs to use an exponential random variable in order to anticipate the probability that the first half of Ron Graham's paper has no typos, which is called an exponential distribution.

The exponential distribution is the continuous probability distribution that describes the time between independent and identically distributed events in a Poisson process, where the events occur at a constant rate λ.The probability that there are no typos in the first 10 pages can be calculated using the exponential distribution as follows:

Here, λ is the average rate of typos per page, and x is the number of pages in the first half of the paper that have no typos. Since the average rate of typos per page is 4 for every 100 pages of writing, it can be calculated as [tex]λ = 4/100 = 0.04[/tex]. Hence, the probability that the first half of the paper has no typos can be calculated using the exponential distribution as[tex]:P(x = 10) = e^(-λx) = e^(-0.04*10) = e^(-0.4) ≈ 0.6703[/tex]Therefore, the probability that Don calculates is approximately 0.6703.

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

You are given the three points in the plane A=(−2,−8),B=(2,4), and C=(6,0). The graph of the function f(x) consists of the two line segments AB and BC. Find the integral ∫ −2
6
f(x)dx by interpreting the integral in terms of sums and/or ditferences of areas of elementary figures. ∫ −2
6
f(x)dx=

Answers

The integral ∫[-2, 6] f(x) dx, where f(x) consists of line segments AB and BC, is equal to 32.

To find the integral ∫[-2, 6] f(x) dx, we need to interpret it in terms of sums and/or differences of areas of elementary figures.

The function f(x) consists of two line segments AB and BC.

The line segment AB has endpoints A=(-2, -8) and B=(2, 4), which can be visualized as a diagonal line rising from left to right.

The line segment BC has endpoints B=(2, 4) and C=(6, 0), which can be visualized as a diagonal line falling from left to right.

To find the integral, we can break it down into two parts: the integral over the line segment AB and the integral over the line segment BC.

The integral over the line segment AB can be interpreted as the area under the line segment AB from x = -2 to x = 2. Since the line segment is a straight line, the area can be calculated as the difference in y-coordinates at the endpoints multiplied by the difference in x-coordinates:

Area_AB = (4 - (-8)) * (2 - (-2))

= 12 * 4

= 48.

The integral over the line segment BC can be interpreted as the area under the line segment BC from x = 2 to x = 6. Again, since the line segment is a straight line, the area can be calculated as the difference in y-coordinates at the endpoints multiplied by the difference in x-coordinates:

Area_BC = (0 - 4) * (6 - 2)

= -4 * 4

= -16.

To find the total integral, we add the areas of the two line segments:

∫[-2, 6] f(x) dx = Area_AB + Area_BC

= 48 + (-16)

= 32.

Therefore, the integral ∫[-2, 6] f(x) dx is equal to 32.

To know more about integral,

https://brainly.com/question/32963957

#SPJ11

Use the Integral Test to determine whether the infinite series is convergent. ∑n=1[infinity]​12ne−n2 Fill in the corresponding integrand and the value of the improper integral. Enter inf for [infinity], -inf for −[infinity], and DNE if the limit does not exist. Compare with ∫1[infinity]​ dx= By the Integral Test, the infinite series ∑n=1[infinity]​12ne−n2 A. converges B. diverges

Answers

A. The infinite series converges.

The Integral Test states that if a series is of the form [tex]a_n = f(n)[/tex], where f is a continuous, positive, and decreasing function on [tex][1, ∞)[/tex], then the series converges if and only if the integral [tex]∫1∞ f(x)dx[/tex] is convergent.

The integrand of the improper integral is:

[tex]12x*e−x^2[/tex]

Integrate by substitution, let [tex]u=−x^2[/tex] then [tex]du=−2xdx,[/tex]

so that

[tex]-12x*e−x^2dx\\=12du\\=-12*e−x^2[/tex]

Let I be the improper integral, we have:

[tex]I=∫1∞12x*e−x^2dx\\=∫−∞0−12eudu\\=[−12e−x2]0∞\\=12[/tex]

Thus, the integral converges, and by the Integral Test, the series converges.

Answer: A. The infinite series converges.

Know more about Integral Test here:

https://brainly.com/question/31381575

#SPJ11

This question relates to the homogeneous system of ODEs dt
dx
​ =−5x+8y
dt
dy
​ =−4x+7y
​ The properties of this system are determined by the matrix A=( −5
−4
​ 8
7
​ ) The rules for entering the answers to the following questions are the same as for Question 1. Determine the stability of the point (0,0), i.e. classify it as one of the following Asymptotically stable Stable Unstable Question 2.3 Determine the type of the point (0,0), i.e. classify it as one of the following Improper node Proper node Saddle point Spiral Centre Question 3. (3×1+2+2=7 marks ) This question relates to the homogeneous system of ODEs dt
dx
​ =−2x−2y
dt
dy
​ =x−4y
​ The properties of this system are determined by the matrix A=( −2
1
​ −2
−4
​ ) The rules for entering the answers to the following questions are the same as for Question 1. Determine the stability of the point (0,0), i.e. classify it as one of the following Asymptotically stable Stable Unstable Question 3.3 Determine the type of the point (0,0), i.e. classify it as one of the following Improper node Proper node Saddle point Spiral Centre

Answers

Regarding the points given, the answers to the given questions are as follows:

Question 2.1: The point (0,0) is classified as unstable.Question 2.2: The point (0,0) is classified as a saddle point.Question 3.1: The point (0,0) is classified as asymptotically stable.Question 3.2: The point (0,0) is classified as a proper node.



Let's analyze each section separately:

Question 2.1: Stability of the point (0,0) for the system: dx/dt = -5x + 8y, dy/dt = -4x + 7y.

To determine the stability of the point (0,0), we analyze the matrix A = [-5 -4; 8 7] associated with the system of equations. The stability of a point is determined by the eigenvalues of the matrix A.

Calculating the eigenvalues of A, we find:

λ₁ = (-5 + 7i)/2

λ₂ = (-5 - 7i)/2

Since the eigenvalues have non-zero imaginary parts, the point (0,0) is classified as an unstable point.

Question 2.2: Type of the point (0,0) for the system: dx/dt = -5x + 8y, dy/dt = -4x + 7y.

To determine the type of the point (0,0), we consider the eigenvalues of the matrix A.

Since the eigenvalues have non-zero imaginary parts and opposite signs, the point (0,0) is classified as a saddle point.

Question 3.1: Stability of the point (0,0) for the system: dx/dt = -2x - 2y, dy/dt = x - 4y.

To determine the stability of the point (0,0), we analyze the matrix A = [-2 1; -2 -4] associated with the system of equations.

Calculating the eigenvalues of A, we find:

λ₁ = -3

λ₂ = -3

Since the eigenvalues have negative real parts, the point (0,0) is classified as asymptotically stable.

Question 3.2: Type of the point (0,0) for the system: dx/dt = -2x - 2y, dy/dt = x - 4y.

To determine the type of the point (0,0), we consider the eigenvalues of the matrix A.

Since the eigenvalues have the same negative real part, the point (0,0) is classified as a proper node.

To know more about homogeneous systems of ODEs, refer here:

https://brainly.com/question/30504189#

#SPJ11

2. The production process for sodium hydroxide (NaOH) yields a 28 % by mass solution of sodium hydroxide in water. The 28 wt% NaOH solution is to process that produces 100 lbm per hour of 10 wt% NaOH solution. Calculate the quantities of the 28 wt% NaOH solution and the water needed to produce the product.

Answers

Approximately 35.71 lbm of the 28 wt% NaOH solution and 64.29 lbm of water are needed to produce 100 lbm per hour of the 10 wt% NaOH solution.

Let's denote the quantity of the 28 wt% NaOH solution as x lbm and the quantity of water as y lbm. We can set up a mass balance equation based on the NaOH content in the solutions.

The mass of NaOH in the 28 wt% solution is 0.28x lbm, and the mass of NaOH in the final 10 wt% solution is 0.10 ×100 lbm = 10 lbm.

Since NaOH is the only component contributing to the mass change, the mass balance equation becomes:

0.28x +( 0 ×y )= 10

Simplifying the equation, we get:

0.28x = 10

Solving for x, we find:

x = [tex]\frac{10}{0.28}[/tex] ≈ 35.71 lbm

So, approximately 35.71 lbm of the 28 wt% NaOH solution is needed.

To determine the quantity of water, we subtract the mass of the 28 wt% NaOH solution from the total mass required:

y = 100 - 35.71 ≈ 64.29 lbm

Learn more about  solution here :

brainly.com/question/30038172

#SPJ11

calculate the length of a square 7 cm long​

Answers

The length of the square, which is equivalent to its perimeter, is 28 cm.

The length of a square is typically referred to as the side length, as all sides of a square are equal. Given that the side length of the square is 7 cm, we can calculate the length of the square using the formula for the perimeter of a square.

The perimeter of a square is defined as the sum of the lengths of all four sides. Since all sides of a square are equal, we can simply multiply the side length by 4 to find the perimeter.

Perimeter of the square = 4 * side length

In this case, the side length of the square is 7 cm. Substituting this value into the formula, we get:

Perimeter = 4 * 7 cm

Perimeter = 28 cm

The length of a square is equal to its perimeter. Given a square with a side length of 7 cm, we can calculate the length by multiplying the side length by 4. In this case, the length of the square is 28 cm.

For more such question on perimeter. visit :

https://brainly.com/question/19819849

#SPJ8

For the equation given below, evaluate y' at the point (-2,2). y' at (-2,2)= e² + 40-e² = 6x² + 4y².

Answers

The value of y' at the point (-2, 2) is 40. Given the equation y' at (-2,2)= e² + 40-e² = 6x² + 4y², the value of y' at the point (-2, 2) can be evaluated as follows:

Substitute the value of x = -2 and y = 2 in the given equation:

y' at (-2,2) = e² + 40-e²

= 6(-2)² + 4(2)²

= e² + 40-e²

= 24 + 16

= 40

Thus, the value of y' at the point (-2, 2) is 40.Derivatives play a significant role in calculus and are used to find the rate of change of a function. The derivative of a function represents its slope at a particular point and is denoted by

f'(x) or dy/dx.

Suppose we have a function y = f(x), then the derivative of the function y' is given by

dy/dx = f'(x) = lim(Δx→0)[f(x + Δx) - f(x)]/Δx

The above equation represents the slope of the function at a particular point (x, y). If we substitute the value of x = -2 and y = 2 in the given equation, we get:

y' at (-2,2) = e² + 40-e² = 6(-2)² + 4(2)²

= e² + 40-e² = 24 + 16

= 40

To know more about point visit:-

https://brainly.com/question/32083389

#SPJ11

please help! thank you
Find the exact value of each of the following under the given conditions. \( \tan \alpha=-\frac{8}{15}, \alpha \) lies in quadrant II, and \( \cos \beta=\frac{3}{8}, \beta \) lies in quadrant I a. \(

Answers

The exact value of \( \tan \alpha \) is \( -\frac{8}{15} \) and the exact value of \( \sin \alpha \) is \( \frac{1}{5} \).


In quadrant II, the tangent function is negative. So, we know that \( \tan \alpha = -\frac{8}{15} \) is negative.

To find the exact value, we can use the trigonometric identity [tex]\( \tan^2 \alpha = \frac{\sin^2 \alpha}{\cos^2 \alpha} \).[/tex]

Since \( \tan \alpha \) is negative, we can write [tex]\( \tan^2 \alpha = \left(-\frac{8}{15}\right)^2 \)[/tex].

Next, we need to find [tex]\( \cos^2 \alpha \)[/tex]. We can use the identity [tex]\( \sin^2 \alpha + \cos^2 \alpha = 1 \) to find \( \sin^2 \alpha \).[/tex]

Since \( \alpha \) lies in quadrant II, we know that \( \cos \alpha \) is negative. From the given information, we have \( \cos \alpha = \frac{3}{8} \). Therefore, [tex]\( \cos^2 \alpha = \left(-\frac{3}{8}\right)^2 \)[/tex].

Now we can substitute the values into the identity:

[tex]\( \left(-\frac{8}{15}\right)^2 = \frac{\sin^2 \alpha}{\left(-\frac{3}{8}\right)^2} \)[/tex]

Simplifying, we have:

[tex]\( \frac{64}{225} = \frac{\sin^2 \alpha}{\frac{9}{64}} \)[/tex]

Cross-multiplying, we get:

[tex]\( \sin^2 \alpha = \frac{64}{225} \cdot \frac{9}{64} \)[/tex]
Simplifying further, we have:

[tex]\( \sin^2 \alpha = \frac{9}{225} \)[/tex]
Taking the square root of both sides, we find:

[tex]\( \sin \alpha = \frac{3}{15} = \frac{1}{5} \)[/tex]

To know more about exact value visit:

https://brainly.com/question/31743339

#SPJ11

Find all the minors of the elements in the matrix. M11​ =⎣⎡​20−3​489​−120​⎦⎤​ M12​=M13​=M21​=M22​=M23​=M31​=M32​=M33​=​ Find all the cofactors of the elements in the matrix.A11​=A12​=A13​=A21​=A22​=A23​=A31​=A32​=A33​​=

Answers

The minors of the elements in the matrix are:

M11​ = -18

M12​ = 0

M13​ = -4

M21​ = 6

M22​ = 0

M23​ = -20

M31​ = 8

M32​ = 12

M33​ = 76

The cofactors of the elements in the matrix are:

A11​ = 18

A12​ = 0

A13​ = 4

A21​ = 6

A22​ = 0

A23​ = 20

A31​ = -8

A32​ = 12

A33​ = 76

To find the minors and cofactors of the elements in the matrix, we need to calculate the determinants of the corresponding submatrices.

The given matrix is:

A = ⎣⎡20 -3⎦⎤

       ⎡ 4 8 9 ⎤

       ⎣−1 2 0⎦

To find the minors, we calculate the determinants of the 2x2 submatrices formed by excluding the row and column of each element:

M11​ = determinant of the submatrix ⎣⎡ 8 9 ⎦⎤ = (8 * 0) - (9 * 2) = -18

M12​ = determinant of the submatrix ⎣⎡-1 0⎦⎤ = (-1 * 0) - (0 * -1) = 0

M13​ = determinant of the submatrix ⎣⎡-1 2⎦⎤ = (-1 * 2) - (2 * -1) = -4

M21​ = determinant of the submatrix ⎣⎡20 -3⎦⎤ = (20 * 0) - (-3 * 2) = 6

M22​ = determinant of the submatrix ⎣⎡-1 0⎦⎤ = (-1 * 0) - (0 * -1) = 0

M23​ = determinant of the submatrix ⎣⎡20 -3⎦⎤ = (20 * -1) - (-3 * 20) = -20

M31​ = determinant of the submatrix ⎣⎡ 4 8 ⎦⎤ = (4 * 0) - (8 * -1) = 8

M32​ = determinant of the submatrix ⎣⎡20 -3⎦⎤ = (20 * 0) - (-3 * 4) = 12

M33​ = determinant of the submatrix ⎣⎡20 -3⎦⎤ = (20 * 2) - (-3 * 8) = 76

To find the cofactors, we multiply each minor by (-1)^(i+j), where i and j are the row and column indices:

A11​ = (-1)^(1+1) * M11​ = -1 * (-18) = 18

A12​ = (-1)^(1+2) * M12​ = 1 * 0 = 0

A13​ = (-1)^(1+3) * M13​ = -1 * (-4) = 4

A21​ = (-1)^(2+1) * M21​ = 1 * 6 = 6

A22​ = (-1)^(2+2) * M22​ = 1 * 0 = 0

A23​ = (-1)^(2+3) * M23​ = -1 * (-20) = 20

A31​ = (-1)^(3+1) * M31​ = -1 * 8 = -8

A32​ = (-1)^(3+2) * M32​ = 1 * 12 = 12

A33​ = (-1)^(3+3) * M33​ = 1 * 76 = 76

Therefore, the minors of the elements in the

matrix are:

M11​ = -18

M12​ = 0

M13​ = -4

M21​ = 6

M22​ = 0

M23​ = -20

M31​ = 8

M32​ = 12

M33​ = 76

And the cofactors of the elements in the matrix are:

A11​ = 18

A12​ = 0

A13​ = 4

A21​ = 6

A22​ = 0

A23​ = 20

A31​ = -8

A32​ = 12

A33​ = 76

Learn more about matrix here

https://brainly.com/question/30389982

#SPJ11

Find an equation of the plane. the plane through the point (6, −3, 6) and perpendicular to the vector -i + 3j + 4k

Answers

The equation of the plane through the point (6, -3, 6) and perpendicular to the vector -i + 3j + 4k is -x + 3y + 4z - 9 = 0.

The point-normal form of the equation of a plane can be used to determine the equation of a plane passing through a given point and perpendicular to a given vector.

An equation in a plane has a point-normal form when it

A(x - x₁) + B(y - y₁) + C(z - z₁) = 0,

where (x₁, y₁, z₁) is a point on the plane and (A, B, C) is a vector perpendicular to the plane.

Point on the plane: P₁ = (6, -3, 6)

Normal vector: N = -i + 3j + 4k

Substituting the values into the point-normal form equation, we get:

(-1)(x - 6) + (3)(y + 3) + (4)(z - 6) = 0

Simplifying the equation, we have:

-(x - 6) + 3(y + 3) + 4(z - 6) = 0

-x + 6 + 3y + 9 + 4z - 24 = 0

-x + 3y + 4z - 9 = 0

To learn more about equation of the plane link is here

brainly.com/question/32163454

#SPJ4

The lateral side of an isosceles trapezoid is equal to its smaller base, the angle at the base is 60 °, the larger base is 88. Find the radius of the circumscribed circle of this trapezoid.

Answers

the radius of the circumscribed circle of the isosceles trapezoid is (88√3) / 3.

How do we determine?

We will use the  properties of cyclic quadrilaterals.

R = radius of the circumscribed circle

"s" =  lateral side length  and

"b" =  the smaller base length

In a cyclic quadrilateral, opposite angles are supplementary.

angle at the base=  60°, t

the opposite angle 180° - 60° = 120°.

The equation for the isosceles triangle is set as :

sin(60°) = (b/2) / R

We know that  sin(60°) = √3 / 2,

√3 / 2 = (b/2) / R

R = (b/2) / (√3 / 2)

R = b / √3

Te smaller base =  88,

R = 88 / √3

R = (88√3) / (√3 * √3)

R = (88√3) / 3

Learn more about isosceles triangle  at:

https://brainly.com/question/29793403

#SPJ1

Calculate dx 2
d 2
y

dx 2
d 2
y

= /1 Points] WANEFMAC7 12.3.012. The position s of a point (in feet) is given as a function of time t (in seconds). s=−17+t−15t 2
;t=4 (a) Find the point's acceleration as a function of t. s ′′
(t)=ft/sec 2
(b) Find the point's acceleration at the specified time.

Answers

A -  the point's acceleration as a function of t is given by: s''(t) = a = -30 ft/sec^2

B -  at t = 4, the point's acceleration is -30 ft/sec^2.

To find the acceleration of the point, we need to differentiate the position function twice with respect to time. Let's calculate it step by step:

Given position function:

s = -17 + t - 15t^2

(a) Acceleration as a function of time:

To find the acceleration, we need to differentiate the position function twice with respect to time.

First, we differentiate s with respect to t to find the velocity function:

v = s' = d(s)/dt = d(-17 + t - 15t^2)/dt = 1 - 30t

Next, we differentiate v with respect to t to find the acceleration function:

a = v' = d(v)/dt = d(1 - 30t)/dt = -30

Therefore, the point's acceleration as a function of t is given by:

s''(t) = a = -30 ft/sec^2

(b) Acceleration at the specified time t = 4:

To find the acceleration at t = 4, we substitute t = 4 into the acceleration function we found in part (a).

s''(4) = -30 ft/sec^2

So, at t = 4, the point's acceleration is -30 ft/sec^2.

learn more about acceleration here:

https://brainly.com/question/2303856

#SPJ11

5. Prove that any integer of the form \( 8^{n}+1, n \geq 1 \) is composite.

Answers

By mathematical induction, we have shown that any integer of the form [tex]\(8^n + 1, n \geq 1\)[/tex] is composite.

When [tex]\(n = 1\), \(8^n + 1 = 8 + 1 = 9\)[/tex], which is a composite number. Therefore, the statement is true for the base case.

Now suppose that [tex]\(8^k + 1\)[/tex] is composite for some integer [tex]\(k \geq 1\)[/tex].

We want to show that [tex]\(8^{k+1} + 1\)[/tex] is also composite.

Expanding, we have:[tex]\[8^{k+1} + 1 = 8 \cdot 8^k + 1 = 8 \cdot (8^k + 1) - 7\][/tex]

By the induction hypothesis, [tex]\(8^k + 1\)[/tex] is composite, so it can be written as a product of two integers, say [tex]\(a\)[/tex] and [tex]\(b\)[/tex], where [tex]\(a\)[/tex] and[tex]\(b\)[/tex] are both greater than 1.

Thus, we have[tex]:\[8 \cdot (8^k + 1) - 7 = 8ab - 7\][/tex]

We can see that [tex]\(8ab - 7\)[/tex] is the difference of two odd numbers and is therefore even.

We can factor out a 2 to obtain:[tex]\[8ab - 7 = 2(4ab - 3)\][/tex]

Thus, [tex]\(8^{k+1} + 1\)[/tex] is composite, since it can be expressed as the product of 2 and the odd integer [tex]\(4ab - 3\).[/tex]

Thus, by mathematical induction, we have shown that any integer of the form [tex]\(8^n + 1, n \geq 1\)[/tex] is composite.

To know more about mathematical induction, click here

https://brainly.com/question/29503103

#SPJ11

1-What is the probability of randomly selecting a New service?
New service Old service Totals
Student 12 22 34
Professor 17 10 27
Totals 29 32 61
2-Calculate the median for products sold per store using this data.
0, 77, 38, -5, 44, 62

Answers

the median is:(38 + 44) / 2 = 41. Therefore, the median for products sold per store using this data is 41.

1. Probability of randomly selecting a new service:In order to calculate the probability of selecting a new service randomly, you need to know the total number of services available and the number of new services available.

If you have this data available, you can use the following formula to calculate the probability:

Probability of selecting a new service = Number of new services / Total number of services. For example, if there are 20 services available and 5 of them are new, the probability of selecting a new service randomly would be:

Probability of selecting a new service = 5 / 20 = 0.25 or 25%Therefore, the probability of randomly selecting a new service is equal to the number of new services divided by the total number of services available.

2. Median calculation for products sold per store:

To calculate the median for products sold per store using this data (0, 77, 38, -5, 44, 62), you need to follow these steps:

Step 1: Arrange the data in ascending order: -5, 0, 38, 44, 62, 77

Step 2: Find the middle value of the data set. Since there are six numbers in the data set, the middle value is the average of the two middle numbers.

Therefore, the median is:(38 + 44) / 2 = 41. Therefore, the median for products sold per store using this data is 41.

To know more about median here

https://brainly.com/question/300591

#SPJ11

Solve the following system of congruences showing all of your work: 3x = 2 (mod 5) x = 1 (mod 7) 13x3 (mod 16) by reading the handout on the Chinese Remainder Theorem.

Answers

To solve the system of congruences 3x ≡ 2 (mod 5), x ≡ 1 (mod 7), and 13x ≡ 3 (mod 16), we can apply the Chinese Remainder Theorem.

First, let's solve the congruence 3x ≡ 2 (mod 5):
Since gcd(3, 5) = 1, the congruence has a unique solution.
To find x, we multiply both sides by the modular inverse of 3 modulo 5, which is 2.
So, 2 * 3x ≡ 2 * 2 (mod 5) gives us 6x ≡ 4 (mod 5).

Now, let's solve the congruence x ≡ 1 (mod 7):
The congruence is already in the form x ≡ a (mod m), where a = 1 and m = 7.

Finally, let's solve the congruence 13x ≡ 3 (mod 16):
Since gcd(13, 16) = 1, the congruence has a unique solution.
To find x, we multiply both sides by the modular inverse of 13 modulo 16, which is 5.
So, 5 * 13x ≡ 5 * 3 (mod 16) gives us 65x ≡ 15 (mod 16).

Using the Chinese Remainder Theorem, we can combine the solutions of the individual congruences.
The system of congruences is now:
6x ≡ 4 (mod 5)
x ≡ 1 (mod 7)
65x ≡ 15 (mod 16)

To solve this system, we can use the method of simultaneous equations or substitution.

Let's use the substitution method:
From the first congruence, we can rewrite it as x ≡ 4 (mod 5).
Substituting this into the second congruence, we have:
4 ≡ 1 (mod 7).

Simplifying, we get 3 ≡ 0 (mod 7).
This means that x ≡ 4 (mod 5) and x ≡ 0 (mod 7).

Now, let's find the solution for x using the Chinese Remainder Theorem.
We can express the solution as x ≡ a (mod m), where a is the remainder obtained from the substitution method, and m is the product of the moduli (5 and 7).

Calculating the product of the moduli, we get m = 5 * 7 = 35.
So, the solution is x ≡ 0 (mod 35).

Therefore, the solution to the system of congruences is x ≡ 0 (mod 35).

To know more about congruences , visit:

https://brainly.com/question/31992651

#SPJ11

Evaluate the definite integral (a) √3.5 √7 - 2xdx (b) Ste-2/2dt.

Answers

(b) the value of the definite integral ∫[0, 2] [tex]e^{(-2t/2)}[/tex] dt is -[tex]e^{(-2)}[/tex] + 1.

(a) To evaluate the definite integral ∫[√3.5, √7] (√7 - 2x) dx:

Let's first find the antiderivative of (√7 - 2x):

∫(√7 - 2x) dx = (√7x - [tex]x^2[/tex]) - [tex]x^2[/tex]/2 + C

Now, we can evaluate the definite integral:

∫[√3.5, √7] (√7 - 2x) dx = [((√7 * √7) - [tex](sqrt7)^2[/tex]) - (√[tex]7)^2[/tex]/2] - [((√3.5 * √3.5) - (√[tex]3.5)^2[/tex]) - (√[tex]3.5)^2[/tex]/2]

Simplifying the expression:

= [7 - 7 - 7/2] - [3.5 - 3.5 - 3.5/2]

= [-7/2] - [-3.5/2]

= -7/2 + 3.5/2

= -3.5/2

= -1.75

Therefore, the value of the definite integral ∫[√3.5, √7] (√7 - 2x) dx is -1.75.

(b) To evaluate the definite integral ∫[0, 2] [tex]e^{(-2t/2)}[/tex] dt:

Notice that [tex]e^{(-2t/2)}[/tex] simplifies to e^(-t).

Now, we can evaluate the definite integral:

∫[0, 2] [tex]e^{(-t)}[/tex] dt = [-[tex]e^{(-t)}[/tex]] from 0 to 2

= -e[tex]^{(-2)} - (-e^0)[/tex]

= -[tex]e^{(-2)}[/tex] + 1

To know more about integral visit:

brainly.com/question/31433890

#SPJ11

Michael is paid $9 per hour to work at the movie theater and $7 per hour when he helps his aunt at her bakery. Michael cannot work more than 32 hours in a week, but he wishes to earn at least $251 each week. Which weekly work schedule is within Michael’s constraints?
8 hours at the movie theater and 25 hours at the bakery
15 hours at the movie theater and 20 hours at the bakery
19 hours at the movie theater and 12 hours at the bakery
21 hours at the movie theater and 8 hours at the bakery

Answers

The weekly work schedule within Michael’s constraints is 19 hours at the movie theater and 12 hours at the bakery.

Let,

[tex]x=[/tex] number of hours working at the movie theater

[tex]y=[/tex] the number of hours working at the bakery

we know that

[tex]x + y < = 32 ----(1)[/tex]

[tex]9x + 7y > $251 - - - - (2)[/tex]

Now we will check by verifying the inequality for option C

[tex]x=19 \ hours[/tex]

[tex]y=12 \ hours[/tex]

Verify inequality 1

[tex]19 + 12 < = 32 \ hours[/tex]

[tex]31 < = 32 \ hours[/tex] which is True.

Verify inequality 2

[tex]9 * 19 + 7 * 12 > =\$251[/tex]

[tex]\$ 255 > =\$251[/tex] which is true.

therefore,

The work schedule of case C) is within Michael's limitations

Read more about equality:

https://brainly.com/question/42013 .

what is the 3.63 x 10^8 in standard notation?

Answers

3.63 x 10^8 in standard notation is 363,000,000.

C- Show that B=1/T for an ideal gas having the equation of state (pv=nRT)

Answers

The equation of state for an ideal gas is given by pv = nRT, where p is the pressure, v is the volume, n is the number of moles, R is the gas constant, and T is the temperature. By rearranging the equation, we can demonstrate that B = 1/T, where B is the second virial coefficient.

The second virial coefficient, B, is a thermodynamic property that describes the interactions between gas molecules. For an ideal gas, the second virial coefficient is zero, indicating no intermolecular interactions. By substituting the ideal gas equation of state (pv = nRT) into the expression for B, we can demonstrate that B = 1/T.

Starting with the ideal gas equation pv = nRT, we can rearrange it as p = (nRT)/v. Then, we substitute this expression for p into the equation for B, which is B = -RT/v + p/(RT)^2. Simplifying this expression, we get B = -RT/v + (nRT)/(v(RT))^2.

Since we are considering an ideal gas, which means there are no intermolecular forces or interactions, the first term in the equation becomes zero (RT/v = 0). Therefore, the equation simplifies to B = (nRT)/(v(RT))^2.

Further simplifying, we cancel out the R and T terms, resulting in B = 1/(vT). Since n/v represents the number density of the gas, we can rewrite B as B = 1/(n/V)T. Finally, recognizing that n/V is equal to the molar concentration, we have B = 1/cT, and B = 1/T.

Hence, it is demonstrated that for an ideal gas described by the equation of state pv = nRT, the second virial coefficient B is equal to 1/T.

Learn more about density here:

https://brainly.com/question/29107073

#SPJ11

HARMATHAP12 10.1.052. MY NOTES Analysis of daily output of a factory shows that, on average, the number of units per hour y produced after t hours of production is y 140 0.5-Posts 12. (a) Find the critical values of this function. (Assume-<< Enter your answers as a comma-separated list.) AM (b) which cntical values make sense in this particular problem? (Enter your answers as a comma-separated list.) TH (For which values of t, for osts 12, is y increasing? (Enter your answer using interval notation.) (d) Graph this function. 200 DETAILS 600 500 400 300 700 600 500 400 300 ASK YOUR TEACHER PRACTICE ANC Points] DETAILS alysis of daily output of a factory shows that, on average, the number of units per hour y produced after t hours of production is y = 140t + 0.5t²t³, osts 12. (a) Find the critical values of this function. (Assume - t= t= (b) Which critical values make sense in this particular problem? (Enter your answers as a comma-separated list.) (d) Graph this function. y (c) For which values of t, for 0 ≤ t ≤ 12, is y increasing? (Enter your answer using interval notation.) 700 600 HARMATHAP12 10.1.052. 500 400 300 -

Answers

(a) The critical values of the function are t = 0 and t = 12.

(b) In this particular problem, the critical value t = 12 makes sense.

(a) To find the critical values of the function, we need to determine the values of t where the derivative of the function is equal to zero or does not exist. Taking the derivative of the given function, we have y' = 140 + t + 0.5t².

Setting y' equal to zero, we can solve for t:

140 + t + 0.5t² = 0

Simplifying the equation and factoring, we get:

0.5t² + t + 140 = 0

Using the quadratic formula, we find the solutions for t:

t = (-1 ± √(1 - 4 * 0.5 * 140)) / (2 * 0.5)

After solving the equation, we obtain two solutions: t = 0 and t = 12. These are the critical values of the function.

(b) In this specific problem, the critical value t = 12 makes sense because it falls within the given context of the analysis. The function represents the number of units produced per hour after t hours of production. Therefore, it is logical to consider the critical value t = 12, which indicates the maximum or minimum point in the production process.

(c) To determine the values of t for which y is increasing, we need to examine the sign of the derivative. Since y' = 140 + t + 0.5t², we can observe that the derivative is positive for all values of t. Thus, the function y is increasing for the interval 0 ≤ t ≤ 12.

(d) To graph the function, we can plot the points on a coordinate plane. The y-axis represents the number of units produced per hour (y), and the x-axis represents the hours of production (t). By plotting the points using the equation y = 140t + 0.5t², we can visualize the shape of the function and observe any trends or patterns.

Learn more about Critical functions

brainly.com/question/36886

#SPJ11

Find the number of ways of arranging the letters in the word BEACHFRONT if the second and third letters must be vowels and the last letter must be a consonant. Show all your work.

Answers

The number of ways of arranging the letters in the word BEACHFRONT such that the second and third letters are vowels and the last letter is a consonant can be found using combinatorics.

The number of ways of arranging the letters satisfying the given conditions is 4,320.

To find the number of arrangements, we need to consider the positions of the vowels (E, A, and O) and the consonants (B, C, H, F, R, N, and T) separately.

1) Vowels: The second and third letters must be vowels (E, A, or O). We have 3 choices for the second letter and 2 choices for the third letter. The remaining 8 letters (including the other vowels) can be arranged in any order in the remaining 7 positions. Therefore, the number of arrangements for the vowels is 3 * 2 * 8! = 2,880.

2) Consonants: The last letter must be a consonant. We have 8 consonants to choose from. The remaining 8 letters (including the vowels) can be arranged in any order in the remaining 8 positions. Therefore, the number of arrangements for the consonants is 8 * 8! = 32,768.

3) Total Arrangements: To find the total number of arrangements that satisfy the given conditions, we multiply the number of arrangements for the vowels and consonants. Therefore, the total number of arrangements is 2,880 * 32,768 = 4,320.

Thus, there are 4,320 ways to arrange the letters in the word BEACHFRONT such that the second and third letters are vowels and the last letter is a consonant.

To know more about combinatorics, refer here:

https://brainly.com/question/31293479

#SPJ11

Find the cosine of ∠G. Simplify your answer and write it as a proper fraction, improper fraction, or whole number. Help please ASAP.

Answers

The cosine of angle G can be written as:

cos(G) = 3/5

How to find the cosine of angle G?

Remember that for a right triangle, the cosine of one angle is given by the trigonometric relation:

cos(G) = (adjacent cathetus)/(hypotenuse)

In this diagram, we can see that the measures are:

adjacent cathetus = 3

hypotenuse = 5

Then the cosine of angle G is:

cos(G) = 3/5

Learn more about right triangles at:

https://brainly.com/question/2217700

#SPJ1

Given The Recursive Definition Below A1=3an=21an−1 For N≥2 A) Write Out The First 5 Terms Of The Sequence B) Determine If

Answers

We can conclude that the sequence is increasing.

A) To write out the first 5 terms of the sequence, we can use the recursive definition:

A1 = 3

An = 2^(An-1)

Using this definition, we can find the subsequent terms as follows:

A2 = 2^(A1) = 2^3 = 8

A3 = 2^(A2) = 2^8 = 256

A4 = 2^(A3) = 2^256 (a very large number)

A5 = 2^(A4) = 2^(a very large number) (an extremely large number)

The first 5 terms of the sequence are: 3, 8, 256, a very large number, an extremely large number.

B) To determine if the sequence is increasing or decreasing, we can compare adjacent terms.

Looking at the first few terms, we can observe that the sequence is increasing:

3 < 8 < 256 < a very large number < an extremely large number.

Therefore, we can conclude that the sequence is increasing.

Learn more about  sequence from

https://brainly.com/question/28036578

#SPJ11

Time X spent on a computer is gamma distributed with mean 20 min and variance 80 min². A. The shape of this gamma distribution is B. The rate of this gamma distribution is C.P(X<24) is D. P (20 < X < 40) is For each of these values, write a number with three decimal places

Answers

The shape of this gamma distribution is 2,B. The rate of this gamma distribution is 0.05,C. P(X<24) is 0.868,D. P (20 < X < 40) is 0.486

The shape of the Gamma distribution is determined by the parameter k (k > 0) which is called the shape parameter or the index of the Gamma distribution.When the value of k is close to 0, the Gamma distribution is approximately equivalent to an exponential distribution.The shape of the gamma distribution is determined by the shape parameter k, and it is a right-skewed distribution since k>1. The smaller the value of k, the more it tends towards a normal distribution.For k=1, the gamma distribution is equivalent to an exponential distribution, which is used for modelling the waiting time between Poisson processes.

The Gamma distribution is determined by two parameters, a shape parameter k (k > 0) and a scale parameter θ (θ > 0).The rate of the Gamma distribution is given by the formula:rate = 1/θ

The rate of the Gamma distribution is 1/20 or 0.05 (given that the mean is 20 min)

To find P(X < 24), we need to standardize the distribution into a standard normal distribution as below:X ~ Γ(k, θ)Mean (μ) = kθVariance (σ²) = kθ²

Given, mean = 20 min, and variance = 80 min²

Therefore, kθ = 20 ....(1)And, kθ² = 80....(2)From (1), θ = 20/k

Substituting θ = 20/k in (2), k (20/k)² = 80k = 2

Substituting k=2 in (1), θ = 20/2 = 10

Now,X ~ Γ(2, 10)

Standardizing the gamma distribution as below:Z = (X - μ) / σZ = (X - 2 * 10) / sqrt(2 * 10²)Z = (X - 20) / sqrt(200)P(X < 24) = P(Z < (24 - 20) / sqrt(200))= P(Z < 1.118) = 0.868

To find P(20 < X < 40), we need to standardize the distribution into a standard normal distribution as below:X ~ Γ(k, θ)Mean (μ) = kθVariance (σ²) = kθ²

Given, mean = 20 min, and variance = 80 min²

kθ = 20 ....(1)And, kθ² = 80....(2)From (1), θ = 20/k

Substituting θ = 20/k in (2), we get:k (20/k)² = 80k = 2

Substituting k=2 in (1), we get:θ = 20/2 = 10

Now,X ~ Γ(2, 10)

[tex]Standardizing the gamma distribution as below:Z = (X - μ) / σZ = (X - 2 * 10) / sqrt(2 * 10²)Z = (X - 20) / sqrt(200)P(20 < X < 40) = P((20 - 20) / sqrt(200) < Z < (40 - 20) / sqrt(200))= P(0 < Z < 2.236) = 0.486[/tex]

To know more about gamma distribution visit:

https://brainly.com/question/28077799

#SPJ11

Other Questions
Linear Algebra($#) (Please explain innon-mathematical language as best you can)Recall that elementary row operations are one of threetype1. Switch two rows.2. Replace a row by the row plus a multiple of another row.3. Multiply ( scale ) a row by a non-zero scalar.Show that E is invertible by finding the inverse of E. Note that E1 is also an elementary matrix of the second type. Which of the following statement correctly describes the relationship between latitude and rotational velocity of the Earth?A. Rotational velocity is at a maxmimum at mid-latitudes (approximately the location of Buffalo) and decreases moving either north or south from thereB. Rotational velocity is not affected by latitude (no difference moving in a north-south direction)C. Rotational velocity decreases with increasing latitude (i.e. moving away from the equator)D. Rotational velocity increases with increasing latitude (i.e. moving away from the equator) Determine wo, R, and 8 so as to write the given expression in the form u R cos(wot - 6). = NOTE: Enter exact answers. R= wo= u =2 cos(7t) 3sin(rt) 8 = please help I need this ASAP What is the value of c?a)4 unitsb)5 unitsc)6 unitsd)7 units wind what do the arrows indicate? The capital gains yield, as used for supernormal dividend growth period in the non-constant dividend growth model, is equal to: r. g. D 1/P 0. none of the above he of the first drugs to be approved for use in treatment of acquired immune deficiency syndrome (AIDS) was azidothymidine (AZT). a. How many carbon atoms are sp 3hybridized? b. How many carbon atoms are sp 2hybridized? c. Which atom is sp hybridized? d. How many a bonds are in the molecule? d. How many bonds are in the molecule? e. How many bonds are in the molecule? f. What is the NNN bond angle in the azide (N 3) group? what is the expected financial value of a bet where you will win $52 if you draw a queen of hearts?group of answer choices How did enlightment philosphers influence the founding fathers of american government A: They provided the religous basis for representative democracy.B: They formed new ideas on monarchy and the role of the king in government C: Because Enlightment philosophers advocated for the absolute power of kings, the Founding Fathers sought to ensure that America remained loyal to the british crown.D: They provided the ideas of natural rights, government by consent, and seperation of powers, which promote the greatest possible liberty for the people Briefly discuss physical capital investment and long-run average cost in relation to a perfectly competitive market. Briefly explain what a market will show if perfectly competitive firms produce at the minimum of the long-run average cost curve and explain why this happens. Briefly explain what the market will illustrate when perfectly competitive firms produce at the quantity where P = MC and explain why this happens. EVO Conversion Systems and the Black Soldier Fly It's just April of 2G2] and Maggie Choi is already having a busy year.r Born and raised on a small farm outside of Brownwoo-d, in central Texas, she left the state as a young woman to study biology and anthropology at Williams College in Massachusetts. After college, homesick, she turned down a wellpayingjob at a Bostonbased pharmaceutical company and instead took a modestly paid job at the district office of US. Representative Kay Granger {RTX 12'II Congressional District) in Fort Worth. TX] 2 is a district that stretches from Fort Worth to encompass many nlral areas to its west (see Appendix I for description of district as well as Rep. Granger). Alter working in Representative Granger's office for five years, where she ultimately was promoted to deputy district director. she decided to return to school to pursue her doctoral studies in entomology at Texas A&M University (TAMU). At TAMU, she worked in Dr. Vineeta Roy's lab and wrote her dissertation on a remarkable insect, the black soldier fly (BSF). After receiving her masters and PhD. in 2020. Dr. Choi joined EVO Conversion Systems {hereinafter EVO; more below), Dr. Roy's small. 8-person, start-up company, in College Station. EVE), using technology and knowhow developed at TAMU. was in the business of rearing and selling BSFs. BSF has several uses, but one of its primary ones is as a high protein feed. especially for poultry, hogs and fish (via aquaculture). As part ofher many duties at EVD, Dr. Choi had the task of understanding the policies that could drive or hinder their business. This was particularly important to know now, because EVO was gearing up for their Series A funding and the investors were worried about the policy environment surrounding their business. The politics of food, in general, especially how food is grown or reared, in particular, was becoming increasingly complicated. At one point, all that poultry or hog producers needed to worry about on the public policy side were the agricultural support programs contained in the farm bills that made their way every few years through the Agriculture committees in the U.S. House of Representatives and the Senate and were administered by the LLS. Department of Agriculture (USDA). Feed companies stepped into the fold, just trying to maximize their production and drive down costs of the various feeds that they sold to these customers. Now. the issues about food policies have expanded on almost every dimension. The range is huge: human health concerns related to obesity, cardiac and coronary diseases; the use ofgrowth hormones and steroids and other concerns about what is fed to animals for human consumption [like hogs and chickens]: animal husbandry; land management; greenhouse gases; the use of human food {e.g., soy, corn. rice) for animal feeds: and unjust labor practices, just to name a few. Additionally, many stakeholders, including environmental and animal rights groups, protested against many elements of the commercial poultry, meat. and aquaculture industries. For example, the Sierra Club, an environmental NGO, sued commercial hog producers for contaminated run off from many of the water holding ponds associated with pig farms. Many humanitarian groups lamented that foods suitable for human consumption like corn {maize} and soybeans are used for feedstock for animals and fish. Academic studies linked meat production, particularly raising hogs and beefcattle, as contributing towards greenhouse gases and climate warming. In the U.S.. P.E.T.A.. a NGD fighting against animal cruelty. in 2020 began a social media campaign to educate people about the diseases and suffering of chickens kept in close quarters for industrial production. Moreover, "Iron Chef' Masaharu Morimoto. famous for his fish-based dishes, in a Six Mile Electronics completed these selected transactions during March 2018 Click the icon to view the transactions) Requirement 1. Report these hame on Six Mie Electronics' balance sheet at March 31, 2018 Select the balance sheet accounts, then calculate each accounts' balance and the total ourent abilities amount at March 31, 2018. (For the FICA tax, be sure to include both the employer and employee share of the tax Round all amounts to the nearest whole dollar if a box is not used in the table leave the box empty: do not select a label or enter a z) Account Ourent Sabes Long-lem kabiles Six Mile Electronics Balance Sheet (partial) March 31, 2018 Amount Transactions a Sales of $3,250,000 are subject to an accrued warranty cost of 2% The acoued warranty payable at the beginning of the year was $35.000, and warranty payments for the year totaled $61,000 On March 1, Six Mile Electronics signed a $40,000 note payable that requires annual payments of $8,000 plus 4% interest on the unpaid balance beginning March 1, 2019 e. Bonta inc, a chain of discount stores, ondared $150,000 worth of wireless speakers and related products with its order, Bonita ine, sent a check for $150,000 in advance, and Six Mile shipped $80,000 of the goods Six Mie will shop the remainder of the goods on April 3, 2018 d. Six Mie's March payroll of $320.000 is subject to employee withheld income tax of $30,200 and FICA tax of 765% On March 31, Six Mile pays employees their take home pay and accruesa x amounts Print Done Six Mile Electronics completed these selected transactions during March 2018: (Click the icon to view the transactions.) Requirement 1. Report these items on Six Mile Electronics' balance sheet at March 31, 2018. Select the balance sheet accounts, then calculate each accounts' balance and the total current liabilities amount at March 31, 2018. (For the FICA t nearest whole dollar. If a box is not used in the table leave the box empty, do not select a label or enter a zero.) Account Current liabilities: Six Mile Electronics Balance Sheet (partial) March 31, 2018 Previous que Amount Gaseous methane (CH 4) feacts with gaseous axygen gas (O 2) to produce gaseous cerbon dioxide (CO 2) and gaseous water (H 2O). What is the theoretcal vied of carton dioxlde formed from the resction of 0.48 g of methane and 1.6 s of oxygen gas? Be sure your answer has the correct number of significant digits in it. Design a code converter circuit that takes a 4-bits binary number as inputs and find the corresponding output as follows -If the input number is multiple of 5 then the output = (input * 4 + 2)/3 - If the input number is not multiple of 5 then output = (input * 3 - 1)/4 (Note that 0 is multiple of 5,, Note if the output = 5.7 the floor of 5.7 which = 5) Follow the steps for combinational circuit design and find the minimum POS for each output. Implement the design using Verilog, verify it by using waveform then download your circuit on the altera board, for Inputs switches will be used and for Outputs use LEDs. "Find the critical numbers of the functions.1. f(x) = te^5t2. f(x) = x^2ln(x)3. f(x) = 6tan^-1(x)-xPlease help!!!!!!" conversionsIncorrect Question 2 Unanswered Covert 44.4 m to dm 0.444 on 2 Question 3 Convert 175,000,000 dam to kim 0/1 pts 0/1 pts Evaluate Jeff Bezos's capacity for management and leadership, as well as whether his management philosophy influences how his company operates.? (long answer preferred) Pink Company has beginning inventory of 24 units at a cost of $13.00 each on May 1. On June 5, it purchases 13 units at $14.00 per unit. On June 12 it purchases 22 units at $18.00 per unit. On June 15, it sells 37 units for $32 each. Using the LIFO perpetual inventory method, what is the value of the inventory on June 15 after the sale? C++ Problem Statement:in C++ Write a program that computes and displays the charges for a patients hospital stay. First, the program should ask if the patient was admitted as an in-patient or an out-patient. If the patient was an in-patient, the following data should be entered: The number of days spent in the hospital The daily rate Hospital medication charges Charges for hospital services (lab tests, etc.)The program should ask for the following data if the patient was an out-patient: Charges for hospital services (lab tests, etc.) Hospital medication chargesThe program should use two overloaded functions to calculate the total charges. One of the functions should accept arguments for the in-patient data, while the other function accepts arguments for out-patient information. Both functions should return the total charges.Input Validation: Do not accept negative numbers for any data.