Evaluate in closed form the sum f(\Theta)=sin(\Theta)+1/3sin(2\Theta)+1/5sin(3\Theta)+1/7sin(4\Theta)+...(you may assume 0<\Theta<\Pifor definiteness).

True. The statement "if the range of feasibility indicates that the original amount of a resource, which was 20, can increase by 5, then the amount of the resource can increase to 25" is true.

When a range of feasibility is given, the lower and upper bounds of the values that can be chosen for the variables in a linear programming problem are given. The range of feasibility reflects the range within which the optimum answer can be found. It is a parameter that measures the extent to which the variables can change and still allow the same optimal answer to be obtained. In this case, the range of feasibility suggests that the initial amount of a resource was 20 and could be increased by 5, implying that the total amount of the resource can be 25. Therefore, statement is true.

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Answer:

The car is going at 8.125 m/s²

Step-by-step explanation:

Answer:

2.26m/s^2

Step-by-step explanation:

65km/hr = 18.05m/s

\(a = \frac{v - u}{t} \)

v = 18.05m/s

u = 0 m/s

t = 8s

\(a = \frac{18.05 - 0}{8} \)

\(a = \frac{18.05}{8} \)

a = 2.26m/s^2

The first operation we have to take into account will be the product of a number and two, this is 2 times a number or 2*x, taking x as any number

The second one is an addition, eight more is written as +8.

The expression that represents the statement is 2x+8

The length of the g is approximate to 4.0 inches.

We have the information from the question is:

In triangle ΔEFG,

e = 6. 9 inches,

f = 8. 7 inches and

∠G=27°

We have to find the length of g

Now, According to the question:

Using the law of cosine:

\(CosA=\frac{b^2+c^2-a^2}{2bc}\)

We have, \(a^2=b^2+c^2-2bc\,cos A\)

In this case,

\(g^2=e^2+f^2-2ef\,cos G\)

\(g^2=6.9^2+8.7^2-2(6.9)(8.7)cos27\)

\(g^2=\) 47.61 + 75.69 - 106.97

\(g^2=16.33\\\\g = \sqrt{16.33}\) ≈ 4.0

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Answer:

Step-by-step explanation:

15(x + 3) = 24x

15x + 45 = 24x

45 = 9x

5 = x

Answer:d

Step-by-step explanation:

The answer is d. None of the above is true.

To calculate velocity, we need to use the equation:

Velocity = M * P / Y

Given:

M = 1,000

P = 2.25

Y = 2,000

Plugging in the values:

Velocity = 1,000 * 2.25 / 2,000

Simplifying:

Velocity = 2.25 / 2

The result is:

Velocity = 1.125

Therefore, the correct answer is: d. None of the above is true.

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Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

Answer:

\(\frac{14}{17}\)

Step-by-step explanation:

Number of phones broken = 3

Number of phones not broken = 15

Total number of phone in the shipment = 18

Since a not broken phone has been randomly selected, the number of phones not broken reduces to 14. And the total number of phones would be 17.

Pr(of newly selected phone NOT broken) = \(\frac{number of not broken phones}{total number of phones}\)

                                           = \(\frac{14}{17}\)

Therefore, the probability of the selected phone not being broken is \(\frac{14}{17}\).

Answer:

it would be honestly idj

Step-by-step explanation:

im tryin to get point

Answer:

H = 3

Step-by-step explanation:

V of Large box = 4 x (V of Small box)

96/4 = 24

24 = V Small box.

V = L x W x H

24 = 2 x 4 x H

24 = 8 x H

3 = H

Therefore height of small box is 3.

The height of the one small box is 4 cm if Jessica puts the four small boxes into the large box. there’s no space leftover.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape.

Jessica has four small boxes that are the same size and one large box.

The dimensions for the small boxes:

Width w = 4 cm

Length l = 2 cm

Volume of a large box = 96 cubic centimetres

As Jessica puts the four small boxes into the large box. there’s no space leftover, mathematically,

The volume of the large box = 4(Volume of the small boxes)

The volume of the large box = 4(l×w×h)

Where h is the height of the small box.

96 = 4(3×2×h)

24h = 96

h = 4 cm   (divide by 48 on both sides)

Thus, the height of the one small box is 4 cm if Jessica puts the four small boxes into the large box. there’s no space leftover.

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Answer: International Date Line

The inverse of the matrix as calculated from the data with a scalar coefficient is,

[ -7 ]

[ -1  ]

x -6y = -1

−2x9y=5

which can be written as ,

[ 1  -6  -1 ]

[  -2 9  5 ]  

A = [ 1  -6

       -2  9  ]

A' = 1 / ( ad - bc ) [ 9  6 ]

                           [  2  1 ]

= [ -3       - 2 ]

  [-2/3  -1/3  ]

on solving them we get the coefficient as ,

[ -7 ]

[ -1  ]

The quantity of rows and columns in a matrix determines its size. As long as they are positive integers, there is no restriction on how many rows and columns a matrix (in the conventional sense) can have. An m n matrix, also known as an m-by-n matrix, is a matrix having m rows and n columns. M and n are referred to as the matrix's dimensions.

Row and column vectors are terms used to describe matrices with a single row or column. A square matrix is one that has the same number of rows and columns.

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Step-by-step explanation:

x-y^x-y

2-(-2)^2-(-2)

2-(-2)^2+2

2-(-2)^4

2-(16)

=-14

Answer:

Thanks! Hi luck panda! I guess I'll do that?

Step-by-step explanation:

Answer:

This is luck panda he gives you luck of your test copy and paste him onto your next brainly answer to wish that person luck!

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Step-by-step explanation:

it doesn't look like a panda :(

Answer:

\(\textsf{Midpoint rule}: \quad \dfrac{2\pi}{\sqrt[3]{2}}\)

\(\textsf{Trapezium rule}: \quad \pi\)

\(\textsf{Simpson's rule}: \quad \dfrac{4 \pi}{3}\)

Step-by-step explanation:

Midpoint rule

\(\displaystyle \int_{a}^{b} f(x) \:\:\text{d}x \approx h\left[f(x_{\frac{1}{2}})+f(x_{\frac{3}{2}})+...+f(x_{n-\frac{3}{2}})+f(x_{n-\frac{1}{2}})\right]\\\\ \quad \textsf{where }h=\dfrac{b-a}{n}\)

Trapezium rule

\(\displaystyle \int_{a}^{b} y\: \:\text{d}x \approx \dfrac{1}{2}h\left[(y_0+y_n)+2(y_1+y_2+...+y_{n-1})\right] \quad \textsf{where }h=\dfrac{b-a}{n}\)

Simpson's rule

\(\displaystyle \int_{a}^{b} y \:\:\text{d}x \approx \dfrac{1}{3}h\left(y_0+4y_1+2y_2+4y_3+2y_4+...+2y_{n-2}+4y_{n-1}+y_n\right)\\\\ \quad \textsf{where }h=\dfrac{b-a}{n}\)

Given definite integral:

\(\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x\)

Therefore:

Calculate the subdivisions:

\(\implies h=\dfrac{2 \pi - 0}{4}=\dfrac{1}{2}\pi\)

Midpoint rule

Sub-intervals are:

\(\left[0, \dfrac{1}{2}\pi \right], \left[\dfrac{1}{2}\pi, \pi \right], \left[\pi , \dfrac{3}{2}\pi \right], \left[\dfrac{3}{2}\pi, 2 \pi \right]\)

The midpoints of these sub-intervals are:

\(\dfrac{1}{4} \pi, \dfrac{3}{4} \pi, \dfrac{5}{4} \pi, \dfrac{7}{4} \pi\)

Therefore:

\(\begin{aligned}\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x & \approx \dfrac{1}{2}\pi \left[f \left(\dfrac{1}{4} \pi \right)+f \left(\dfrac{3}{4} \pi \right)+f \left(\dfrac{5}{4} \pi \right)+f \left(\dfrac{7}{4} \pi \right)\right]\\\\& = \dfrac{1}{2}\pi \left[\sqrt[3]{\dfrac{1}{2}} +\sqrt[3]{\dfrac{1}{2}}+\sqrt[3]{\dfrac{1}{2}}+\sqrt[3]{\dfrac{1}{2}}\right]\\\\ & = \dfrac{2\pi}{\sqrt[3]{2}}\\\\& = 4.986967483...\end{aligned}\)

Trapezium rule

\(\begin{array}{| c | c | c | c | c | c |}\cline{1-6} &&&&&\\ x & 0 & \dfrac{1}{2}\pi & \pi & \dfrac{3}{2} \pi & 2 \pi \\ &&&&&\\\cline{1-6} &&&&& \\y & 0 & 1 & 0 & 1 & 0\\ &&&&&\\\cline{1-6}\end{array}\)

\(\begin{aligned}\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x & \approx \dfrac{1}{2} \cdot \dfrac{1}{2} \pi \left[(0+0)+2(1+0+1)\right]\\\\& = \dfrac{1}{4} \pi \left[4\right]\\\\& = \pi\end{aligned}\)

Simpson's rule

\(\begin{aligned}\displaystyle \int^{2 \pi}_0 \sqrt[3]{\sin^2 (x)}\:\:\text{d}x & \approx \dfrac{1}{3}\cdot \dfrac{1}{2} \pi \left(0+4(1)+2(0)+4(1)+0\right)\\\\& = \dfrac{1}{3}\cdot \dfrac{1}{2} \pi \left(8\right)\\\\& = \dfrac{4}{3} \pi\end{aligned}\)

Answer:

525

Step-by-step explanation:

i really dont know what it asking

Answer:

x = - 5, x = 2

Step-by-step explanation:

Given

x(x + 7) = 4x + 10 ← distribute left side

x² + 7x = 4x + 10 ( subtract 4x + 10 from both sides )

x² + 3x - 10 = 0 ← in standard form

(x + 5)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 2 = 0 ⇒ x = 2

A population has a standard deviation of 10 and a mean of 75.

The sample mean has a standard deviation of 5 and an expectation of 100.The empirical rule states that there is a 68% probability of being between 95 and 105 (within one standard deviation of its expected value) if it is approximately normal.

What is meant by a standard deviation?

A measure of how dispersed the data are in relation to the mean is called the standard deviation (or ).Data with a low standard deviation are grouped around the mean, while data with a high standard deviation are more dispersed.

How can I determine the standard deviation?

Step 1: Locate the mean. Step 2: Find the square of the distance from the mean for each data point. Step 3: Sum the results of Step 2's values. Step 4: Divide by how many data points there are.

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Answer: 6 and 7

Step-by-step explanation:

The harmonic mean would give equal weight to both of these trails, despite their different distances.

The harmonic mean would make the most sense when calculating the average one-way mileages for trails to different lakes. When it comes to calculating the average of one-way mileages for trails to different lakes, it's important to choose the appropriate type of average based on the nature of the data.

In this case, since we're dealing with mileages, one-way distances, and travel times, the best option would be the harmonic mean. The harmonic mean is defined as the reciprocal of the arithmetic mean of the reciprocals of a set of numbers. In other words, it's a weighted average of the reciprocals of the numbers.

This type of average is useful in situations where rates, speeds, or frequencies are involved.  In this case, the harmonic mean would be the most appropriate choice for calculating the average one-way mileage for trails to different lakes because it takes into account the fact that distances and travel times are inversely related.

For example, if one trail has a distance of 10 miles and a speed of 2 miles per hour, it will take 5 hours to travel that distance. On the other hand, if another trail has a distance of 20 miles and a speed of 4 miles per hour, it will also take 5 hours to travel that distance.

Therefore, the harmonic mean would give equal weight to both of these trails, despite their different distances.

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(a) The cost function C(x) in dollars for a run of x hockey jerseys is C(x) = 2500 + 10x + 0.2x^2.

The revenue function R(x) in dollars for selling x hockey jerseys is R(x) = 85x.

The profit function P(x) in dollars for selling x hockey jerseys is P(x) = R(x) - C(x).

(b) The profit (or loss) resulting from the sale of 500 copies of The Collegiate Investigator can be calculated by substituting x = 500 into the profit function P(x).

(c) The number of copies that need to be sold in order to break even can be found by determining the value of x where the profit function P(x) equals zero.

(a) The cost function C(x) represents the total cost in dollars incurred by Gymnast Clothing for manufacturing a run of x hockey jerseys. It consists of three components: a fixed cost of $2500, a variable cost of $10 per jersey, and a quadratic cost term of 0.2x^2, which represents additional costs as the number of jerseys produced increases.

The revenue function R(x) represents the total revenue in dollars generated by selling x hockey jerseys. Since each jersey is sold at a price of $85, the revenue is simply the selling price multiplied by the number of jerseys sold, which is x.

The profit function P(x) represents the difference between the revenue and the cost. It is calculated by subtracting the cost function C(x) from the revenue function R(x). This gives the profit in dollars obtained by selling x hockey jerseys.

(b) To find the profit (or loss) resulting from the sale of 500 copies of The Collegiate Investigator, we substitute x = 500 into the profit function P(x). Thus, P(500) = R(500) - C(500). By evaluating this expression, we can determine the profit or loss.

(c) To determine the number of copies that need to be sold in order to break even, we need to find the value of x for which the profit function P(x) equals zero. In other words, we solve the equation P(x) = 0. By finding the value of x that satisfies this equation, we can determine the break-even point where the revenue is equal to the cost, resulting in zero profit.

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The gardener will need to purchase an additional 6 1/2 ft of fencing to complete his square garden for his flowers.

You want to know how much more fencing the gardener will need to purchase if he already has 4 1/2 ft of fencing and

the length of one side of the square garden is 2 3/4 ft.

Since the garden is square, all sides have the same length. We know one side is 2 3/4 ft.

Multiply the length of one side (2 3/4 ft) by 4 to find the total amount of fencing needed for the entire garden:

2 3/4 × 4 = 11 ft.

Now, subtract the amount of fencing the gardener already has (4 1/2 ft) from the total amount needed (11 ft):

11 - 4 1/2 = 6 1/2 ft.

So, the gardener will need to purchase an additional 6 1/2 ft of fencing to complete his square garden for his flowers.

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Answer:

Step-by-step explanation:

(-5x-4)-(-3x-2)

-5x-4+3x+2

-2x-2

-2(x+1)

(a) Let S be a subset of an n-dimensional vector space V. Suppose S contains less than n vectors. Then, the maximum number of linearly independent vectors in S is also less than n. Therefore, the dimension of the span of S is less than n, and hence, S cannot span V.

(b) The nullity of a matrix is the dimension of its null space, which is the set of all solutions to the homogeneous equation Ax = 0, where A is the matrix. The smallest possible nullity for a 4 x 7 matrix is 3, since the nullity cannot be greater than the minimum of the number of rows and columns. The largest possible rank is 4, since the rank cannot be greater than the number of rows.

(c) The smallest possible nullity for a 7 x 4 matrix is also 3, since the nullity cannot be greater than the minimum of the number of rows and columns. The largest possible rank is 4, since the rank cannot be greater than the number of columns. This follows from the rank-nullity theorem, which states that the rank plus the nullity of a matrix equals its number of columns.

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Therefore, all possible values of aa that satisfy the conditions are aa such that a<34a<43​.

To find all possible values of aa such that the quadratic equation ax2+(2a+2)x+a+3=0ax2+(2a+2)x+a+3=0 has two roots with a distance greater than 1 on the number line, we can use the discriminant.

The discriminant of a quadratic equation ax2+bx+c=0ax2+bx+c=0 is given by Δ=b2−4acΔ=b2−4ac. For the equation to have two distinct real roots, the discriminant must be greater than 0.

In our case, the discriminant is Δ=(2a+2)2−4a(a+3)=4a2+8a+4−4a2−12a=−4a+4Δ=(2a+2)2−4a(a+3)=4a2+8a+4−4a2−12a=−4a+4.

For the equation to have two distinct roots with a distance greater than 1, we want Δ>12Δ>12, which simplifies to −4a+4>1−4a+4>1.

Solving this inequality, we have −4a>−3−4a>−3, which leads to a<34a<43​.

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Answer: A). It is 1/6 throughout the line

Step-by-step explanation:

The surface area and the volume of each solid are listed below:

Case 23

A = 216 + 153√3 cm² = 481 cm², V = 324√3 cm³ = 561.18 cm³

Case 13

A = 575π m² = 1806.42 m², V = 4000π / 3 m³ = 4188.79  m³

In this problem we must determine the surface area and the volume of each of the two solids, the following area and volume formulas are listed below:

Triangles

A = 0.5 · w · h

Rectangle

A = w · h

Circle

A = π · r²

Surface of a hemisphere

A = 2π · r²

Surface of the inclined section of a cone

A = π · r · l

Lateral surface of a cylinder

A = 2π · r · l

Volume of a prism

V = A' · l

Volume of a hemisphere

V = (2π / 3) · r³

Volume of a pyramid

V = (1 / 3) · A' · l

Where:

Now we proceed to determine the surface area and the volume of each solid:

Case 23

Surface area

A = (9 cm) · (8 cm) + (9√3 cm) · (8 cm) + (18 cm) · (8 cm) + (9 cm) · (9√3 cm)

A = 72 cm² + 72√3 cm² + 144 cm² + 81√3 cm²

A = 216 + 153√3 cm²

A = 481 cm²

V = 0.5 · (9 cm) · (9√3 cm) · (8 cm)

V = 324√3 cm³

V = 561.18 cm³

Case 13

Surface area

A = 2π · (5 m)² + 2π · (5 m) · (45 m) + π · (5 m) · (15 m)

A = 575π m²

A = 1806.42 m²

Volume

V = (2π / 3) · (5 m)³ + π · (5 m)² · (45 m) + (π / 3) · (5 m)² · (15 m)

V = 4000π / 3 m³

V = 4188.79  m³

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