The Stable Matching Problem, as discussed in the text, assumes that all men and women have a fully ordered list of preferences. In this problem we will consider a version of the problem in which men and women can be indifferent between certain options. As before we have a set M of n men and a set Wof n women. Assume each man and each woman ranks the members of the opposite gender, but now we allow ties in the ranking. For example (with n- 4), a woman could say that m1 is ranked in first place; second place is a tie between m2 and m3 (she has no preference between them); and m4 is in last place. We will say that w prefers m to m' if m is ranked higher than m' on her preference list (they are not tied) With indifferences in the rankings, there could be two natural notions for stability. And for each we can ask about the existence of stable matchings, as follows. (a) A strong instability in a perfect matching S consists of a man m and a woman w, such that each of m and w prefers the other to their partner in S. Does there always exist a perfect matching with no strong instability? Either give an example of a set of men and women with preference lists for which every perfect matching has a strong instability; or give an algorithm that is guaranteed to find a perfect matching with no strong instability. (b) A weak instability in a perfect matching S consists of a man m and a woman w, such that their partners in S are w and m', respectively, and one of the following holds: m prefers w to w', and w either prefers m to m' or is indifferent between these two choices; or w prefers m to m', and m either prefers w to w' or is indifferent between these two choices. In other words, the pairing between m and w is either preferred by both, or preferred by one while the other is indifferent. Does there always exist a perfect matching with no weak instability? Either give an example of a set of men and women with preference lists for which every perfect matching has a weak instability; or give an algorithm that is guaranteed to find a perfect matching with no weak instability.

The speed of the faster cyclist is 3 miles per hour.

We can use the information given to set up the following equation:

r + (2r) = (r + 2r) / 2t

Where r is the speed of the slower cyclist, (2*r) is the speed of the faster cyclist, t is the time in hours, and the distance between the two cyclists is (r + 2r) miles.

We can use the given information that the two cyclists meet 2 hours later to solve for r:

r + (2r) = 30 / 22

Simplifying the equation we get:

r + (2*r) = 15

3r = 15

r = 5

We know that the faster cyclist is going 2 times faster than the slower cyclist, so we can use the value of r to find the speed of the faster cyclist:

2r = 25 = 10

So, the speed of the faster cyclist is 10 miles per hour.

Answer:

x = 5

Step-by-step explanation:

5(2x-11) = -5

5(2x-11) = -510x - 55 = -5

5(2x-11) = -510x - 55 = -510x - 55 + 55 = -5 + 55

5(2x-11) = -510x - 55 = -510x - 55 + 55 = -5 + 5510x = 50

5(2x-11) = -510x - 55 = -510x - 55 + 55 = -5 + 5510x = 5010x / 10 = 50 / 10

x = 5

The correct answer is B. While the measures of variation can be found they do not make sense because the data are nominal, they don't measure or count anything.

Any difference between the individuals in a species or between groups of organisms from any species is referred to as variation. Genetic variety is mostly caused through mutation, although other processes like sexual reproduction and gene flow also play a role.

Environmental variation refers to environmental elements that can contribute to variances. Inherited variation refers to the variance that is genetically transmitted during reproduction from parents to children.

The variable of interest is a nominal variable, which means it merely belongs to categories and doesn't actually have any "numerical" values. Only the categories' names—1, 2, 3, and 4—have been utilized.

Only "sample proportions" can be determined for nominal variables, and the variance between sample proportions of various samples may be calculated and compared, but measurements of variation within a single sample (as is the case here) are useless for nominal variables.

Therefore, Option B is the correct answer.

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The ordered pair that describes the location of R′′ is (-4,-2)

Explanation:

When a point is reflected over the x-axis, the x-coordinate remains the same and the y-coordinate changes sign. So, the point R' will be (4,-2)

When a point is reflected over the y-axis, the x-coordinate changes sign and the y-coordinate remains the same. So, the point R′′ will be (-4,-2)

Answer:

1.339 Canisters

Step-by-step explanation:

Because you are making 5 meatloafs for a party, and according to the recipe you need 1 1/4 cup of breadcrumbs per each meatloaf. In each canister there is 14/3 cups of breadcrumbs which you can see by multiplying the serving size by the servings per container.

Since you need five meatloafs, you can figure out how many cups of breadcrumbs you need by multiplying 1 1/4 cups by 5. This gives you 6 1/4 or 6.25 cups.

In each canister of breadcrumbs, there are 14/3 cups or 4.667 cups of breadcrumbs.

To figure out how many canisters you need, you divide the amount of breadcrumbs you need (6.25 cups) by the amount of breadcrumbs you have (4.667) which gives you 1.339 canisters.

The midline of function be 5 , an amplitude of 4 and a period of 3/2 then the sine function be y = 4 sin (4π/3 x) + 5.

The ratio of the opposing side's length to the hypotenuse of a right-angled triangle is known as the sine function in trigonometry. A right triangle's unknown sides or angle can be determined using the sine function.

The ratio of the lengths of the opposing side and the hypotenuse of a right-angled triangle is known as the sine function in trigonometry. Use the sine function to calculate the unknown side or angles of a right triangle.

The sine of the angle is the ratio of the hypotenuse to the perpendicular of a right-angled triangle. The formula for sin is sin = Perpendicular / Hypotenuse.

General sine function a sin b (x - c) + d

amplitude = absolute value of a

b = 2π / period

c = phase shift (horizontal shift)

d = vertical shift (midline is y = d)

Here a = 4, d = 5, and b = 2π / (3/2) = 4π/3, c = 0

Therefore, the sine function be y = 4 sin (4π/3 x) + 5,

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Answer:

If a certain company has 900 employees and two out of every five employees have worked for the company for 10 years or more, then that company would have 360 employees who have worked for the company for 10 years or more.

The average velocity for the time period beginning when t=3 and lasting for

1) 0.01 s: -9051.12 ft/sec

2) 0.005 s: -18051.06 ft/sec

3) 0.002 s: -45051.1 ft/sec

4) 0.001 s: -90051  ft/sec

Here, a ball is thrown with initial velocity of 46 ft/s.

The height of the ball in feet after t seconds is given by an equation,

 y = 21t - 12t²

Let us assume that P represents the average velocity.

The average velocity is given by formula,

P = [y(t₂) - y(t₁)]/[t₂ - t₁]

i) the average velocity for the time period beginning when t=3 and lasting  0.01 s

Here, t₂ = 3.01 s and  t₁ = 3 s

y(t₂) =  21(3.01) - 12(3.01)²

      = -45.5112

y(t₁) =  21(3) - 12(3)²

      = 45

y(t₂) - y(t₁) = -45.5112 - 45

                = -90.5112

So, P = -90.5112 / (0.01)

     P = -9051.12 ft/sec

ii) the average velocity for the time period beginning when t=3 and lasting  0.005 s

Here, t₂ = 3.005 s and  t₁ = 3 s

y(t₂) - y(t₁) = -45.5112 - 45

                = -90.2553

So, P = -90.2553 / (0.005)

     P = -18051.06 ft/sec

iii) the average velocity for the time period beginning when t=3 and lasting  0.002 s

Here, t₂ = 3.002 s and  t₁ = 3 s

y(t₂) - y(t₁) = -45.1021 - 45

                = -90.1021

So, P = -90.1021 / (0.002)

     P = -45051.1 ft/sec

iv) the average velocity for the time period beginning when t=3 and lasting  0.001 s

Here, t₂ = 3.001 s and  t₁ = 3 s

y(t₂) - y(t₁) = -45.051 - 45

                = -90.051

So, P = -90.051 / (0.001)

     P = -90051 ft/sec

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The complete question is:

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 46 ft/s. Its height in feet after t seconds is given by   y = 21t - 12t² .  A. Find the average velocity for the time period beginning when t=3 and lasting  .01 s:     .005 s:      .002 s:   .001 s:      NOTE: For the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator.  Estimate the instanteneous velocity when t=3.  

The arc of length on the unit circle corresponds to the point (√3, 1) on the unit circle because the unit circle is a circle with a radius of 1, centered at the origin (0, 0).

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Answer:

A. x = 3

Step-by-step explanation:

See picture

Answer:

4658

Step-by-step explanation:

This formula is used to get the values of the sine and cosine products for angle A and to solve different trigonometry issues.

SinA cosA = sin2A / 2 is the formula for sinA and cosA. This formula is used to get the values of the sine and cosine products for angle A and to solve different trigonometry issues.

Let LHS =

[tex]\frac{tan A}{1+ tan^{2} A} + \frac{cot A}{1+ cot^{2} A}[/tex]

= [tex]\frac{tan A}{(sec^{2}A) ^{2} } +\frac{cot A}{(cosec^{2}A) ^{2} }[/tex]

= [tex]\frac{\frac{sin A}{cos A} }{\frac{1}{cos^{4}A } } + \frac{\frac{cos A}{sin A} }{\frac{1}{sin^{4}A } }[/tex]

= [tex]sin A cos^{3} A + cos A sin^{3}A[/tex]

= [tex]sin A cos A (sin^{2}A + cos^{2}A)[/tex]

= [tex]sin A cos A[/tex] = R.H.S

Hence proved  as L.H.S= R.H.S

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The complete question is:

Prove that (tan A)/((1 + tan2 A) 2) + (cot A)/((1 + cot2 A) 2) for cotA  = sinA cosA.

The polynomial y = x⁶ + 7 · x⁴ - 17 · x² + 9 has two real zeros: x = 1, x = - 1. The polynomial diverges to + ∞ when x → ± ∞.

Sextic equations are polynomials of grade six, whose form is described below:

y = a · x⁶ + b · x⁵ + c · x⁴ + d · x³ + e · x² + f · x + g

Where a, b, c, d, e, f, g are real coefficients.

According to Bolzano's theorem, given a function f(x) defined for interval [a, b], there is at least a value of x such that f(x) = 0. For polynomials with integer coefficients, zeros may be divisors of grade zero coefficient. Then, the possible candidates for zeros of the sextic equation:

Possible roots = - 9, + 9, - 3, + 3, - 1, + 1

Now we proceed to check possible roots:

x = - 9

y = (- 9)⁶ + 7 · (- 9)⁴ - 17 · (- 9)² + 9

y = 576000

x = 9

y = 9⁶ + 7 · 9⁴ - 17 · 9² + 9

y = 576000

x = - 3

y = (- 3)⁶ + 7 · (- 3)⁴ - 17 · (- 3)² + 9

y = 1152

x = 3

y = 3⁶ + 7 · 3⁴ - 17 · 3² + 9

y = 1152

x = - 1

y = (- 1)⁶ + 7 · (- 1)⁴ - 17 · (- 1)² + 9

y = 0

x = 1

y = 1⁶ + 7 · 1⁴ - 17 · 1² + 1

y = 0

The end behavior of polynomial is defined by sign of lead coefficient, that is, the real coefficient of the highest exponent of the polynomial. In addition, polynomials does not converge at any value for x → ± ∞.

According to given information, the lead coefficient of polynomial y = x⁶ + 7 · x⁴ - 17 · x² + 9 diverges to + ∞ when x → ± ∞, since grade of polynomial is an even number.

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The highest score with an "F" grade is the 10th percentile score. To find the 10th percentile score, count 10% of the total number of scores, which is 100. So, the 10th percentile score is the 10th score from the bottom, which is 43.

A percentile score is a value on a scale that indicates the percentage of a set of observations that are below it. For example, a score of 80% on a test means that 80% of the test-takers scored below that score and 20% scored above it. In other words, the score separates the bottom 80% from the top 20%.

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The complete question is as follows:

Based on the student's work, the equation was solved incorrectly. B. The equation solved correctly would show that it has one solution(s).

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For instance, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.

In correct solution of the equation is given as:

4(2 - 3x) = x - 2(2x + 1)

8 - 12x = x - 4x - 2

8 - 12x = -3x - 2

8 + 2 = 12x - 3x

10 = 9x

x = 10/9

Hence, based on the student's work, the equation was solved incorrectly.

The equation solved correctly would show that it has one solution(s).

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Answer:

16 % points

Step-by-step explanation:

From the table   1963-1972   is 58 %

                          2003 - 2013 is 42%

58 - 42 =  16 percentage points

(a) The probability that at least 29% of the sample are from poverty level households is 0.0466.

(b) Based on the answer to part (a), there is not enough evidence to suggest that the percentage of children under the age of 6 living in households with incomes less than the official poverty level in this state is greater than the national value of 22%.

The probability of finding at least 29% of the sample from poverty level households is low, indicating that the difference between the observed percentage and the national value is not statistically significant.

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A' ∩ B ∩ C is region VI where B ∩ C but A is not included.

A Venn diagram can also be referred to as a set diagram or a logic diagram that illustrates various set operations including the intersection, union, and difference of sets. Subsets of a set are also represented using it. A subset of whole numbers, which is a subset of integers, is a collection of natural numbers, as an example.

Given:

The region I represent A.

and, The region III represent B

and, The region VII represent C.

and, the region show A∩B.

and, the region IV shows A ∩ C

and, the region VI shows B ∩ C

and, the region V shows A ∩ B ∩ C.

Now, we want a region where B and C should be intersected but not include region A (A').

So, the regions shows A' ∩ B ∩ C is region VI where B ∩ C but A is not included.

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A addition to a large number line is indeed a diagram of a graduated single direction used to represent real numbers in introductory mathematics.

2 November 2020 A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number just on line could be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when a point.graphing

The midpoint is indeed the "average" of a two numbers, so for the first: (4 + (-6))/2 = -2/2 = -1 for such second,

you are provided the "average," so choose one of the ends as x, multiplying by 2 to get 2+x = -8 and x = -10.

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The area of hubcap in shape of circle is 121π cm^2.

What is a circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.

The equation of circle in the plane is given as:

(x-h)^2 + (y-k)^2 = r^2

where (x, y) are the coordinate points

(h, k) is the coordinate of the center of a circle

and r is the radius of a circle.

and Area of circle = πr²

Circumference of circle=2πr

Now,

As shape of hubcap is circular.

Area of circle = πr^2

where r=D/2  D=diameter

Given diameter of hubcap is 22cm. --> r=11 cm.

Therefore,

                Area=π*11^2=121π cm^2

Hence,

          The area of hubcap in shape of circle is 121π cm^2.

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Answer:

To find the y-intercept, set x = 0 and solve for y:

13 * 0 - 21 * y = 7

-21 * y = 7

y = -7/21

y = -1/3

So the y-intercept is at (0, -1/3).

Answer: -1/3

Step-by-step explanation:

13x-21y=7

y=13x/21-1/3

y=-1/3

Answer:16

Step-by-step explanation:

Answer: 44

Step-by-step explanation:

The interior and exterior in these type of problems equal 180. 180 – 136 = 44

Dummy variables:

Ice Clean Flavor, Gender, Shoe Color, Number on an Athlete's Jersey, Ice Cream Flavor

Quantitative Variables:

Time to run a marathon, Flat-Screen TV, Height, Hours Spent Researching Core, Calories in Desserts

A dummy variable, often known as an indicator variable or simply a dummy, is a variable in regression analysis that accepts the values 0 or 1 to signify the lack or presence of a category effect that would be anticipated to change the outcome. 

Any variable where the data indicate amounts is referred to be a quantitative variable (e.g. height, weight, or age). Any variable where the data represent groupings is referred to as a categorical variable. This comprises categories (like where people placed in a race), rankings (like cereal brands), and binary results (e.g. coin flips).

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The complete question is:

For use in a linear regression model, categorize which of the following variables should be represented as dummy variables and which can be represented as quantitative variables.

ITEMS

CATEGORY

Answer:

A) 6centimeters (cm) LONG

B) 6 gallons/Liters of water

C) 32 milligrams

Step-by-step explanation: contact me through discord Acathia#0103, its easier to help, I can help with multiple questions aswell or send me ur SC

the height of fall of the bungee jumper is 9216 feet.

What is Distance?

a velocity is a unit of measurement for the Distance an object travels in a predetermined period of time. Here is a word equation that illustrates the connection between space, speed, and time: velocity is calculated by dividing the total Distance traveled by the journey time.

Diane and Douglas both drive at an average rate of 50 miles per hour. So if they travel for the same time they will end up covering the same Distance as well.

As we know velocity = rate of change of displacement

The distance the bungee jumper falls is estimated as follows when the time of motion is 6 seconds;

6 = [tex]\frac{\sqrt{d} }{16}[/tex]

√d = 16*6

√d = 96

d = 9216

Hence the height of fall of the bungee jumper is 9216feet.

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