I need help with my microeconomics hw​

Answer:

x = 7 years

Step-by-step explanation:

The mean (M) is defined as the average of the sum of all the data points in a set:

[tex]M=\frac{r_{1}...r_{n} }{n}[/tex]

Thus, since there are five data points and we're given the mean, we can use the following formula to find x:

[tex]M=10\\10=\frac{(8+x+13+12+10)}{5}\\ 50=43+x\\7=x[/tex]

Answer:

see what you got to do is you have to find n

Each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.

Let's consider the number of ways to seat n couples around a circular table without any restrictions first.

Since there are 2 people in each couple, there are a total of 2n people. The number of ways to seat 2n people around a circular table is (2n-1)!/2n,

where we divide by 2n to account for rotations of the same seating arrangement.

Now, let's consider the restriction that no couple can sit together.

We can start by fixing one person in a couple, and then there are (2n-2) ways to seat the other person in that couple so that they don't sit together.

After that, we can fix another person and their partner, and there are (2n-4) ways to seat the remaining two people in their couple so that they don't sit together.

We can continue this process until all couples are seated.

Therefore, the total number of ways to seat n couples around a circular table so that no couple sits together is:

[tex](2n-2)(2n-4)(2n-6)...2 = 2^{n-1} * (n-1)![/tex]

We multiply by[tex]2^{n-1}[/tex] to account for the fact that each couple can sit in two different seats (either clockwise or counterclockwise from their partner), and we multiply by (n-1)! to account for the number of ways to arrange the couples around the table.

Note that reflected seatings are considered to be different, so we don't need to worry about dividing by 2 as we did in the unrestricted case.

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Answer:

To determine which proportion is equivalent to 15/60 = 8/32, we can simplify both fractions to their lowest terms and compare them:

15/60 = 1/4 (by dividing both numerator and denominator by 15)

8/32 = 1/4 (by dividing both numerator and denominator by 8)

We can see that both simplified fractions are equal to 1/4. Therefore, the proportion that is equivalent to 15/60 = 8/32 is:

15/60 = 8/32 = 1/4

Answer:

480

Step-by-step explanation:

To find which proportion is equivalent to 15/60 = 8/32, we can cross-multiply and simplify:

15/60 = 8/32

(15)(32) = (60)(8)

480 = 480

Therefore, the two proportions are equivalent.

I hope this helps! Let me know if you have any other questions.

Answer:

4x - y = 2,

Step-by-step explanation:

The point-slope form of the equation of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. In this case, we are given that the line passes through the points (4, -3) and (12, 1). The slope of the line is then m = (1 - (-3)) / (12 - 4) = 1/4.

Substituting the slope and the point (4, -3) into the point-slope form of the equation, we get y - (-3) = 1/4(x - 4). Simplifying, we get y + 3 = 1/4x - 1.

To convert the equation to standard form, we multiply both sides of the equation by 4. This gives 4y + 12 = x - 4. Simplifying, we get 4x - y = 8.

Therefore, the standard form of the equation of the line is 4x - y = 8.

A. We can see here that triangles ABX and DCX are similar because using the Angle-Angle Similarity:

B. Length XD = 12.5cm.

Similar triangles are triangles that have the same shape but not necessarily the same size. In other words, corresponding angles of similar triangles are equal, and corresponding sides are in proportion.

More formally, two triangles ABC and DEF are similar if and only if:

The length of XD:

CD/AB = XD/AX

10/4 = XD/5

XD = 50/4 = 12.5cm.

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From the figures, AB is a tangent to the C because they make a right angles (90⁰)

Recall that in n Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs.

We shall be determining the angle at C to see if it gives 90⁰

Using trigonometrical ratios of tangent

TanB = Opposite/Adjacent

Tan B. = 4.8/7.2

Tan B = 0.6667

B = Tan⁻¹0.6667

<B = 33.69⁰

Also in the same manner,

TanS = opp/Adj

Tan S = 7.2/4.8

Tan S = 1.5

S = Tan⁺¹1.5

< S = 56.31⁰

Npw <S + <B = 56.32 + 33.69 = 89.9999247 = 90⁰

Therefore AB makes tangent at C

20.  

Tan C = Opp/Adj

Tan C = 15/11.2

Tan C = 1.3393

C = Tan⁺¹1.3393

< C = 53.25

Also, Tan B = 11.2/15

Tan B = 0.7467

B = 36.75

<B + <C = 36.75 + 53.25 = 89.9986 = 90⁰

Therefore AB makes a tangent at C

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k(x) can have any minimum value, which means it can have the greatest minimum value among the given functions.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output.

The given graph represents the function [tex]f(x) = x^2 - 2x - 6[/tex], which is an upward-opening parabola with vertex at (1, -7) and passes through the points (-2, 2) and (4, 2).

Function [tex]h(x) = 2(x - 1)^2[/tex] is a quadratic function that opens upwards and its vertex is at (1, 0). The minimum value of h(x) is 0, which is the value at the vertex. Therefore, h(x) has the least minimum value among the given functions.

Function k(x) can be any linear function or a constant function. If k(x) is a linear function, then its minimum value is either negative infinity or 0, depending on the slope of the function. If k(x) is a constant function, then its minimum value is the same as its constant value.

Therefore, k(x) can have any minimum value, which means it can have the greatest minimum value among the given functions.

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If M is the midpoint of the leg CG, then the

a) Area of ABD = 18.75 ft^2

b) Area of MOC = 15 ft^2

To solve this problem, we need to use the properties of trapezoids and their diagonals. Let's start with finding the area of ABD.

First, notice that ABD and COD are similar triangles because they share angle O. Thus, we can write

AB/CD = AD/CO

Since AD = BC (opposite sides of a trapezoid are parallel), we can simplify to:

AB/CD = BC/CO

We also know that the area of AOD is 15 ft^2

Area of ABD/ Area of COD = AB/CD

We can substitute the ratio AB/CD from the similarity relation above to get

Area of ABD/ Area of COD = BC/CO

Since the bases of the trapezoids are parallel

Area of ABD/ Area of COD = BD/CO

Finally, we can use the fact that the altitudes from B and O to the longer base are in a 5:3 ratio to write

Area of ABD/ Area of COD = 5/3

Area of ABD = 5/8 × Area of COD

We know that the area of AOD is 15 ft^2, so the area of COD is twice that, or 30 ft^2. Therefore

Area of ABD = 5/8 × 30 = 18.75 ft^2

Next, we need to find the area of MOC. To do this, we can use the fact that the diagonals of a trapezoid divide it into four triangles, and the areas of these triangles are proportional to the lengths of the diagonals.

Let x be the length of OC, and let y be the length of OG. Then we have

Area of MOC/ Area of MOG = x/y

Also, since M is the midpoint of CG, we have

x = 2y

Substituting this into the first equation, we get

Area of MOC/ Area of MOG = 2

We know that the area of MOG is half the area of AOD, so

Area of MOG = 15/2 ft^2

Therefore, we have

Area of MOC = 2 × Area of MOG = 15 ft^2

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A survey is taken at a movie theater in Wayside. The first 200 people who entered the theater were asked about their favorite type of movie. The true about this situation is: The population is the total number of people who go to the movie theater, and the sample is the first 200 people at the theater.

In this situation, the population refers to the entire group of people who go to the movie theater in Wayside. The population includes all individuals who have the potential to be surveyed about their favorite type of movie.

The sample, on the other hand, is a subset of the population and represents the first 200 people who entered the theater. These 200 individuals are selected to provide information about the preferences of the larger population.

It is important to note that the sample is not the entire population but rather a smaller representative group. By surveying the sample, we aim to gather insights and make inferences about the preferences of the larger population of moviegoers in Wayside.

The correct answer is: The population is the total number of people who go to the movie theater, and the sample is the first 200 people at the theater.

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Ordered pair is represented by the function g(4) = 22 is (4,22)

An ordered pair is a pair of mathematical elements written in a specific order, typically represented by the notation (a, b). The first element in the pair is called the x-coordinate, while the second element is called the y-coordinate. The order of the elements is important, so (a, b) is not the same as (b, a) unless a = b.

Ordered pairs are commonly used in mathematics to represent points in the Cartesian plane, where the x-coordinate represents the horizontal distance from the origin and the y-coordinate represents the vertical distance from the origin. They can also be used to represent solutions to equations, inputs and outputs of functions, and many other mathematical concepts.

Given Function

g(4)=22

For the value of x=4

The output of function is y=22

So, the ordered pair is (4,22).

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The difference in the place value of the two seven in the number 872574 is  69,930.

In the given value we have to find the place value of two 7. To find the place value of the two seven we need to find the occurrence of seven in the value.

In the given value of 8,72,574,

the first 7 occur at ten thousand place

Its place value = 7 × 10000 = 70000

The second 7 occurs at ten’s place

Its place value = 7 × 10 = 70

The difference between the two place values of 7

= 70000 - 70

= 69930

Therefore, the difference in the place value of two 7 is 69,930

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1. Formula for the area of a sector of a circle, which is  A = (θ/360)π[tex]r^2[/tex] 2. The area of sector HIJ is 2.51 square units. 3. The measure of angle KLM is approximately 0.29 degrees

A circle is a geometric shape consisting of all the points in a plane that are a fixed distance (called the radius) away from a given point (called the center).

BLANK 1: To solve this problem, we can use the formula for the area of a sector of a circle, which is A = (θ/360)π[tex]r^2[/tex], where θ is the central angle of the sector, r is the radius of the circle, and π is pi (approximately 3.14).

BLANK 2: To find the area of sector HIJ, we need to know the radius of circle I and the measure of angle HIJ. From the given information, we know that circle I has a radius of 8, and angle HIJ is 45 degrees. Therefore, the area of sector HIJ is:

A = (45/360) x 3.14 x [tex]8^2[/tex]

A = 3.14 x 8 x (45/360)

A = 3.14 x 8 x 0.125

A = 2.51 square units (rounded to two decimal places)

Therefore, the area of sector HIJ is 2.51 square units.

BLANK 3: We know that sector KLM has the same area as sector HIJ, and circle L has a radius of 10. Therefore, we can use the formula for the area of a sector of a circle again to find the measure of angle KLM. Let x be the measure of angle KLM in degrees. Then:

A = (x/360) x 3.14 x [tex]10^2[/tex] = 2.51

Simplifying this equation gives:

(x/360) = 2.51/(3.14 x [tex]10^2[/tex])

(x/360) = 0.0008

x = 360 x 0.0008

x = 0.288

Therefore, the measure of angle KLM is approximately 0.29 degrees (rounded to two decimal places).

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Answer:

hope this helps

Step-by-step explanation:

Let "x" be the number.

The algebraic expression for "a number divided by 12" can be written as:

x/12

Here, "x" is being divided by 12, which means that we are finding the quotient of "x" when it is divided by 12.

Answer:

The answer is *some variable* upon 12 or *some variable* ÷ 12

Examples:

x÷12 or x upon 12

y÷12 or y upon 12

m÷12 or m upon 12

Step-by-step explanation:

You must apply a variable, such as "x,y,m,... etc" to "some number." Your expression then changes to the examples I have given above.

Hope this helped you :)

The prism has an 8/27 cubic centimetre volume.

The following formula determines a cube's volume:

V = s³

where V is the volume of the cube and s is the length of one of its sides.

In other words, to find the volume of a cube, you simply need to raise the length of one of its sides to the third power (cube it).

The volume of a cube = s³

Given that the prism is composed of cubes with a one-third-centimeter side measurement.

Volume of a cube = (1/3)³ = 1/27

There are 8 cubes in the prism.

Therefore, the volume of the prism is;

=8(1/27)

= 8/27 cubic centimeter.

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The complete question is:

The prism below is made of cubes which measure of a centimeter on one side. What is the volume?

Note: Figure is not drawn to scale.

The prism below is made of cubes which measure 1/3 of a centimeter on one side. What is the volume?

Image is attached below.

39 degrees of freedom will be used to find the t-critical statistic value.

We need to find degrees of freedom for the t-critical statistic value with 40 sample towers and a normally distributed population. According to the given dataset we can assume that we have the 95% confidence interval which is taken as default if nothing is mentioned about it.

The degrees of freedom (df) for a t-distribution are calculated as given below:

df = n - 1

where n is the sample size of the problem.

In this case, the sample size is 40, so the degrees of freedom would be:

df = 40 - 1 = 39

Therefore, we would use 39 degrees of freedom to find the t-critical statistic value for a 95% confidence interval.

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Answer:

Population: 21 million; parameter: 57%; sample: 85,349; statistic: 72%.

Explanation:

The population is the entire group being studied, which in this case is all the residents of Florida, with a total population of 21 million.

The parameter is a numerical summary of the population, which in this case is the proportion of residents who visit a doctor annually and is stated as 57% in the problem.

The sample is a subset of the population that is selected for study, which in this case is the 85,349 adults surveyed by the surveyor.

The statistic is a numerical summary of the sample, which in this case is the proportion of adults in the sample who stated that they have visited a doctor within the past year and is stated as 72% in the problem.

The scale factor of 10cm to 5m is 50.

The scale factor is a measure for similar figures, who look the same but have different scales or measures.

For example ,if a length of 5cm is doubled and it gives a length 10cm, the scale factor is 10/5 = 2. This means that we can express scale factor with a formula;

scale factor = new dimension / old dimension

Here, the old dimension is 10cm and the new dimension is 5m. We need to convert the 5m into cm

therefore 5m = 5× 100 = 500cm

therefore scale factor = 500/10 = 50

This means the scale factor of 10cm = 5m is 50

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Answer:

y = [tex]\frac{x(k+1)}{k-1}[/tex]

Step-by-step explanation:

First, recall that in a proportion (a set of equivalent ratios), the product of means is equal to the product of extremes. For example,

if [tex]\frac{a}{b} = \frac{c}{d}[/tex] (or a:b = c:d) the product of means (b and c) is equal to the product of extremes (a and d), and we have ad = cb.

Using this knowledge, in the proportion (y+x):(y-x) = k:1, let us find the product of means and extremes and set them equal, like so:

(y+x):(y-x) = k:1 =

k(y-x) = y+x =

ky - kx = y+x

To solve for y, move all terms including y to one side, like so:

ky - kx = y+x =

ky - y = kx + x

Now, factor out y.

ky - y = kx + x =

y(k - 1) = kx + x

Then, factor out the common term x.

y(k - 1) = kx + x =

y(k - 1) = k(x + 1)

Now, finish isolating the variable by dividing by (k-1), and we have:

y =  [tex]\frac{x(k+1)}{(k-1)}[/tex]

Step-by-step explanation:

Given :

d = 3.6m

r = d/2

r = 3.6/2

r = 1.8 m

We know that,

C = 2πr

C = 2 * 22/7 * 1.8

C = 11.3 m

Now,

A = π r²

A = 22/7 × (1.8)²

A = 22/7 × 3.24

A = 10.1 m²

Answer:

The Radius is 1.8, The circumference is 11.3 ,The area is 10.2

Step-by-step explanation:

The radius of a circle from diameter: if you know the diameter d , the radius is r = d / 2 .

To calculate the circumference, you need the radius of the circle: Multiply the radius by 2 to get the diameter. Multiply the result by π, or 3.14 for an estimation.That's it; you found the circumference of the circle.Or you can use the circle's diameter:Multiply the diameter by π, or 3.14.The result is the circle's circumference.


Diameter of circle= 3.6cm So, radius of circle=3.6/2Radius of circle = 1.8 Now ,Area of circle =πr². [r=radius] so 3.14 times 1.8 times 1.8 and you get 10.17 then round it to the nearest tenth and it is 10.2

Considering the attached figure, the transformation questions are answered as follows

5. Hassan

6. Liv

7. Both

8. Liv

9. Neither

Reflection is a type of transformation in geometry that involves flipping a shape over a line of reflection, such that the image is a mirror image of the original shape. The line of reflection is a fixed line that acts as the axis of symmetry for the transformation.

Liv was a translation, that moved the preimage from the second quadrant  to an image in quadrant 1. But Hassan image was a reflection that flipped the preimage from the first quadrant to an image in quadrant 2

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Step-by-step explanation:

For right triangles     tan B = opposite leg / adjacent leg

tan B = 3/4  

arctan (3/4) = B = 36.87 degrees

Step-by-step explanation:

18-2x<3(2x-1)-3

21-2x<6x-3

24<8x

3<x

Interval notation

(3, ∞)

The two statements that completes the above proof are:

ΔABC ~ ΔDEC - Side - Angle - Side Postulate

∠1≅∠2 - Corresponding angles.

The Side-Angle-Side (SAS) postulate states that if two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent.

Corresponding angles are equal because of the congruence of the triangles. Two angles are corresponding if they occupy the same relative position in two distinct intersecting lines, such that they are on the same side of the transversal and are in the same position in relation to the intersection. Corresponding angles are equal if the two intersecting lines are parallel.

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Answer:

6,368 chocolate

Step-by-step explanation:

First, we need to find the mass of chocolate chips in the bag:

Mass of Chocolate Chips=Mass of Chocolate Chips + Bag - Mass of Bag ONLY

Mass of Chocolate Chips = 2041 g - 67 g

Mass of Chocolate Chips = 1974 g

Next, we need to use the given information to estimate the number of chocolate chips in the bag:

31 grams of chocolate chips = 100 chips

1 gram of chocolate chips = 100/31 chips

Using this conversion factor, we can find the estimated number of chocolate chips in the bag:

1974 g of chocolate chips = (100/31) x 1974 chips

1974 g of chocolate chips ≈ 6,368 chips (rounded to four significant figures)

Therefore, it is estimated that there are about 6,368 chocolate chips in the bag.

Answer:

csc θ + cot θ

Step-by-step explanation:

(z + y)/x = z/x + y/x

sin θ = x/z

csc θ = 1/sin θ

csc θ = z/x

tan θ = x/y

cot θ = 1/tan θ

cot θ = y/x

z/x + y/x = csc θ + cot θ

Answer:

[tex]2((1 \frac{1}{3} )(1 \frac{1}{2} ) + (1 \frac{1}{2} )(5) + (1 \frac{1}{3}) (5))[/tex]

[tex]2(( \frac{4}{3} )( \frac{3}{2} ) + ( \frac{3}{2} )(5) + ( \frac{4}{3} )(5))[/tex]

[tex]2(2 + \frac{15}{2} + \frac{20}{3} )[/tex]

[tex]2( \frac{12 + 45 + 40}{6} )[/tex]

[tex] \frac{97}{3} = 32 \frac{1}{3} [/tex]

The surface area of this rectangular prism is 32 1/3 square feet.

The value of function k(f(x)) is 12x³ + 32x - 8.

Function composition is a way to combine two or more functions to form a new function. In this case, we are given two functions f(x) and k(x), and we need to find the value of k(f(x)), which means we need to apply the function k(x) to the output of the function f(x).

Here we have

Functions f(x)= 3x³ +8x -2 and k(x) = 4x

To find k(f(x)), we need to substitute the expression for f(x) into k(x) wherever we see x. So, we have:

k(f(x)) = 4(f(x)) = 4(3x³ + 8x - 2)

We can simplify this expression by distributing the 4:

k(f(x)) = 12x³ + 32x - 8

Therefore,

The value of function k(f(x)) is 12x³ + 32x - 8.

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