Solve for x and graph the solution on the number line below. x+6≥16

Combination X will still have an opportunity cost, society might judge other combinations on the line as preferable to combination X, and it may be allocatively efficient, but it may not be productively efficient.

The Production Possibilities Curve (PPC) is a model used to illustrate the tradeoff between producing two goods. Combination X is a point on the PPC, and is not the same as other combinations on the same line.

A) This statement is not correct. Combination X will still have an opportunity cost associated with it. Opportunity cost is the cost of choosing one option over another, and it is the difference in the total outputs between the chosen combination and the next best combination. For example, if combination X produces 8 units of good A and 10 units of good B, and the next best combination produces 10 units of good A and 8 units of good B, the opportunity cost of combination X is 2 units of good B.

B) This statement is correct. Society might judge other combinations on the line as preferable to combination X because of their comparative advantage in producing one good over another.

C) This statement is correct. Allocative efficiency is the optimal combination of goods and services that maximizes the total benefit of society. Combination X may be allocatively efficient if it maximizes the total benefit of society.

D) This statement is not correct. Productive efficiency is the optimal combination of inputs that maximizes the

output of a good or service. Combination X may not be productively efficient if it does not maximize the output of a good or service.

Combination X will still have an opportunity cost, society might judge other combinations on the line as preferable to combination X, and it may be allocatively efficient, but it may not be productively efficient.

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Answer:

S₁₀ = - 40

Step-by-step explanation:

given the first term a₁ = 5 and the nth term [tex]a_{n}[/tex] = - 13

then the sum to n terms is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] (a₁ + [tex]a_{n}[/tex] )

here n = 10 , then

S₁₀ = [tex]\frac{10}{2}[/tex] (5 + (- 13)) = 5(5 - 13) = 5 × - 8 = - 40

Answer: one senior ticket is $8 and one student ticket is $14

Hope this helps a little

No, I don't agree with Sundeep. The mixture wont simply add up

When two liquids are mixed together, their volumes don't simply add up to equal the total volume of the mixture.

When sugar is mixed with water, the total volume of the mixture is usually slightly greater than the volume of the water alone, because the sugar particles take up space between the water molecules.

The volume of the mixture will be equal to the sum of the individual volumes only if the two liquids are completely immiscible, meaning they don't mix together at all. In this case, the total volume of the mixture will be equal to the sum of the volumes of water and sugar, which is 400 mL.

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Step-by-step explanation:

Here's how you can use partial fraction decomposition to write (x^3 + 2x^2 + 3x + 4)/(x^2 + x - 2) as the sum of simpler terms:

Factor the denominator to simplify the expression: x^2 + x - 2 = (x - 1)(x + 2)

Write the partial fraction decomposition of the integrand as the sum of simpler terms: (x^3 + 2x^2 + 3x + 4)/(x^2 + x - 2) = A/(x - 1) + B/(x + 2) + Cx + D, where A, B, C, and D are constants.

Multiply both sides of the equation by (x^2 + x - 2) to find the values of A, B, C, and D: x^3 + 2x^2 + 3x + 4 = A(x + 2) + B(x - 1) + (Cx + D)(x^2 + x - 2)

Substitute x = 1 and x = -2 into the equation to find two equations for A, B, C, and D:

x = 1: 4 + 2 + 3 + 4 = 9 = A(-2) + B + (C + D)(-1)

x = -2: -8 - 4 + 6 - 8 = -16 = A(1) + B(-2) + (C - 2D)(4)

Solve the system of equations to find the values of A, B, C, and D:

A = 9/3, B = 5, C = -11/3, D = 7/3

So the partial fraction decomposition of (x^3 + 2x^2 + 3x + 4)/(x^2 + x - 2) is (9/3)/(x - 1) + (5)/(x + 2) - (11/3)x + (7/3).

We will use six square tables and eight round tables.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let's call the number of square tables used "x". Then, the number of round tables used would be x + 2.

We know that the total number of people that can be seated is represented by 8 × number of round tables + 10 × number of square tables, or 8(x + 2) + 10x = 124.

Expanding and solving for x, we get 18x + 16 = 124.

Subtracting 16 from both sides, we get 18x = 108.

Dividing both sides by 18, we find that x = 6.

So, we will use 6 square tables and 8 round tables.

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We have the appropriate response to the inquiry b) The polygon's area is 99 inch2.

A polygon is a two-dimensional, closed shape that is flat or plane and is bounded by straight sides. Its sides are not curled. The edges of a polygon are another term for its sides. The vertices (or angles) of a polygon are the places where two sides converge.

According to the diagram we have the following:

DP = 10 ₋ 4 ₋ 6inch EP = 12 ₋ 5 = 7inch

Area of rectangle = l x b

Area of Triangle = [tex]\frac{1}{2}[/tex] x base x height

Area of polygon Area MBCD + Area AMPE + Area EPD = (5x10) + (4x27) + ([tex]\frac{1}{2}[/tex]x7x6) .

= 50 + 28 + 21 = 99 inch²

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Answer:

Step-by-step explanation:

The function h(x) = (f o g)(x) means that h is the composition of functions f and g, where g(x) is applied first and then the result is passed to f.

Without further information, it is impossible to determine the specific functions f(x) and g(x). The composition of functions is unique only when both f and g are specified.

The surface area of the cone is 113.09 square units.

A three-dimensional object's surface area is the sum of all of its faces. Real-world applications of the concept of surface areas include wrapping, painting, and eventually building things to achieve the best possible design.

Given that the height of the cone is 3 units and the radius of the base is 4 units.

The surface area of the cone is calculated by the formula:-

SA = πrl + πr²

Slant height will be calculated as:-

l² = h² + r²

l² = 3 ² + 4²

l² = 25

l = 5 units

The surface area will be:-

SA = πrl + πr²

SA = ( πx 4 x 5 ) + ( π x 4² )

SA = 113.09 square units

Therefore, the surface area will be 113.09 square units.

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The approximate volume of the astroid is 2.57 * 10^9 m^3

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

Radius = 8.5 × 10^2 m.

Using the formula 4/3 π r^3 for the volume, we get

Volume = 4/3 * (22/7) * (8.5 × 10^2)^3

Evaluate

Volume = 2.57 * 10^9 m^3

Hence, the volume is 2.57 * 10^9 m^3

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1. a. Probability (X ≤ 7000) = 0.40; b. P(X > 5000) = 0.95; c. P(5000 < X ≤ 7000) = 0.40.

2. a. P(0 < X) = 1; b. P(-0.5 ≤ X ≤ 0.5) = 1; c. P(X < -2) = 0; d. x = -1.645.

3. a. x = 9; b. x = 12; c. x = 7; d. x = 6.

1. a. The probability that the life of a semiconductor laser is less than or equal to 7000 hours can be calculated by subtracting the probability that it is less than or equal to 5000 hours from 1: P(X ≤ 7000) = 1 - 0.05 = 0.40. b. The probability that the life is greater than 5000 hours can be calculated by subtracting the probability that it is less than or equal to 5000 hours from 1: P(X > 5000) = 1 - 0.05 = 0.95. c. The probability that the life is between 5000 and 7000 hours can be calculated by subtracting the probability that it is less than or equal to 5000 hours from the probability that it is less than or equal to 7000 hours: P(5000 < X ≤ 7000) = 0.40 - 0.05 = 0.35.

2. a. The probability that X is greater than 0 can be calculated by subtracting the probability that X is less than or equal to 0 from 1: P(0 < X) = 1 - 0 = 1. b. The probability that X is between -0.5 and 0.5 can be calculated by subtracting the probability that it is less than or equal to -0.5 from the probability that it is less than or equal to 0.5: P(-0.5 ≤ X ≤ 0.5) = 1 - 0 = 1. c. The probability that X is less than -2 can be calculated by simply looking at the upper limit of the function: P(X < -2) = 0. d. The value x such that P(x < X) = 0.05 can be found by solving the equation: x = -1.645.

3. a. The value x such that P(X > x) = 0.5 can be found by solving the equation: x = 9. b. The value x such that P(X > x) = 0.95 can be found by solving the equation: x = 12. c. The value x such that P(3 < X < x) = 0.2 can be found by solving the equation: x = 7. d. The value x such that P(3 < X < x) = 0.8 can be found by solving the equation: x = 6.

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The circumference of the larger circle is 94.3 inches.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

Let's call the radius of the larger circle "R" and the radius of the smaller circle "r".

Since the circumference of the smaller circle is 20% of the circumference of the larger circle, we have:

2πr = 0.2 × 2πR

Dividing both sides by 2π:

r = 0.2 × R

Since the diameter of the smaller circle is 6 inches, we have:

2r = 6

So:

r = 3

And, since r = 0.2 R:

3 = 0.2 × R

Solving for R:

R = 15

So the circumference of the larger circle is:

C = 2πR = 2π × 15 = 94.25

Rounding to the nearest tenth, the circumference of the larger circle is 94.3 inches.

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The graph of the linear function y = 15x + 20 is given by the image presented at the end of the answer.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The function in this problem is defined as follows:

y = 15x + 20.

Hence the graph is constructed as follows:

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In a case whereby three friends got the prize money worth 120000 The first friend would get three times the amount of the third friends portion. the third friend would get twice the amount of the second friends  the amount that each friend would receive are:$10909, $21818 and $87272 respectively.

The concept that willbe used here is simplification.

Let assume that the amount that is gotten by the second friend be $X,

then the amount that is gotten by the third friend be $2X

then the amount that is gotten by the third friend be $8X

Then perform the summation as $X+$2X+ $8X=120000

11X= 120000

X=120000/11 = 10909

X=$10909

$2X= 2*10909=$21818

$8X=8*10909=$87272

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These intervals were calculated assuming that the differential equation coefficients and initial value are continuous on the intervals. Additional analysis may be required in practice to confirm the precise duration of existence and uniqueness.

The existence and uniqueness theorem for first order linear differential equations states that if the differential equation's coefficients and the initial value are continuous on an interval containing the initial value, then the differential equation has a unique solution on that interval.

It should be noted that these intervals were determined under the assumption that the differential equation coefficients and initial value are continuous on the intervals. In practice, additional analysis may be required to confirm the precise duration of existence and uniqueness.

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The ordered pairs in table T. (3, 4) and (3, - 4) are the same, indicating that it is not a function.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

We know a relation is a function if it is one-to-one and many-to-one.

And, A relation is not a function if it is one to many meaning no two distinct ordered pairs have the same first coordinate.

Observing the given tables we conclude that in table T the ordered pairs

(3, 4) and (3, - 4) have the same first coordinate so it is not a function.

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now, we're making the assumption that the monthly payments Ricky is doing are at the beginning of every month.

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 400\\ r=rate\to 1\%\to \frac{1}{100}\dotfill &0.01\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &28 \end{cases}[/tex]

[tex]A=400\left[ \cfrac{\left( 1+\frac{0.01}{12} \right)^{12 \cdot 28}-1}{\frac{0.01}{12}} \right]\left(1+\frac{0.01}{12}\right) \\\\\\ A=400\left[ \cfrac{\left( \frac{1201}{1200} \right)^{336}-1}{\frac{1}{1200}} \right]\left(\frac{1201}{1200}\right) \implies \boxed{A \approx 155157.45}[/tex]

171 is 1.8 standard deviations below the mean.

Using the 68-95-99.7 rule, approximately 5.5% of the population scored 171 or lower. This translates to 66 people.

1. Calculate the z-score: z = (171 - 225) / 18 = -1.8

2. Use the 68-95-99.7 rule to calculate the percentage of the population that scored 171 or lower: 5.5%

3. Calculate the number of people that scored 171 or lower: 66 (5.5% of 1200) mean

The complete question is :

What is the population of people who scored 171 out of a population of 1200 with a mean of 225 and a standard deviation of 18?

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The weight range is 10 ≤ x < 30.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

For health reasons her doctor advises that she gain weight before her next appointment in 3 months.

She should gain at least 10 pounds but  less than 30 pounds.

let her weight is x pounds then the range for her weight to be healthy.

10 ≤ x < 30.

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The minimum value of the function f(x) = 2x^2 + 8.1x + 15.4 is 15.96 to the nearest hundredth.

Minimum value is the lowest y-value the function reaches.

The minimum value of a parabolic function like f(x) = 2x^2 + 8.1x + 15.4 is achieved at the vertex of the parabola.

The x-coordinate of the vertex is given by the formula:

x = -b / (2a

where a = 2, b = 8.1, and c = 15.4.

Plugging in these values, we get:

x = -8.1 / (2 * 2) = -2.05

So, the x-coordinate of the vertex is -2.05. To find the y-coordinate (i.e., the minimum value of the function), we plug in this x-coordinate and solve for y:

y = f(-2.05) = 2(-2.05)^2 + 8.1(-2.05) + 15.4 = 15.96

So, the minimum value of the function f(x) = 2x^2 + 8.1x + 15.4 is 15.96 to the nearest hundredth.

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Answer:

a. Total Cost Function: The total cost function for Birat tea packaging company is given by: Total Cost = 8,000,000 + 80x + 15x + 10x + 20x = 8,360,000 + 125x

b. Total Revenue Function: The total revenue function for Birat tea packaging company is given by: Total Revenue = 160x

c. Total Profit Function: The total profit function for Birat tea packaging company is given by: Total Profit = Total Revenue - Total Cost = 160x – 8,360,000 - 125x = 7,225,000 - 125x

d. If you were the owner of the company, you would need to sell at least 58,000 Kgs of tea in order to reach neither loss nor profit.

e. If the market is very competitive and there are lots of substitute products, the Birat Tea Packaging Company can use a variety of strategies to stay competitive. These strategies can include offering discounts, loyalty programs, promotional campaigns, product diversification, and improved marketing efforts. The company should also focus on providing superior customer service to build and maintain customer loyalty. Additionally, the company should stay up-to-date on the latest trends in the industry and explore opportunities to collaborate with other companies to gain a competitive advantage.

Step-by-step explanation:

The graph of function y = 1/2 (x - 3) - 10 is shown in figure.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The equation of function is,

⇒ y = 1/2 (x - 3) - 10

Now, The equation of function is,

⇒ y = 1/2 (x - 3) - 10

Clearly, This represent the equation of line.

Hence, By using tool;

The graph of function y = 1/2 (x - 3) - 10 is shown in figure.

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The number of ways you can draw n chords in a circle combination with 2 x n points such that no 2 chords intersect is n! / (2! * (n - 2)!).

Given a number n, the number of ways you can draw n chords in a circle with 2 * n points such that no two chords intersect is given by n choose 2. This is because you have 2 * n points, and for each chord, you must choose two of these points to be its endpoints.

The number of ways to choose two points out of 2 * n points is given by the binomial coefficient (n choose 2), which is equal to n! / (2! * (n - 2)!). This formula counts the number of combinations of n chords that can be drawn in a circle without any intersections.

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The vertical asymptote and horizontal asymptote of the rational function will be x = 3 and y = -2, respectively.

An asymptote is a line that constantly reaches a given curve but does not touch at an infinite distance.

The rational function is given below.

f(x) = - 2x / (x - 3)

The vertical asymptote is given as,

x - 3 = 0

x = 3

Then the horizontal asymptote is given as,

y = lim x → ∞ f(x)

y = lim x → ∞ - 2x / (x - 3)

y = lim x → ∞ - 2

y = - 2

The vertical asymptote and horizontal asymptote of the rational function will be x = 3 and y = -2, respectively.

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Open-ended questions are often used in market research, customer satisfaction surveys, and other social sciences research to gather in-depth information from respondents.

Open-ended questions are a type of qualitative research method that seeks to gather unrestricted comments or opinions from respondents. These questions are usually framed in a way that allows the respondent to express their thoughts and feelings without being limited by pre-determined response options. This method can provide valuable insights into the perspectives, experiences, and motivations of the individuals being studied. Open-ended questions are often used in market research, customer satisfaction surveys, and other social sciences research to gather in-depth information from respondents.

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This expression [tex]t(x) = 4 * \pi * (x/2)^2[/tex]  gives the total area of the four circles as a function of x, the side of the square.

The area of a single circle with radius r can be calculated using the formula:

[tex]A = \pi r^2[/tex]

In this problem, the radius of each circle is the same and equal to r. Therefore, the area of a single circle can be calculated as:

[tex]A = \pi r^2[/tex]

The total area of the four circles, t, can be found by adding the area of each circle:

[tex]t = 4 * \pi r^2[/tex]

The radius of each circle can be expressed as a function of the side of the square, x, as follows:

[tex]r = x/2[/tex]

Substituting this expression for r into the equation for the total area of the four circles, we get:

[tex]t(x) = 4 * \pi * (x/2)^2[/tex]

This expression gives the total area of the four circles as a function of x, the side of the square.

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The distance between the two points S( -5, 7) to V(- 2, 4) is 3.5 units.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is given by,

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given, We have to find the distance between the points S(- 5, 7) to V(-2, 4).

Therefore, [tex]|SV| =\sqrt{(- 2 + 5)^2 + (4 - 7)^2}[/tex].

[tex]|SV| =\sqrt{(3)^2 + (-3)^2}[/tex].

[tex]|SV| =\sqrt{9 + 9}[/tex].

|SV| = √18.

|SV| = 2√3.

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The measure of {x} is equivalent to 18.

In Euclidean geometry -

an angle is the figure formed by two rays known as the sides of the angle and sharing a common endpoint known as the vertex of the angle.

Given is a circle with sectors.

Now, the measure of ∠MCP = 180°. We can write -

∠MCL + ∠LCA + ∠ACP = 180°

(2x - 4) + 101 + 47 = 180

2x - 4 + 148 = 180

2x + 144 = 180

2x = 36

x = 18

Therefore, the measure of {x} is equivalent to 18.

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The area swept by the blade in model 3 is 66932 square feet.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The word "area" refers to a free space. A shape's length and width are used to calculate its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc. But a shape's area is a two-dimensional measurement.

The blade length for model 3 is r = 146.

The area of the circle is given by:

A = pi(r)²

A= (3.14) (146)²

A = 66932

Hence, the area swept by the blade in model 3 is 66932 square feet.

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