(i) A baker has found that the number of muffins he/she sells, q, depends on the price, Sp, of his/her muffins as q = 11 - p. Each muffin costs the baker $3 to produce. Write down the expression for profit in terms of p. (ii) What price should the baker charge per muffin in order to maximise profit?

The contour integral of the function f(z) over the contour C is zero because the function f(z) is analytic inside and on the contour C.

In this case, the function f(z) = (8² - 16)5 = 64 × 5 = 320 is a constant function. Constant functions are always analytic within their domain. Therefore, f(z) is analytic within the region enclosed by the contour C.

According to Cauchy's Integral Formula, the contour integral of a function over a closed contour C is given by:

∮C f(z) dz = 2πi × sum of the residues of f(z) at its isolated singularities within C.

Since f(z) is a constant function, it does not have any singularities. Therefore, all the residues of f(z) are zero.

Hence, the contour integral of f(z) over the contour C is zero:

∮C f(z) dz = 0.

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Answer:

-1.889 rad

Step-by-step explanation:

180 degrees = [tex]\pi[/tex]

-340 x [tex]\frac{\pi }{180}[/tex]

-340[tex]\pi[/tex]/180

-34[tex]\pi[/tex]/18

-1.889 rad

Answer:

3(y-9)^2

Step-by-step explanation:

Answer:

See in the picture mark brainliest if correct

The preliminary sample size is undefined since the projected misstatement is zero.

In determining the appropriate sample size for testing inventory valuation using MUS, the following steps are taken;

Given that the population has 2,620 inventory items valued at $12,625,000 and the tolerable misstatement is $500,000 at a 10% ARIA, we can calculate the preliminary sample size using the formula;

Preliminary sample size = (Confidence Factor2 × Tolerable Misstatement)/Projected misstatement.

Considering that no misstatements are expected in the population, the projected misstatement will be zero.

Thus; the Preliminary sample size = (2.31 × 500,000)/0. Preliminary sample size = (2.31 × ∞) / 0. The preliminary sample size is undefined.

In conclusion, the preliminary sample size is undefined since the projected misstatement is zero.

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Answer:

she have 29 seed for the pasture

Answer: Singing

Mode: The value that appears the most in a list

Also by the way, the frequency table is most likely just a table of every single value and how many times they appear in the list. Its super easy all you have to do is count them

The volume of the cylinder inside the given sphere is 8 cubic units.

To determine the volume of the cylinder inside the given sphere, we need to find the limits of integration and set up the integral.

Let's analyze the equations:

Cylinder equation:[tex]r^2 + y^2 = 4[/tex]

Sphere equation: [tex]r^2 + y^2 + 2^2 = 16[/tex]

From the equations, we can see that the cylinder is centered at the origin (0, 0) with a radius of 2 and an infinite height along the y-axis. The sphere is centered at the origin as well, with a radius of 4.

To find the limits of integration, we need to determine where the cylinder intersects the sphere. By substituting the cylinder equation into the sphere equation, we can solve for the values of r and y:

[tex](2^2) + y^2 + 2^2 = 16\\4 + y^2 + 4 = 16\\y^2 = 8[/tex]

y = ±√8

We can see that the cylinder intersects the sphere at y = √8 and y = -√8. Since the cylinder has infinite height, the limits of integration for y will be from -√8 to √8.

Now we can set up the integral to calculate the volume of the cylinder:

V = ∫∫∫ dV

  = [tex]\int_0^ 2 \int_{\sqrt -8} ^ {\sqrt 8}\int _{\sqrt-(16 - r^2 - y^2)} ^{\sqrt (16 - r^2 - y^2)} dz dy dr[/tex]

Since the integrand is equal to 1, we can simplify the integral to:

V = [tex]\int_0 ^ 2 \int _{-\sqrt8} ^ {\sqrt8} 2\sqrt{(16 - r^2 - y^2)}[/tex] dy dr

Evaluating this integral will give us the volume of the cylinder inside the sphere.

To evaluate the integral and calculate the volume, we can integrate the given expression with respect to y first and then with respect to r.

[tex]\int_0 ^ 2 \int _{-\sqrt8} ^ {\sqrt8} 2\sqrt{(16 - r^2 - y^2)}[/tex]

Let's begin by integrating with respect to y:

[tex]\int_{-\sqrt8} ^ {\sqrt8} 2\sqrt(16 - r^2 - y^2) dy[/tex]

We can simplify the integrand using the trigonometric substitution y = √8sinθ:

dy = √8cosθ dθ

y = √8sinθ

Replacing y and dy in the integral:

[tex]\int _{-\pi /2} ^{\pi/2} 2\sqrt(16 - r^2 - (\sqrt 8sin\theta)^2) \sqrt 8cos\theta d\theta[/tex]

= 16[tex]\int _{-\pi /2} ^ {\pi /2} \sqrt(1 - (r/4)^2 - sin^2\theta)[/tex]cosθ dθ

To simplify the integral further, we can use the trigonometric identity [tex]sin^2\theta + cos^2\theta = 1:[/tex]

16[tex]\int _{-\pi /2} ^ {\pi /2} \sqrt(1 - (r/4)^2 - sin^2\theta)[/tex]cosθ dθ

= 16 [tex]\int _{-\pi /2} ^ {\pi /2} \sqrt(r^2/16)[1 - cos^2\theta][/tex]cosθ dθ

= 4r[tex]\int _{-\pi/2} ^ {\pi/2}[/tex] sinθ cosθ dθ

= 4r [tex][ -cos^2\theta/2[/tex] ]| [-π/2 to π/2 ]

= 4r [ [tex]-cos^2(\pi/2)/2 + cos^2(-\pi/2)/2[/tex] ]

= 4r [ -1/2 + 1/2 ]

= 4r

Now, we can integrate with respect to r:

[tex]\int_0 ^ 2[/tex] 4r dr

= 2[tex]r^2[/tex]| [0 to 2]

= 2[tex](2^2 - 0^2)[/tex]

= 2(4)

= 8

Therefore, the volume of the cylinder is 8 cubic units.

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Part A:

Six Tents Holds 42 People

Nine Tents Holds 63 People

10 Tents Holds 70 People

Part B:

Number of tents|||Number of people

1                          |||7

6                         |||42

9                         |||63

10                        |||70

Part C:

Tents=x

1x=7 people

Answer: 22.94 cubic meters

I'm pretty sure it is this.

I think it's 25.23 cubic meters if not then I don't know

Answer: 891ft^3

Step-by-step explanation:

Answer:

See explanations below

Step-by-step explanation:

evaluate sin 60. cos 30 sin +sin 30 .cos 60 what is the value of sin(30-60) what can you conclude​

According to the trigonometry identity

Sin 30  = 1/2

Sin 60 = √3/2

Cos 30 = √3/2

Cos 60 = 1/2

sin 60. cos 30 +sin 30 .cos 60

= √3/2(√3/2) + 1/2(1/2)

= √9/4 + 1/4

= 3/4 + 1/4

= 4/4

= 1

sin(30-60) = sin30cos60 - cos30sin60

sin(30-60) =1/2(1/2) - √3/2(√3/2)

sin(30-60) = 1/4 -  √9/4

sin(30-60) = 1/4 - 3/4

sin(30-60) = (1-3)/4

sin(30-60) = -2/4

sin(30-60)  = -1/2

hence the former fraction gives a positive values while the later gives a negative

Answer:

1

Step-by-step explanation:

(a) The area between the curve of f(x) and the x-axis best describes the result of integrating a positive function f(x).

(b) The general antiderivative of the function f(x) = 23 + 8x is 2x³ + 4x² + C.

Hence, option (C) is the correct answer.

(c) An odd function satisfies f(-x) = -f(x). Thus, for an odd function f(x), the integral from -a to a is equal to zero because f(x) and -f(x) will have opposite signs, and the areas will cancel each other out. Hence, option (A) is the correct answer.

(d) To use the substitution u = 4x + 2, we need to find dx in terms of du.du = d/dx (4x + 2) dx= 4dxIntegrating both sides gives ∫du/4 = ∫dx/ (4x + 2). Therefore, the given expression becomes, ∫ 1/(4x + 2) dx = (1/4)∫du/u= (1/4)ln|u|+C= (1/4) ln|4x + 2| + C. Hence, (1/4) ln|4x + 2| + C is true by using the substitution 4x + 2 = u.

(e) The given function can be graphed as below: [tex]\int_0^1 (x^2 + 1) dx = \frac{4}{3}[/tex] We need to use the disk method to find the volume of the solid generated by rotating the region bounded by the curves about the x-axis. We need to consider an elemental area, find its volume, and integrate it over the region of interest. We know that the volume of the disk is given by V = πr²h, where r is the radius and h is the height of the disk. Let us consider an elemental area, A of the region rotated about the x-axis. If we rotate this area through a small angle, θ, then the area of the sector generated is given by d A = πr²dθ/2π = r²dθ/2. The radius of the disk is x, and the height is given by g(x) - f(x). Thus, V = ∫[g(x) - f(x)]²πx²dx.In this case, we have g(x) = x + 1 and f(x) = x². Substituting these values, V = π∫(x + 1 - x²)² x² dx. The limits of integration are from 0 to 1.

Therefore, V = π∫[x⁴ - 2x³ + x² + 2x + 1]dx= π[x⁵/5 - x⁴/2 + x³/3 + x² + x]₀¹= π[(1/5) - (1/2) + (1/3) + 1 + 1]

The volume of the solid obtained is, V = π[(8/15) + 2] = (14π/15).

Hence, the volume of the solid obtained when the area bounded by the curves below is rotated about the x-axis is (14π/15).

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To find the volume and total area of the right circular cone, we will use the formulas below. Volume of the right circular cone: $$V = \frac{1}{3}πr^2h$$

Total surface area of the right circular cone:$$A = πr^2 + πrl$$, Where r is the radius, l is the slant height and h is the height of the cone.π (pi) is a mathematical constant that is approximately equal to 3.14159 and is used to calculate the circumference and area of a circle. The radius of the right circular cone is 3.5 cm and its height is 7 cm. To calculate the slant height, we will use the Pythagorean theorem which states that the square of the hypotenuse (l) is equal to the sum of the squares of the other two sides:$$l^2 = r^2 + h^2$$$$l = \sqrt{r^2 + h^2} = \sqrt{3.5^2 + 7^2} \approx 7.98\ cm$$

Volume of the right circular cone:$$V = \frac{1}{3}πr^2h = \frac{1}{3}π(3.5)^2(7) \approx 89.75\ cm^3$$. Total surface area of the right circular cone:$$A = πr^2 + πrl = π(3.5)^2 + π(3.5)(7.98) \approx 91.86\ cm^2$$. Hence, the volume of the right circular cone is approximately 89.75 cm³ and the total surface area is approximately 91.86 cm².

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There are no points in C for which the function g(z) is holomorphic.

The functions given are :

f(z) = z² and g(z) = x² - y² + 2xy (where z = x + iy)

We need to determine the points in C for which the functions are holomorphic.

(a) To check whether f(z) = z² is holomorphic or not, we will verify the Cauchy-Riemann equations (CRE) which are:

u x = v y and v x = - u y

Let us assume that f(z) = u(x, y) + iv(x, y)

Substituting in f(z) = z², we have f(z) = (x + iy)²= x² + 2ixy - y²

Now comparing with u(x, y) + iv(x, y), we get :

u(x, y) = x² - y² and v(x, y) = 2xy

Now applying the CRE, we get :

u x = 2xv

y = 2xu

y = - 2yv

x = 2y

We can see that both the CRE are satisfied.

Hence, f(z) = z² is holomorphic for all values of z in C.

(b) Similarly, for g(z) = x² - y² + 2xy (where z = x + iy), we have g(z) = u(x, y) + iv(x, y)

Substituting in g(z) = x² - y² + 2xy, we have g(z) = x² - y² + 2ixy

Now comparing with u(x, y) + iv(x, y), we get :

u(x, y) = x² - y² and v(x, y) = 2xy

Now applying the CRE, we get :

u x = 2xv

y = 2xu

y = - 2yv

x = 2x

Since the CRE are not satisfied, g(z) = x² - y² + 2xy (where z = x + iy) is not holomorphic at any point in C.

Therefore, we can say that there are no points in C for which the function g(z) is holomorphic.

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Answer: $17.55

Step-by-step explanation:

36 x 0.65 = $23.40 total for all cookies

($23.40/1) x (3/4) = (70.2/4)

70.2 divided by 4 = $17.55

or

$23.40 x .75 = $17.55

Answer:

1 : 30

Step-by-step explanation:

300mm:9m​

We need to change the meters to mm

1 meter is 1000 mm

so 9 m is 9000 mm

300mm:9000mm

Divide both sides by 300

​300mm/300 : 9000/300

1 : 30

Answer:

x = 1

Step-by-step explanation:

5x^5 + 5 = 10

Start the solution by subtracting 5 from both sides:

5x^5 = 5

Dividing both sides by 5 yields x^5 = 1.

Taking the 5th root of both sides, we get x = 1

The test statistic value can be calculated using the formula (sample mean - population mean) / (sample standard deviation / sqrt(sample size)).

To calculate the test statistic value, we use the formula (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). In this case, the sample mean is 122, the population mean is 130, the sample standard deviation is 20, and the sample size is 20.

Test Statistic Value = (122 - 130) / (20 / sqrt(20))

                     = (-8) / (20 / 4.47)

                     = -8 / 4.47

                     ≈ -1.79

Therefore, the test statistic value is approximately -1.79.

The test statistic value (t) measures the difference between the sample mean and the assumed population mean in terms of the standard error. It helps us determine the likelihood of obtaining such a sample mean if the population mean is indeed equal to the assumed value.

In this case, the test statistic value is -1.79, indicating that the sample mean is 1.79 standard errors below the assumed population mean of 130. The negative sign indicates that the sample mean is lower than the assumed value.

To determine the significance of this difference, we would compare the test statistic to critical values from the t-distribution or calculate the p-value associated with the observed test statistic. This would allow us to make conclusions about the statistical significance of the difference between the sample mean and the assumed population mean.

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Answer:

V = 339.12

Step-by-step explanation:

Volume of a cone:

V = πr²(h/3)

Given:

r = 6

h = 9

Work:

V = πr²(h/3)

V = 3.14(6²)(9/3)

V = 3.14(36)(3)

V = 113.04(3)

V = 339.12

Answer:

16,-8,4,-2,1

-15,-18,-21.6,25.92,-31.104...

625,125,25,5,1

Step-by-step explanation:

Answer: 16, –8, 4, –2, 1. has a common ratio,r = (-1/2)

-15, –18, –21.6, –25.92, –31.104 has a common ratio, r = (1.2)

625, 125, 25, 5, 1 has a common ratio, r= (1/5)

Step-by-step explanation: just took the test

Answer:

the answer is 35

Step-by-step explanation:

because if BC is 35 that means AB will have to be that same because it's a triangle

The required value of AB is 33 units for the given right triangle.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Triangle ACB is a right-angle triangle. The length of AC is 12 and BC is 35.

Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

Assume BC is the hypotenuse,

Since this is a right triangle, use the formula AB² + AC² = BC² and substitute values of AC = 12 and BC = 35.

AB² + AC² = BC²

AB² + (12)² = (35)²

AB² + 144 = 1225

AB² = 1225 -144

AB² = 1081

AB = 32.8785

Rounded to two decimal places,

AB = 33 units

Therefore, the required value of AB is 33 units.

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Answer:17

Step-by-step Experlation: The volume is 108 cm. 3,2,15.a square prism with a base edge of 9.5 inches and a height of 17 ... amount for a landowner

Answer:

2.5 liters of gas is used with per liter of oil

Step-by-step explanation:

Max is missing oil and gas for his moped.

Amount of gas used = 3.75 liters

Amount of oil required = 1.5 liters

Ratio in which gas and oil are mixed = [tex]\frac{3.75}{1.5}[/tex]

                                                             = [tex]\frac{2.5}{1}[/tex]

That means if he uses 1 liter of oil then the gas required for the mixture = 2.5 liters

Therefore, 2.5 liters of gas is used per liter of oil.

Answer:

28.26

Step-by-step explanation:

The formula for finding the circumference is C=2pi(radius) and the radius is half of the diameter, which in our case is 4.5. So 2*3.14*4.5=28.26

Answer:

One solution

I actually do not think you're going to give me brainliest

Answer:

7:00 = 6:60

Step-by-step explanation:

6:60 - 3:30 = 3 hours and 30 minutes

Answer:

1/4 is x and 1 is b

Step-by-step explanation:

Answer:

I have

Step-by-step explanation: