The formulas for total revenue and total cost, in hundreds of dollars, for selling and producing q hundred Items are: total revenue: TR(q) = 30q total cost: Tc(q) = q^3-15q^2+75q+10. (a) Find the smallest quantity at which marginal cost is equal to 15 dollars per Item. (b) Recall: Fixed cost is given by FC = TC(0). Variable cost is given by VC(q) = TC(q) - FC. Average variable cost is given by AVC(q) = VC(q)/q. Find a positive value of q at which average variable cost is equal to marginal cost. (c) Find the longest interval on which marginal revenue exceeds marginal cost. (d) Recall that profit is given by P(q) = TR(q)-TC(q) and On an interval of quantities where MR(q) < MC(q), profit is decreasing. On an interval of quantities where MR(q) > MC(q), profit is increasing Use the sketch you drew in part (c) to find the quantity at which profit is greatest. What is the maximum value of profit?

According to the problem the expression is 2x + 9.

Expression in mathematics is an arrangement of symbols that represents a value, quantity, or an idea. Expressions are used to represent a wide range of concepts, from equations, inequalities, and functions, to more abstract topics such as probability and set theory. An expression is composed of a combination of symbols and numbers that are used to create a mathematical statement. Expressions can include constants, variables, operators, and functions. Constants are values that remain unchanged throughout a calculation, such as numbers like 2, 4, or 6. Variables are used to represent unknown quantities and are usually represented as letters like x, y, and z.

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The surface area of the pyramid is A = 265.23 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of hexagonal pyramid be represented as A

Surface area of hexagonal pyramid = Area of base + area of lateral surface

Area of the base = 93.5 inches²

Now , the Area of the lateral surface = 3a √ ( h² + ( 3a²/4 ) )

where a = 6 inches

h = 8 inches

Substituting the values in the equation , we get

Area of the lateral surface = ( 3 x 6 ) √ ( 64 + ( 3 x 36 / 4 ) )

On simplifying the equation , we get

Area of the lateral surface = 171.7 inches²

So , Surface area of hexagonal pyramid = Area of base + area of lateral surface

Surface area of hexagonal pyramid A = 93.5 inches² + 171.7 inches²

Surface area of hexagonal pyramid A = 265.23 inches²

Hence , the surface area of hexagonal pyramid is 265.23 inches²

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The fence's shortest overall length is 808 meters.

Describe the rectangle.

A quadrilateral having all four interior angles at 90 degrees is a rectangle.

Given that the square field has an area of 800 m2.

Let the rectangle's length and breadth be x and y.

The rectangle's area is then:

A= xy

Or, xy = 800

x = 800/y (1) (1)

The triangle's perimeter is:

2x +2y

The total length of the fence is equal to the perimeter of the triangle plus twice the length or width of the triangle since the fence divides the triangle into three equal portions.

Consequently, the fence's overall length is:

L = 2x + 2y + 2x

L = 4x +2y

the equation above with x = 800/y as a replacement:

L = 4(800/y) + 2y

L = 3200/y +2y         (2)

Differentiate the equation with respect to y:

L' = -3200/y² +2

Substitute L'= 0 into the above equation:

0 = -3200/y² + 2

y² = 3200/2

y² = 1600

y = 400

Substitute y = 400 into equation (2):

L = 3200/400 + 2(400)

L = 8 + 800

L = 808

Hence, The fence's shortest overall length is 808 meters

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The required sample space randomly picked balls S = {A, B, C, D, E, F} and the outcomes for the event of choosing c to f is S' = {C, D, E, F}.

Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form.

here,
For six ball sample space is given as,
S = {A, B, C, D, E, F}
n(s) = 6

Now,
Sample space choosing a ball at a time =
n(s) = 6

Outcomes for the event of choosing c to f.
From C to F there are 4 balls,
Sample space = {C, D, E, F}
n(S') = 4

Thus, the required sample space randomly picked balls S = {A, B, C, D, E, F} and the outcomes for the event of choosing c to f is S' = {C, D, E, F}.

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Answer:

Step-by-step explanation:

Let the height of the house be "h".

Using the triangle formed by the object, the man, and the base of the house, and using the tangent function, we have:

tan(45°) = h / 18√2

h = (18√2) * tan(45°)

Since tan(45°) = 1,

h = 18√2 * 1 = 18√2 m

So the height of the house is 18√2 meters.

18√2 can be simplified to:

18 * √2 = 18 * 1.414 = 25.656 (approximately)

Answer: 55%

Step-by-step explanation:

Step 1

To find the students who participate in at least one activity after school, take the number of students who participate (825) and divide by the total number of students (1500).

825/1500 = 0.55

Step 2

Take the answer from step 1 and multiple it by 100 to find the percentage.

0.55 x 100% = 55%

Answer:

3 - 4x + 2x + 11 + 5x - 9 - x = 3 + (2x - 4x) + (5x - x) + 11 - 9 = 3 + -2x + 4x + 11 - 9 = 3 - 2x + 2 = -2x + 5

The polynomial equation is 4x³ - 16x² - 5x - 75 = 0.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The passenger section of a train has a width of (2x - 7), a length of (2x + 3), and a height of (x - 2).

Now,

Volume = 117 m³

Length x width x height = 117

(2x + 3) x (2x - 7)  x (x - 2) = 117

(2x + 3) x (2x² - 4x - 7x + 14 = 117

(2x + 3) x (2x² - 11x + 14) = 117

4x³ - 22x² + 28x + 6x² - 33x + 42 = 117

4x³ - 16x² - 5x - 75 = 0

Thus,

The equation is

4x³ - 16x² - 5x - 75 = 0

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More than once a week: 0.11

Once a week: 0.51

Every other week: 0.26

Every three weeks: 0.05

Less often than every three weeks: 0.07

To make a relative frequency distribution, follow these steps:

Count the number of occurrences of each category in the data. In this case, 11% of the 251 participants responded "more than once a week", so the number of occurrences for this category is 0.11 * 251 = 27.61 (rounded to 28). Similarly, 51% of the participants responded "once a week", so the number of occurrences for this category is 0.51 * 251 = 127.51 (rounded to 128). And so on for the other categories.

Divide the number of occurrences for each category by the total number of participants. In this case, the total number of participants is 251, so the relative frequency for "more than once a week" is 28 / 251 = 0.11. The relative frequency for "once a week" is 128 / 251 = 0.51. And so on for the other categories.

And that's it! These are the relative frequencies for each category in the data.

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The probability that the disposal of such capacitors can be regulated is

0.2266.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values.

Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

Given:

Population mean μ = 47.9

Standard deviation σ = 5

Sample size n = 39

Event to compute its probability [tex]\bar X[/tex] = [tex]\bar X[/tex] ≥ 48.5.

z = X₁ - μ / σ /√n

Substituting the values,

z = (48.5 - 47.9)/5 / √39

z = 0.6 / 0.800640769.

z = 0.75

From the normal distribution table,

the probability can be calculated as,

P = Pr (Z > 0.75)

P = 1 - 0.7734

P = 0.2266

Therefore, the probability is 0.2266.

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Answer:

b) 15/7

Step-by-step explanation:

The frequency of a signal is a measure of how often the signal repeats over time. In this case, x(t) is a complex exponential signal, represented by the equation x(t) = e^(30πit/7). The variable "t" represents time, and the variable "i" represents the imaginary unit, which is equal to the square root of -1.

The "30πi" term in the exponent represents the angular frequency of the signal, which is a measure of how rapidly the signal oscillates. The "t/7" term in the exponent represents the time scaling of the signal, which determines how quickly or slowly the signal repeats over time.

When we combine these two factors, we can see that the signal repeats every 7 units of time. Therefore, the frequency of the signal is 1/7, which is equivalent to 15/7 in decimal form. Therefore the answer is (b) 15/7

We kindly invite to check the image attached below to see the triangle constructed on Cartesian plane.

The measure of angle A is approximately equal to 46.102° and the measure of side AC is equal to 2√13 centimeters.

Triangles are figures generated by three distinct points set on Cartesian plane, with three line segments (AB, BC, AC) and three internal angles. In this problem we show all steps to construct a triangle with the help of a graphing tool. First, set point B at origin.

B(x, y) = (0, 0)

Second, add point C along x-axis:

C(x, y) = (6, 0)

Third, determine point A and add it on Cartesian plane:

A(x, y) = (8 · cos 60°, 8 · sin 60°)

A(x, y) = (4, 6.928)

Fourth, draw all line segments in triangle ABC. The result is shown in the image attached below.

Finally, we determine the measure of angle A and side AC by trigonometry:

Angle A:

First, determine the length of line segment AC by law of cosine:

AC = √(AB² + BC² - 2 · AB ·BC · cos B)

AC = √(8² + 6² - 2 · 8 · 6 · cos 60°)

AC = 2√13

Second, calculate the angle A by law of cosine:

cos A = (BC² - AB² - AC²) / (- 2 · AB · AC)

cos A = [6² - 8² - (2√13)²] / [- 2 · 8 · 2√13]

A ≈ 46.102°

Side AC:

AC = 2√13

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Answer:

d

Step-by-step explanation: using logic of dimension analysis , since y represent distance and x represent hours of traveling in train means time then 60 must be speed for equality i.e distance traveled by train per hour , for correcting dimensionaly

The study described is a randomized experiment.

A randomized experiment is a typical experimental study design. It is a study design in which the researcher or investigator is in complete control of the research environment. For example, an investigator may wish to assess the effects of certain treatments on some experimental units.

The investigator decides the type of treatment, the type of experimental unit to use, and the allocation and assessment procedures of the treatments and effects, respectively, while in an observational study, the researcher or investigator is usually a passive observer as he only observes and analyses facts and events as they occur naturally.

In experimental studies, the researcher is in complete control of the exposure, and the result should therefore provide stronger evidence of an association or lack of association between exposure and a health problem than would an observational study.  

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"Determine whether the study described below is a randomized experiment or an observational study.

A medical researcher wants to determine whether exercise can lower blood pressure. She recruits 100 people with high blood pressure to participate in the study. She assigns a random sample of 50 of them to pursue an exercise program that includes daily swimming and jogging. She assigns the other 50 to refrain from vigorous activity. She measures the blood pressure of each of the 100 individuals both before and after the study."--

The solution be [tex]$x=\frac{\pi}{4}+\pi n, x=\frac{3 \pi}{4}+\pi n, x=\frac{\pi}{2}+\pi n$$[/tex].

A trigonometric identity is an equation involving the trigonometric functions that holds true regardless of the value of the variables.

Trigonometric Identities are equality conditions that apply to all values of the equation's variables and which require trigonometry functions. There are numerous unique trigonometric identities that involve both the side length and angle of a triangle.

In contrast to trigonometric equations, which ask us to identify the precise values of the variables that make two expressions equal, trigonometric identities describe the equality between related trigonometric expressions.

Let the equation be [tex]$$\cos ^2(2 x)+\cos (2 x)=0$$[/tex]

Solve by substitution

[tex]$$\begin{aligned}& \cos (2 x)=0, \cos (2 x)=-1 \\& \cos (2 x)=0 \quad: \quad x=\frac{\pi}{4}+\pi n, x=\frac{3 \pi}{4}+\pi n \\& \cos (2 x)=-1 \quad: \quad x=\frac{\pi}{2}+\pi n\end{aligned}$$[/tex]

Combine all the solutions

[tex]$x=\frac{\pi}{4}+\pi n, x=\frac{3 \pi}{4}+\pi n, x=\frac{\pi}{2}+\pi n$$[/tex]

Therefore, the solution be [tex]$x=\frac{\pi}{4}+\pi n, x=\frac{3 \pi}{4}+\pi n, x=\frac{\pi}{2}+\pi n$$[/tex].

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Equation of the quadratic kind: ax2+bx+c=0

Our ability to solve any quadratic equation is aided by the quadratic formula. First, we change the equation's form to read as ax2+bx+c=0, where a, b, and c are the coefficients. As a result, we enter these coefficients into the formula: (-b(b2-4ac))/(2a). See illustrations of how the formula can be used to solve various equations.

Ax2 + bx + c = 0 is the form of a quadratic equation, which is an expression in second-degree algebra. Square-sounding "quad" is the root of the term "quadratic," which signifies "quadratic." An "equation of degree 2" is another way to describe a quadratic equation. A quadratic equation is utilised in a wide variety of situations.

For 2nd order polynomial equations of the type an x 2 + b x + c = 0, the quadratic formula is an equation that is employed.

Quadratic Formula

 ax^2+bx+c=0

When a 0 x = the unknown,

a, b, and c are known numbers.

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Equation of the quadratic form: ax²+bx+c=0.

Our ability to solve any quadratic equation is aided by the quadratic formula. First, we change the equation's form to read as ax²+bx+c=0, where a, b, and c are the coefficients. As a result, we enter these coefficients into the formula: (-b(b²-4ac))/(2a).

Ax² + bx + c = 0 is the form of a quadratic equation, which is an expression in second-degree algebra. Square-sounding "quad" is the root of the term "quadratic," which signifies "quadratic." An "equation of degree 2" is another way to describe a quadratic equation. A quadratic equation is utilised in a wide variety of situations

For 2nd order polynomial equations of the type an x² + b x + c = 0, the quadratic formula is an equation that is employed.

Quadratic Formula

ax²+bx+c=0

When a 0 x = the unknown,

a, b, and c are known numbers.

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112 square inches make up the ABCD figure.

The area of trapezoid is given by :Area [tex]$=\frac{1}{2} \times(a+b) h$[/tex], where h is the trapezoid's height and a and b are the parallel opposite sides.

The area of trapezoid A B C D with height 7 inches and opposite parallel sides 14 inches and 18 inches is calculated from the provided image by:-

[tex]& \text { Area }=\frac{1}{2} \times(14+18) 7 \\[/tex]

[tex]& \Rightarrow \text { Area }=\frac{1}{2}(32)(7) \\[/tex]

[tex]& \Rightarrow \text { Area }=16 \times 7 \\[/tex]

[tex]& \Rightarrow \text { Area }=112 \text { inches }^2[/tex]

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Answer:

give a list and then I can help

Answer:

Bangalore

Step-by-step explanation:

new York..

make me brainleast

Answer:

(A) 6

Step-by-step explanation:

since the question is about the integral and not the area of the curve, we indeed need to count the last part under the x-axis as negative.

it is an isoceles (both legs are equally long) right-angled 2×2 triangle. it's area is

2×2/2 = 2 units²

the first part is just a large rectangle 5×2, where we have to deduct two 2×1 right-angled triangles (one top left, one right).

so, we have

5×2 = 10 units²

-

2×1/2 × 2 = -2 units²

= 8 units²

and as we need to subtract the right triangle below the x-axis, the total integral is

8 - 2 = 6 units²

FYI

if the quarto was about the area under the curve, we would have to consider all parts as positron values, and we would have to calculate absolute value of the integral 0 to 5 plus the absolute value of the integral 5 to 7.

On solving the provided question we can say that the equation when factorization we have is (4x³ - 6x³ + 6x - 7)/(-2x + 3) on diving we will have, the quotient will be (-2x² + 6x -7)/(-2x + 3).

A number or other mathematical object is factored, or written as the product of numerous factors—typically smaller or simpler things of the same kind—in mathematics. For instance, the integer 15 is factorized as 3 5, which is the factorization of the polynomial x² – 4. Factorization in mathematics refers to the breakdown of a number into smaller numbers that are multiplied together to produce the original number. Factorization is the division of a number into its factors or factors. 12 is multiplied by 3 and 4 as an example.

the equation we have is

(4x³ - 6x³ + 6x - 7)/(-2x + 3)

on diving we will have

(-2x² + 6x -7)/(-2x + 3)

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Answer:

y=3x-3

y=9/3x-3=3x-3

Answer: The answer is 12

Step-by-step explanation:

a. The model predicts that the economic growth based on a barrel of oil priced at $55 is approximately -5.132 + 0.0912 * 55 = 3.8012.

b. The residual is 0.3 - 3.8012 = -3.5012, which indicates that the model is overestimating the economic growth based on a barrel of oil priced at $55. The negative value of the residual suggests that the model needs to be refined in order to provide more accurate predictions.

The least squares regression line model is used to find the best-fit line that minimizes the sum of the squared differences between the observed and predicted values.

The residual is the difference between the actual and predicted values for a given data point. In this case, the residual of -3.5012 suggests that the model is overestimating the economic growth based on a barrel of oil priced at $55.

To improve the accuracy of the model, we could consider additional factors that may impact the relationship between oil price and economic growth, or use different regression techniques to better fit the data.

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The given expression becomes 5.35-2b.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression is 7j+5-8kb.

Here,  j = 0.5 and k = 0.25

Now, substitute j = 0.5 and k = 0.25 in the given expression, we get

7×0.5+5-8×0.25×b

= 0.35+5-2b

= 5.35-2b

Therefore, the expression is 5.35-2b.

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Answer:

6.5

Step-by-step explanation:

W1 is not a subspace of R3 under the operations of addition and scalar multiplication due to its failure to contain the zero vector. W3 is a subspace that satisfies the three properties of a subspace: it contains the zero vector (0, 0, 0), it is closed under addition, and if two elements of W3 are added together, the result is also an element of W3.

Subspaces are groupings of subspaces inside a larger space or vector space. They are a subset of a wider space described by a set of linear equations. Subspaces are useful in linear algebra for studying linear transformations and other linear operations.

(a) W1 is not a subspace of R3 when addition and scalar multiplication are performed because it fails the closure property of a subspace. Consider the numbers (2, -14, 7) and (3, -21, 10) in W1. When these two vectors are combined, the result is (5, -35, 17), which is not a W1 element.

(b) Since it lacks the zero vector, W2 is not a subspace of R3 for addition and scalar multiplication operations. To constitute a subspace, a set must contain the zero vector, which in this case is (0, 0, 0).

(c) W3 is a subspace of R3 with addition and scalar multiplication operations. To demonstrate this, we must demonstrate that it meets the three qualities of a subspace. It includes the zero vector (0, 0, 0). It is closed under addition, which means that if two W3 items are combined together, the result is likewise a W3 element. This is demonstrated by ensuring that the equation 201 - 4a2 + 5a3 = 0 still applies for any two vectors in W3 joined together. Lastly, it is closed under scalar multiplication, which means that each element of W3 multiplied by a scalar produces an element of W3. This too can be seen by checking that the equation 201 – 4a2 + 5a3 = 0 still holds for any element of W3 multiplied by a scalar.

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The upper bound of a 99% confidence interval is found as 57.07.

A random sample of size 18.

Normal population gives 36.5.

Explain the term upper confidence bound (UCB)?

Whenever a machine is often used frequently than other machines, the border shrinks.

For the stated question-

sample size n = 18

normal population mean x = 36.5

variance  s² = 1148; s = 33.88

z(α/2) for 99% confidence interval = 2.576

Thus, upper confidence bound (UCB) is estimated as;

UCB = [tex]x + z(\frac{\alpha}{2} )*\frac{s}{\sqrt{n} }[/tex]

UCB = 36.5 + 2.576×33.88/√18

UCB = 36.5 + 20.57

UCB = 57.07

Therefore, the upper bound of a 99% confidence interval is found as 57.07.

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Answer:

x÷11+6=54

Step-by-step explanation:

all information is given