Evaluate the indefinite integral.
∫x^5/(x^6 + 4)^8 dx

Answer:  maybe about 45 or 75 i dont know

Step-by-step explanation:

Answer:

D 42

Step-by-step explanation:

45-42 is 3 and 42-3 is 39

The probability for a data point is less than is 0.8413.

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event.

The mean(μ)=4

Standard deviation(σ)=1

(P<5)

From the figure, standard normal distribution curve probability which we have to find P<5

It is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

P(x=4)=x-μ/σ

=4-4/1=0

P(x=4)=50%

P(x<5)=P(x=4)+P(x=1)

=50%+34.13%

=0.8413

P(x<5)=0.8413

Therefore, the probability a data point is less than 5 is 0.8413.

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Assuming no deposits or withdrawals are made,  the amount in the  account after 19 years is: 11,454. 133.

Using this formula

A = P(1+r/100)ⁿ

Where:

A = Amount =?

P = Principal = $4700

r = Interest rate =4.8%

n = the number of periods =19 years

Let plug in the formula

A = 4,700 (1 + 4.8/100)¹⁹

A = 4,700 (1 + 0.048)¹⁹

A = 4,700 (1.048)¹⁹

A = $11,454. 133

Therefore the amount is $11,454. 133.

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The solutions to the equation \(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

To solve the equation \(2/x - 1 = 16/(x^2 + 3x - 4),\) we'll simplify and rearrange the equation to isolate the variable x. Here's the step-by-step solution:

1. Start with the given equation: 2/x - 1 = 16/(x^2 + 3x - 4)

2. Multiply both sides of the equation by x(x^2 + 3x - 4) to eliminate the denominators:

\(2(x^2 + 3x - 4) - x(x^2 + 3x - 4) = 16x\)

3. Simplify the equation:

\(2x^2 + 6x - 8 - x^3 - 3x^2 + 4x - 16x = 16x\)

4. Combine like terms:

  -x^3 - x^2 + 14x - 8 = 16x

5. Move all terms to one side of the equation:

\(-x^3 - x^2 - 2x - 8 = 0\)

6. Rearrange the equation in descending order:

  -x^3 - x^2 - 2x + 8 = 0

7. Try to find a factor of the equation. By trial and error, we find that x = 2 is a root of the equation.

8. Divide the equation by (x - 2):

\(-(x - 2)(x^2 + x - 4) = 0\)

9. Apply the zero product property:

  x - 2 = 0 or x^2 + x - 4 = 0

10. Solve each equation separately:

   x = 2

11. Solve the quadratic equation:

   For x^2 + x - 4 = 0, you can use the quadratic formula or factoring to solve it. The quadratic formula gives:

 \(x = (-1 ± √(1^2 - 4(1)(-4))) / (2(1)) x = (-1 ± √(1 + 16)) / 2 x = (-1 ± √17) / 2\)

Therefore, the solutions to the equation\(2/x - 1 = 16/(x^2 + 3x - 4) are x = 2 and x = (-1 ± √17) / 2.\)

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Sherry's commitment and love for reading allowed her to embark on a literary adventure that spanned two days. From the initial taste of 1/3 to the final bite of the remaining line 2/3, she had read the entire book, savoring every word and getting lost in the magic of storytelling.

Sherry's reading adventure began with her diving into a book, eager to explore its contents. She managed to devour a portion of the book, specifically 1/3 of it, before feeling the sweet embrace of sleep and deciding to call it a night.

The following day arrived, and Sherry's desire to unravel the remaining mysteries of the book was still burning bright within her. Determined to quench her thirst for knowledge, she dedicated herself to reading the rest of the book. With focused determination, she turned page after page, immersing herself in the story's captivating world.

As the hours ticked by, Sherry felt the satisfaction of progress. With each passing chapter, she could sense herself inching closer to the climax and resolution of the story. The characters became like old friends, and the plot twists kept her on the edge of her seat.

Finally, as the sun dipped below the horizon, Sherry turned the last page and completed the final chapter. She had done it. She had finished reading the entire book. The sense of accomplishment washed over her, accompanied by a bittersweet feeling that the journey had come to an end.

Reflecting on her reading experience, Sherry realized that she had initially read 1/3 of the book before retiring for the night. That meant there were still 2/3 of the book left for her to discover on the subsequent day. And indeed, she did just that. She dedicated her time and energy to devouring the remaining 2/3 of the book, leaving no page unturned.

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Answer:

The x-intercept of the graph tells you that as the "number of movie tickets" increase, the less balance Jeremiah has on his bank account.

Step-by-step explanation:

Behavior: The graph is in a downwards linear slope.

Look at the correlation between the x and y axis.

As x increases, y decreases

Answer:

43.96 pls like my answer and rate

Answer: 13?i really dont know

Step-by-step explanation:

Answer: Options 3, 4, 6

Step-by-step explanation:

\(4x-y=6 \\\\-4x+y=-6\\\\y=4x-6\)

This means are looking for lines with a slope of 4 (since parallel lines have the same slope).

Answer:

Which lines are parallel to the graph of 4x – y = 6? Check all that apply.x – 4y = –12y – 2 = –4(x + 1)y + 1 = 4(x – 2)y = 4x + 11y = x – 38x – 2y = 6

Step-by-step explanation:

Which lines are parallel to the graph of 4x – y = 6? Check all that apply.x – 4y = –12y – 2 = –4(x + 1)y + 1 = 4(x – 2)y = 4x + 11y = x – 38x – 2y = 6

Effective leadership can be demonstrated in many different ways, but here are a few examples of actions that may indicate effective leadership by a group leader:

1. Clear communication: A group leader who communicates clearly and effectively with their team is more likely to build trust and respect among the group.

2. Empathy and emotional intelligence: A leader who demonstrates empathy and emotional intelligence can help build a positive team culture by understanding and acknowledging the feelings and needs of their team members.

3. Delegation and empowerment: An effective leader knows how to delegate tasks and responsibilities to team members in a way that maximizes their strengths and abilities, while also providing support and guidance as needed.

4. Leading by example: A leader who sets a positive example for their team by modeling the behaviors and attitudes they want to see in their team is more likely to earn respect and trust from their team members.

5. Strategic thinking: A leader who is able to think strategically and make informed decisions based on data and evidence can help steer their team towards success.

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1. The total amount of candy is 1,080 pieces of candy.

2. Each student would get 72 pieces of candy.

Answer:

each student will get 5 pieces of candy

Step-by-step explanation:

20+15+25+12 =72

72 divided by 15 = 5

Answer:sorry  I’m ish could help

The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.

The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:

(a) Local non-satiation:

This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.

(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:

MU1 = α * xi^(α−1) * x2^(β)

The marginal utility of x2 can be obtained as:

MU2 = β * xi^(α) * x2^(β−1)

Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.

(c) Quasi-concavity:

The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.

(d) Homotheticity:

The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.

In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.

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The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Answer:

wrwhrowurhiuwirhirhiaruarhuaiwrhaihaiowawlrhwauilrhawuirhwauihruaiwhruawilhawuirawlirwairawriahrihawirhlairhawirahwulrihawuilrhawilr to you too. :)

Step-by-step explanation:

Answer:

wrwhrowurhiuwirhirhiaruarhuaiwrhaihaiowawlrhwauilrhawuirhwauihruaiwhruawilhawuirawlirwairawriahrihawirhlairhawirahwulrihawuilrhawilr

Step-by-step explanation:

(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

The result is obtained by using the exponential decay equation.

The exponential decay equation can be used to calculate radioactive decay for the activity, the nuclei, and also the mass. The exponential decay equation for the mass is

\(m = m_{o} e^{-\lambda t}\)

Where

The half-life of radium-226 is 1600 years and the mass of a sample is 27 mg.

(a) What is the remaining mass after 4500 years?

(b) What is the decay time if the remaining mass is 15 mg?

First, let's calculate the decay constant.

λ = 0.693/T½

λ = 0.693/1600

λ = 0,000433

After 4500 years, the remaining mass is

\(m = m_{o} e^{-\lambda t}\)

\(m = 27 e^{-0.000433 \times 4500}\)

m = 27 × 0.142

m = 3.8 mg

If the remaining mass is 15 mg, the decay time is

\(m = m_{o} e^{-\lambda t}\)

\(15 = 27 e^{-0.000433 t}\)

\(ln \frac{15}{27} = ln (e^{-0.000433 t})\)

\(ln \frac{15}{27} = -0.000433 t\)

-0.588 = - 0.000433t

t = 1357.9 years

Hence,

(a) After 4500 years, the sample will remain 3.9 mg.

(b) The sample will remain 15 mg after 1369 years.

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We can group the minterms to obtain the minimum sum of products (SOP):

F(A,B,C,D) = A'B' + CD' + ABC + A'B'CD' + ABCD

Expansion of the function f(A,B,C,D):

f(A,B,C,D) = (A+B+D')(A'C)(C+D)

= A'A'C + A'CC' + BA'C + BC + D'A'C + D'CC' + BD'(A'C) + BD'(C+D)

= 0 + 0 + BA'C + BC + 0 + 0 + BD'A'C + BD'C + BD'D

= BA'C + BC + BD'A'C + BD'C + BD'D

Minterms SOP for the function with K-map 5.16:

The truth table for the given function is:

A B C F

0 0 0 0

0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 0

1 1 1 1

The K-map for this function is:

BC

A 00 01 11 10

0 |  0  1  0  1

1 |  1  0  0  1

We can group the minterms to obtain the minimum sum of products (SOP):

F(A,B,C) = A'B' + A'C + BC

Karnaugh map and minimum sum of products for the function F(A,B,C,D)=A'B'+CD'+ABC+A'B'CD'+ABCD:

The truth table for the given function is:

A B C D F

0 0 0 0 0

0 0 0 1 1

0 0 1 0 0

0 0 1 1 0

0 1 0 0 1

0 1 0 1 0

0 1 1 0 1

0 1 1 1 1

1 0 0 0 0

1 0 0 1 0

1 0 1 0 0

1 0 1 1 0

1 1 0 0 1

1 1 0 1 1

1 1 1 0 1

1 1 1 1 1

The K-map for this function is:

   CD

AB 00 01 11 10

00 |   0  1  0  0

01 |   1  0  0  1

11 |   1  1  1  1

10 |   0  0  1  0

We can group the minterms to obtain the minimum sum of products (SOP):

F(A,B,C,D) = A'B' + CD' + ABC + A'B'CD' + ABCD

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It should be noted that z^4 will be -32 in rectangular form.

Based on the information, z = r(cos θ + i sin θ), and provided positive integer n, then it is implied that:

z^n = r^n (cos nθ + i sin nθ)

In this instance, we need to solve for z^4 in rectangular form when z = -2 - 2i. Firstly, we must calculate |z| and arg(z):

|z| = √((-2)^2 + (-2)^2) = 2√2

arg(z) = arctan(-2/-2) = π/4

Leveraging De Moivre's theorem, we can effectively deduce the value of z^4 as:

z^4 = (2√2)^4 (cos (4π/4) + i sin (4π/4))

= 32 (cos π + i sin π)

= -32

Concludedly, z^4  resolved in rectangular form is -32.

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The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

Answer: 15 - 6i

Step-by-step explanation:

3(5-2i)

3×5+3×(−2i)

Do the multiplications.

15−6i

Answer:

An angle whose measure is equal to 90° is called a right angle. A 180° angle is called a straight angle. Angles such as 270 degrees which are more than 180 but less than 360 degrees are called reflex angles. A 360° angle is called a complete angle.

Answer:

Yes

Step-by-step explanation:

If a triangle is a right triangle, the 3 side lengths will check out in the Pythagorean Theorem.

\(a^2+b^2=c^2\)

where a and b are the legs and c is the hypotenuse.

The legs are the 2 shorter lengths and the hypotenuse is the longest length. The 3 side lengths are: 16,63 and 65. Therefore, 16 and 63 are the legs and 65 is the hypotenuse.

a=16

b=63

c=65

\(16^2+63^2=65^2\)

Evaluate each exponent.

16^2=16*16=256

\(256+63^3=65^2\)

63^2=63*63=3969

\(256+3969=65^2\)

65^2=65*65=4225

\(256+3969= 4225\)

Add 256 and 3969

\(4225=4225\)

The statement above is true; 4225 is equal to 4225. Therefore, this is a right triangle because the side lengths check out when plugged into the Pythagorean Theorem.

The constant variation rate is given as follows:

62.5 miles per hour.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Hence we can solve for the constant as follows:

k = y/x.

In the context of this problem, the constant variation rate is the constant of the proportional relationship, obtained dividing one output by it's respective input, hence:

k = 375/6

k = 62.5 miles per hour.

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Answer:

5

Step-by-step explanation:

\(30 \div 5 = 6\)

Answer:

I would say likely.

Step-by-step explanation:

I hope this helps.

The sides of the right triangle are as follows:

x = 18 units

y = 15.6 units

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the sides of the right triangle using trigonometric ratios

tan 30° = opposite / adjacent

tan 30° = 9 / y

cross multiply

y = 9 / tan 30

y = 15.5884645362

y = 15.6 units

Let's find x

sin 30 = opposite / hypotenuse

sin 30° = 9 / x

x = 9 / 0.5

x = 18 units

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Answer:

The height of the window = x + 2 = 4.23 + 2= 6.23m

Step-by-step explanation:

The angle of elevation of the top of the house and the window is 60 and 45 degree.

We can proceed as drawing a diagram as a man of height 2m and a building of total height 12m.

we don't know the distance between man and the building let it be 'b'

\(\frac{x}{b}=tan 45\) =1

x=b .............(1)

total height of the building is given as 12m

  x + y + 2=12

x + y = 10 .....................(2)

\(\frac{x+y}{b} =\frac{x+y}{x }\)  = tan 60

\(\frac{10}{x} = \sqrt{3}\)

x = \(\frac{10}{\sqrt{3} }\)  ≈ 5.77m

y = 10 -   \(\frac{10}{\sqrt{3} }\)

y= 10(1-\(\frac{1}{\sqrt{3} }\) ) ≈ 4.23m

The height of the window = x + 2 = 4.23 + 2= 6.23m