Evaluate the integral. (Use C for the constant of integration.)
Integral (x − 7)sin(πx) dx

For a company that wants to teach self improvement seminars is holding of its seminar. The company will be take 12 attendees to break even. The company's total expenses and revenues both are equal to $384.

We have a company that teaches self-improvement seminars is holding one of its seminars. Flat fee spent by company to rent a facility, P = $324

Additionally, Spent by company on books for every attendee who registers = $ 5

The fee pay by each attendee for attending the seminar = $32

We have to determine the number of attendees. Let 'x' represent the total number of attendees who are registered. According to the above scenario, the break-even equation is written as R (revenue) = E( expenses), 32x = 5 x + 324

Simplify it,

32x - 5x = 324

=> 27 x = 324

=> x = 324/27

=> x = 12

So, It will take 12 attendees to break even. Now, the company's total expenses

= 5x + 324

= 5×12 + 324

= $384

The net income or revenue will also be

= 32 ×12

= $384

Hence, required value is $384..

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The partial derivatives of the function f(x,y) = xy*e^(-9y) with respect to x and y are: ∂f/∂x = ye^(-9y), and ∂f/∂y = x(-9y*e^(-9y)) + e^(-9y).

The first partial derivative concerning x is obtained by treating y as a constant and differentiating concerning x. The result is ye^(-9y), which means that the rate of change of f concerning x is equal to ye^(-9y).

The second partial derivative concerning y is obtained by treating x as a constant and differentiating concerning y. The result is x(-9ye^(-9y)) + e^(-9y), which means that the rate of change of f concerning y is equal to x times -9ye^(-9y) plus e^(-9y).

To better understand these partial derivatives, we can analyze the behavior of the function f(x,y) = xy*e^(-9y). As we can see, the function is the product of three terms: x, y, and e^(-9y). The term e^(-9y) represents a decreasing exponential function that approaches zero as y increases. Therefore, the value of f(x,y) decreases as y increases. The terms x and y represent a linear function that increases as x and y increase. Therefore, the value of f(x,y) increases as x and y increase.

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Answer:

Step-by-step explanation:

To find the probability that a student is a science major given that they are a graduate student, we need to use Bayes' theorem:

P(Science | Graduate) = P(Graduate | Science) * P(Science) / P(Graduate)

We know that P(Science) = 0.45 and P(Liberal Arts) = 0.55, and that P(Graduate | Science) = 0.35 and P(Graduate | Liberal Arts) = 0.25. We also know that the total probability of being a graduate student is:

P(Graduate) = P(Graduate | Science) * P(Science) + P(Graduate | Liberal Arts) * P(Liberal Arts)

Plugging in the values, we get:

P(Graduate) = 0.35 * 0.45 + 0.25 * 0.55 = 0.305

Now we can calculate the probability of being a science major given that the student is a graduate student:

P(Science | Graduate) = 0.35 * 0.45 / 0.305 = 0.515

Therefore, the probability that a student is a science major, given they are a graduate student, is approximately 0.515.

Answer:

0.72

Step-by-step explanation:

trust me

We can determine the population in 1820 was 8.5753 using a linear equation.

A linear equation is one that has just a constant and a first order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.

When x and y are the variables, the aforementioned is sometimes referred to as a "linear equation of two variables."

dp/dt = [tex]1.37^{t}[/tex]

Integrate both sides.

p[h] = ( [tex]1.37^{t}[/tex])/In (1.37)   + c

1810 ⇒ t = 0

7.4 = 1/In (1.37) + C

C = 4.2235

p(H) = ( [tex]1.37^{t}[/tex])/In (1.37) + 4.2235

P (1) =  [tex]1.37^{t}[/tex]In (1.37) + 4.2235

= 8.5753

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Probability density function for the continuous variable x is:

f(x) = (3/1000)(10-x)², if 0

Total area under the probability density function is equal to 1.

So, we integrate the function from 0 to 10:

∫[0,10] c(10−x)2 dx

= c ∫[0,10] (10−x)2 dx

= c [-(10-x)³/³] evaluated from 0 to 10

= c [(0-(-1000/3))]

= c (1000/3)

Since the area under the probability density function is equal to 1, we have:

∫[0,10] c(10−x)2 dx = 1

Puting the value of the integral:

c (1000/3) = 1

Solving for c, we get:

c = 3/1000

Therefore, the probability density function for the continuous variable x is:

f(x) = (3/1000)(10-x)², if 0

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Answer: 5

5/8/1/8, you can do 5x8 and also do 8x1 because you can not divide fractions after that you get 40/8 then you divide 40/8 is 5 so the answer is 5

The area of q is 20.

The area of a parallelogram determined by two vectors u and v is given by the magnitude of the cross product of u and v: |u x v|.

So, the area of the parallelogram p is:

| [4;1] x [3;-1] | = |(4)(-1) - (1)(3)| = |-7| = 7

To find the area of q, we apply the transformation T to each of the vertices of p and then compute the area of the resulting parallelogram.

First, we find the images of the vertices of p under T:

T([4;1]) = [3 1;1 2][4;1] = [16;6]
T([3;-1]) = [3 1;1 2][3;-1] = [6;1]

The sides of the parallelogram q are determined by the vectors T([4;1]) - T([3;-1]) = [10;5] and T([3;-1]) - [0;0] = [6;1].

The area of q is the magnitude of the cross product of these vectors:

| [10;5] x [6;1] | = |(10)(1) - (5)(6)| = |-20| = 20

Therefore, the area of q is 20.

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In hypothesis testing, making a decision that causes a false alarm is equivalent to committing a type-1 error.

In hypothesis testing, making a decision that causes a false alarm is equivalent to a Type-1 error. This occurs when we reject the null hypothesis even though it is actually true. It is important to control the probability of making type-1 errors, as this can lead to incorrect conclusions and wasted resources. The correct decision in hypothesis testing is to either accept or reject the null hypothesis based on the evidence presented. A type-2 error, on the other hand, occurs when we fail to reject the null hypothesis even though it is false.

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Answer:

-9?

Step-by-step explanation:

A total of 630 thousand bolts must be sold to maximize revenue. The correct answer is A) 630 thousand bolts.

To maximize revenue, we need to first determine the revenue function.

Revenue is given by the product of price (p) and quantity (x).

In this case, p = 63 - x/20.

Write the revenue function:

R(x) = px

= (63 - x/20)x

Simplify the function:

R(x) = 63x - (x²)/20

To maximize the revenue, find the vertex of the parabola formed by the quadratic function.

The x-coordinate of the vertex is given by -b/(2a), where a and b are the coefficients of x² and x, respectively.

In this case, a = -1/20 and b = 63. So, the x-coordinate of the vertex is:

x = -63 / (2  (-1/20))

= 63 (20 / 2)

= 630.

Therefore, option A) is correct.

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After the second outer loop iteration, the list is [6,1,7,8,9].

To determine the list after the second outer loop iteration, let's assume we're working with a simple bubble sort algorithm. Here are the steps:
1. First outer loop iteration:
  - Compare 6 and 9; no swap.
  - Compare 9 and 8; swap to get [6,8,9,1,7].
  - Compare 9 and 1; swap to get [6,8,1,9,7].
  - Compare 9 and 7; swap to get [6,8,1,7,9].
2. Second outer loop iteration:
  - Compare 6 and 8; no swap.
  - Compare 8 and 1; swap to get [6,1,8,7,9].
  - Compare 8 and 7; swap to get [6,1,7,8,9].

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Answer:

Using the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment

P = the principal (initial amount of investment)

r = the interest rate (as a decimal)

n = the number of times per year the interest is compounded

t = the time (in years)

Plugging in the values:

P = $500

r = 6.5% = 0.065

n = 12 (compounded monthly)

t = 10

A = 500(1 + 0.065/12)^(12*10)

A = $935.98

Hannah's investment will be worth $935.98 after 10 years.

We have demonstrated that x² ≥ x for all integers x. Therefore, the statement x² ≥ x for all x ∈ Z is true.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

To prove that x² ≥ x for all x ∈ Z, we need to show that the inequality holds true for any arbitrary integer value of x.

We can prove this by considering two cases:

Case 1: x ≥ 0

If x ≥ 0, then x² ≥ 0 and x ≥ 0. Therefore, x² ≥ x.

Case 2: x < 0

If x < 0, then x² ≥ 0 and x < 0. Therefore, x² > x.

In either case, we have shown that x² ≥ x for all integers x. Therefore, the statement x² ≥ x for all x ∈ Z is true.

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Answer:

16pi/9 in

Step-by-step explanation:

length of arc = (angle/360) x (2πr)

where angle is the central angle of the arc in degrees, r is the radius of the circle, and π is the mathematical constant pi (approximately equal to 3.14159).

In this case, the radius is given as 8 inches and the central angle is 40 degrees. Substituting these values into the formula, we get:

length of arc = (40/360) x (2π x 8)

length of arc = (1/9) x (16π)

length of arc = 16π/9

So the length of the arc is 16π/9 inches. Rounded to the nearest hundredth, this is approximately 5.60 inches. Therefore, the answer is 16 pi 1/9 inches, when expressed in mixed number form.

The number of more sole received by merchant  in the second sale compared to first sale is equal to 130 soles

Let us first calculate the cost of one pole in each sale.

For the first sale, 8 poles cost 2 soles. So, one pole costs.

2 soles / 8 poles = 0.25 soles/pole

For the second sale, 5 poles cost 3 soles. So, one pole costs.

3 soles / 5 poles = 0.6 soles/pole

Next, let us find out the total revenue from each sale.

For the first sale,

The merchant sold 200 poles. If one pole costs 0.25 soles, then 200 poles would cost.

200 poles × 0.25 soles/pole = 50 soles

For the second sale,

The merchant sold 300 poles. If one pole costs 0.6 soles, then 300 poles would cost.

300 poles × 0.6 soles/pole = 180 soles

The difference between what the merchant received from the first sale and the second sale is,

180 soles - 50 soles = 130 soles

Therefore,, the merchant received 130 soles more from the second sale than the first sale.

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Answer:

Step-by-step explanation:

The limit of the given sequence is π/4, and the sequence converges to this value.

The given sequence is {tan^−1(4n/(4n+5))}. To determine if the sequence converges or diverges, we can analyze the limit of the function as n approaches infinity.

As n goes to infinity, the function behaves like tan^−1(4n/4n), which simplifies to tan^−1(1). Since the arctangent function has a range of (-π/2, π/2), tan^−1(1) falls within this range, and it is equal to π/4 (or 45° in degrees).

Now, let's consider the difference between the given function and the simplified one: (4n+5) - 4n = 5. As n becomes larger, the effect of the constant term 5 becomes negligible. Consequently, the function approaches tan^−1(1) as n approaches infinity.

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The value of the series is: ∑ 1/n(n+2) = lim N→∞ S(N) = 1/2.

The series ∑ 1/n(n+2)n=1 converges. To determine its value, we can use the partial fraction decomposition:

1/n(n+2) = 1/2 * (1/n - 1/(n+2))

Using this decomposition, we can rewrite the series as:

∑ 1/n(n+2) = 1/2 * (∑ 1/n - ∑ 1/(n+2))

The first series ∑ 1/n is the harmonic series, which diverges. However, the second series ∑ 1/(n+2) is a shifted version of the harmonic series, and it also diverges. But since we are subtracting a divergent series from another divergent series, we can use the limit comparison test to determine whether the original series converges or diverges. Specifically, we can compare it to the series ∑ 1/n, which we know diverges. This gives:

lim n→∞ 1/n(n+2) / 1/n = lim n→∞ (n+2)/n^2 = 0

Since the limit is less than 1, we can conclude that the series ∑ 1/n(n+2) converges. To find its value, we can evaluate the partial sums:

S(N) = 1/2 * (∑_{n=1}^N 1/n - ∑_{n=1}^N 1/(n+2))
    = 1/2 * (1/1 - 1/3 + 1/2 - 1/4 + ... + 1/(N-1) - 1/(N+1))

As N approaches infinity, the terms in the parentheses cancel out except for the first and last terms:

S(N) → 1/2 * (1 - 1/(N+1))

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Answer: simplified expression is 2√3.

Step-by-step explanation:

√363 = √(121 × 3) = √121 × √3 = 11√3

√27 = √(9 × 3) = √9 × √3 = 3√3

√363 − 3√27 = 11√3 − 3(3√3) = 11√3 − 9√3 = 2√3

The simplified form of the given radical expression is 2√3.

Radical form is the expression that involves radical signs such as square root, cube root, etc instead of using exponents to describe the same entity.

The given expression is √363 − 3√27.

Here, √121×3 − 3√9×3

= 11√3-9√3

= 2√3

Therefore, the simplified form of the given radical expression is 2√3.

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The other root of the quadratic equation include the following (-4, 0).

In Mathematics and Geometry, the vertex form of a quadratic equation is given by this formula:

y = a(x - h)² + k

Where:

For the given quadratic function, we have;

y = a(x - h)² + k

0 = a(8 - 2)² - 5

0 = 36a - 5

5 = 36a

a = 5/36

Therefore, the required quadratic function in vertex form is given by;

y = 5/36(x - 2)² - 5

0 = 5/36(x - 2)² - 5

5 = 5/36(x - 2)²

36 = (x - 2)²

±6 = x - 2

x = -6 + 2

x = -4.

Other root = (-4, 0).

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The volume of the solid formed by rotating the region inside the first quadrant enclosed by y = a°, y = 25 about the r-axis is [tex]V = \pi(25^3 - (a^\circ)^3)[/tex].

To find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y = a°, y = 25 about the r-axis, we can use the method of cylindrical shells.

First, we need to determine the limits of integration for y.

The region is enclosed by y = a° and y = 25, so the limits are a° and 25.

Next, we need to determine the radius of each cylindrical shell. Since we are rotating about the r-axis, the radius is simply the y-value.

So, the radius is r = y.

Finally, we need to determine the height of each cylindrical shell.

The height is the circumference of the shell, which is 2πr.

So, the height is h = 2πy.

The volume of each cylindrical shell is then given by V = 2πy * (y - a°)

To find the total volume, we integrate this expression with respect to y from a° to 25:
[tex]V = \int_{a^\circ}^{25} 2\pi (y - a^\circ) dy[/tex]

Evaluating this integral, we get:
[tex]V = \pi(25^3 - (a^\circ)^3)[/tex]

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Answer: Website A is cheaper, by an amount of, £0.29.

Step-by-step explanation: Here, the problem is simply about, initially adding, and then finding difference between the added results.

That is,

For Website A,

Net Cost = £49.95 + £4.39

= £54.34

Similarly,

For Website B,

Net Cost = £47.68 + £6.95

= £54.63

Therefore, we can clearly see,

Website A is cheaper by,

£(54.63 - 54.34) = £0.29

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The rectangle with the formula x(x+1)=60 using the quadratic formula has  length = 8.26 and width = 7.26.

Given that,

A rectangle has the formula,

x (x + 1) = 60

x² + x = 60

x² + x - 60 = 0

Using the quadratic formula,

x = -1 ± √1 -(4 × 1 × -60) / 2

  = (-1 ± √241) / 2

x = 7.26

Width = 7.26

Length = x + 1 = 8.26

Hence the required length and width are 8.26 and 7.26.

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(d) The function (-5, 1), (0, 3), (5, 5) is not a linear function

From the question, we have the following parameters that can be used in our computation:

(-5, 1), (0, 3), (5, 5).

A linear function has a constant rate of change, meaning that the slope of the line is always the same.

However, if we plot the given points on a graph, we can see that they do not lie on a straight line.

Therefore, the function is not linear.

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Answer:

Step-by-step explanation:

d

The most representative sample of the population would be a random sample of cereal pieces from the box. Therefore, option D is the correct answer.

In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.

Given that, a factory makes boxes of cereal. Each box contains cereal pieces shaped like hearts, stars and rings.

The most representative sample of the population would be a random sample of cereal pieces from the box. This means that the employee should select pieces from the box without looking at or attempting to select any particular shape. This ensures that the sample accurately reflects the distribution of cereal pieces in the box, and gives an accurate representation of the population.

Therefore, option D is the correct answer.

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The required values are -2+√15, -2-√15.

What is a quadratic equation?

Any equation in algebra that can be written in the standard form where x stands for an unknown value, where a, b, and c stand for known values, and where a 0 is true is known as a quadratic equation.

Here, we have

Given:  x² + 4x - 11 = 0

we have to find the values of a and b to complete the solutions.

The given equation is x² + 4x - 11 = 0

The general form of a quadratic equation is ax² + bx + c = 0

Comparing with the given equation we have

a = 1

b = 4

c = -11

Rearranging the equation:

x² + 4x = 11

Finding (b/2)²

(4/2)² = 4

Adding to both sides of the equation

x² + 4x + 4 = 11 + 4

(x+2)² = 15

x + 2 = ±√15

x = -2  ±√15

Hence, the required values are -2+√15, -2-√15.

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When there is a problem with Solver being able to find a solution, many times it is an indication of mistakes in the formulation of the problem. This means that the problem may not be correctly defined, or the constraints may not be properly specified.

However, it is also possible that the problem is a nonlinear programming problem, which can be more difficult for Solver to solve. In either case, it is important to carefully review the problem formulation and constraints to ensure that they are correct and accurately represent the problem at hand. It is also important to note that there may be some problems that cannot be solved using Solver or any other optimization tool, due to their inherent complexity or other factors.

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Answer: I believe -2 is the answer

Step-by-step explanation: To solve for the function over an interval, you need to know the equation of the function. If you have the equation, you can plug in the values of the interval into the equation to find the corresponding y-values. For example, if the function is y = 2x + 1 and the interval is [0,3], you can plug in x = 0 and x = 3 to find the corresponding y-values and get the ordered pairs (0,1) and (3,7).

The value of the function (fg)(x) = = ∛5

A function can be described as an equation or expression that is used to show the relationship between two variables.

The two variables are;

From the information given, we have that;

f(x) = 5x

g(x) = x^1/3

To determine the composite function (fg)(x), substitute the value of(x) as the value of x in the function g(x), we have;

(fg)(x) = 5^1/3

This is written as;

(fg)(x) =(∛5)¹

(fg)(x) = = ∛5

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