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The Gini coefficient is 2(−13/30) = -13/15.

The Lorenz curve L(p) can be expressed as the cumulative distribution function of a random variable X. The Gini coefficient is then given by the area between the diagonal line (representing perfect equality) and the Lorenz curve L(p).

In other words, the Gini coefficient is the ratio of the area between the diagonal line and the Lorenz curve to the total area under the diagonal line.

The Lorenz curve for the state can be given as L(p)=p^4/3.Ron can compute the Gini coefficient by finding the area between the diagonal line and the Lorenz curve.

The diagonal line goes from (0,0) to (1,1).The area under the diagonal line is 1/2.

The area between the diagonal line and the Lorenz curve is given by∫[0,1](L(p)−p)dp=

∫[0,1](p^4/3−p)dp

=(1/15)−(1/2)

= -13/30

The Gini coefficient can be negative when the Lorenz curve lies above the diagonal line, which indicates that the distribution is more equal than the hypothetical distribution of perfect equality.

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Since the point (-4, a) is on the graph of y = x², the value of a is equal to 16.

In Mathematics and Geometry, a quadratic function can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic function is represented by the following equation;

ax² + bx + c = 0

Where:

When x = -4, the value of y or a can be calculated as follows;

y = x²

y = a = (-4)²

y = a = 16.

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Answer:

Step-by-step explanation:

\(\frac{3}{n}\) - 10.

The quotient of 3 and a number translates to \(\frac{3}{n}\), then, all you have to do is subtract 10 from that value, giving the expression above.

Answer:

3 and 9

Step-by-step explanation:

x+y=12

y-x=6

y-x=6

 +x.  +x

y=6+x

x+(6+x)=12

6+2x=12

-6.    -6

2x=6

/2. /2

x=3

3+y=12

-3.  -3

y=9

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Answer:

x = 3

Step-by-step explanation:

2x+6=x+9 subtract x in both sides

x +6 =9 subtract 6 in both sides

x = 3

There are a fixed number of trials is not a condition for a geometric setting

In a geometric setting, we are dealing with a sequence of independent trials, where each trial can result in either a success or a failure.

The key concept in a geometric setting is the number of trials needed until the first success occurs.

The trials are independent  is essential in a geometric setting.

It means that the outcome of one trial does not affect the outcome of subsequent trials.

The probability of success is the same for each trial is also crucial in a geometric setting.

It implies that the probability of achieving a success does not change from trial to trial.

There are a fixed number of trials is not specific to a geometric setting.

The variable of interest is the number of trials required to reach the first success is fundamental to a geometric setting.

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Answer: 225

Step-by-step explanation:

Create a ratio part/whole for radians = part/whole for degrees

\(\frac{\frac{5\pi }{4} }{2\pi } = \frac{x}{360}\)      Keep change flip because you are dividing fractions for left side

\(\frac{5\pi }{4} (\frac{1}{2\pi }\)) = \(\frac{x}{360}\)

\(\frac{5}{8} (\frac{360}{1} ) =x\)

x = 225

Answer:

Multiply , add and then you get your solution.

Step-by-step explanation:

y=2(-3)+3

y= -6+3

y= -3

The number of square feet needed to cover the hole is 44ft²

To find this, we need to find the area of the green region and subtract the little square that it has inside.

Remember that for a rectangle, the area is the product between the dimensions, then the area of the green region is:

A = 12ft*4ft = 48ft²

The little square has an area:

a = 2ft*2ft = 4ft²

Then the area needed is:

area = 48ft² - 4ft² = 44ft²

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Answer:

33.33

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

2x+3x=100x

Combine like terms:

2x+3x=5x

5x=100

Divide by 5 on both sides:

5x/5=100/5x

x=20

Answer:

The circumference of the​ circle is \(C=56.55 \:m\).

Eugene confused the radius with the diameter to find the circumference of the circle.

Step-by-step explanation:

The circumference of a circle is the distance around the outside of the circle.

The circumference of a circle is found using this formula:

\(\begin{matrix} C=\pi \cdot d\\or\\ \, C=2\pi \cdot r \end{matrix}\)

From the information given the diameter of the circle is 18 m. Therefore, the circumference of the​ circle is

\(C=\pi \cdot d\\\\C=3.14 \cdot 18 \approx 56.55 \:m\)

Eugene used the wrong formula to find the circumference of a circle.

\(C=2\cdot(3.14)\cdot 18=113.04 \:m\)

He confused the radius with the diameter.

Answer:

Eugene used the wrong formula to find the circumference of a circle.

He confused the radius with the diameter.

Step-by-step explanation:

Answer:

8a   Yes

8b   f(5) = 1

8c   (0, -0.5)

Step-by-step explanation:

8a

Yes, since it passes the vertical line test.

8b

f(5) = 1

8c

(0, -0.5)

The term that can be added to the list so that the greatest common factor of the three terms  12h3 36h3, 12h6, is 48h5

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, 12, 20, and 24 all share two characteristics.

The term that  can fit in to the list so the GCF is 12h3 would be 48h5, this is so because 48 is first divisible by 12  without any  fraction, and we can remove upon dividing 3 h's from this term as it contains a total of 5 h's.

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The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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Answer:

Here's an interesting project idea for mathematics that can relate three different topics:

Topic 1: Fractals

Topic 2: Chaos Theory

Topic 3: Differential Equations

Research Question: Can fractals be used to model chaotic systems described by differential equations?

In this project, you can explore the concept of fractals and their applications in modeling complex systems. You can also delve into chaos theory and differential equations to understand how they are used to describe chaotic systems. By combining these three topics, you can investigate whether fractals can provide a better understanding of chaotic systems by modeling them more accurately.

Your research paper can cover the following areas:

Introduction: Provide an overview of fractals, chaos theory, and differential equations, and explain their relevance to the research question.

Fractals: Discuss the properties of fractals and how they can be used to model complex systems. Provide examples of fractals in nature and technology.

Chaos Theory: Explain the concept of chaos and how it is described by differential equations. Discuss the importance of chaos theory in understanding complex systems.

Differential Equations: Provide an overview of differential equations and their applications in physics, engineering, and other fields. Explain how differential equations are used to model chaotic systems.

Combining the three topics: Explain how fractals can be used to model chaotic systems described by differential equations. Provide examples of fractals used in modeling chaotic systems and compare the results to traditional methods.

Conclusion: Summarize the findings of your research and discuss the implications of using fractals to model chaotic systems.

Overall, this project can be a challenging and rewarding exploration of the interplay between three different mathematical topics.

Step-by-step explanation:

A)

We will solve using:

The number of ways to choose 4 girls from 12 girls and 0 boys from 10 boys is:

So, the probability() of choosing 4 just 4 girls is:

So, that is the probability to get just 4 girls on the committee.

B)

For the committee to be just 4 boys is found as follows:

And the number of ways to choose 4 boys from 10 boys and 0 girls from 12 girls is:

So, the probability to get just 4 boys on the committee is:

C)

For the committee to have at least one girl is:

No. of ways to selecting at least 1 girl:

22C4 - 10C4 = 7315 - 210 = 7105

Now, we calculate the probability:

The speed of current is \(\rm 2 \:km/h\).

The relationship between distance, time and speed can be presented as:

\(\begin{aligned} \rm Distance &= Speed \times Time\\\\Speed &= \dfrac{\rm Distance}{Time} \\\\\rm Time &= \dfrac{\rm Distance}{\rm Speed} \end\)

Calculations:

Given:

\(\begin{aligned} \rm Distance\: traveled\: on\: motorboat &= 25\:km\\\rm Speed\:of\:motorboat\:in\:still\:water &= 12\:km/h \end\)  

Let the speed of the current be \(\rm x\)

The speed of the boat traveling against the current is \({(12 -\rm x) km/h}\)

Time spent on motorboat is 10 hours less than time spent on raft.

Therefore:

\(\rm \dfrac{25km}{x\:km/h} - \dfrac{25km}{(12 - x)km/h} = 10\)

The equation obtained will be:

\(\dfrac{25}{\rm x} - \dfrac{25}{(12-\rm x)} - = 10\)

Multiplying both sides of the equation by \(\rm x(12 - x )\)

\(\begin{aligned} \rm 25(12 - x) - 25x &= 10\times \rm x(12 - x)\\\\300 - 25x - 25x &= 120x - 10x^2\\\\300 - 50x &= 120x - 10x^2\\\\10x^2 - 120x - 50x + 300 &= 0\\\\10x^2 - 170x +300 &= 0\end\)

Dividing the equation by 10

\(\rm x^2 - 17x + 30 = 0\)

On factoring the equation,

\(\rm =x^2 - 2x -15x + 30 = 0\\\\=x(x - 2) -15(x - 2)\\\\=(x - 2)(x - 15)\)

The values of x is 2 and 15.

Since speed of current i.e  \((12 -\rm x)km/h\) cannot be negative, \(\rm x = 2\) is the only acceptable value.

 Therefore the speed of current is 2 km/h.

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Answer:

-3

Step-by-step explanation:

7x+9=5x+3

2x+9=3

2x=-6

x=-3

Answer:

Step-by-step explanation:

7x +9 = 5x +3

combine like terms

7x - 5x = 3 - 9

2x = -6

x = -6/2

x = -3

proof:

7x +9 = 5x +3

7(-3) +9 = 5(-3) +3

-12 = -12  ---- ok

Answer:

\(22440=6200e^{0.06T}\)

\(\implies \dfrac{561}{155}=e^{0.06T}\)

\(\implies \ln\dfrac{561}{155}=\ln e^{0.06T}\)

\(\implies \ln\dfrac{561}{155}=0.06T\)

\(\implies T=\dfrac{50}{3}\ln\dfrac{561}{155}\)

\(\implies T=21.43826314...\)

\(22440=6200e^{0.1T}\)

\(\implies \dfrac{561}{155}=e^{0.1T}\)

\(\implies \ln\dfrac{561}{155}=\ln e^{0.1T}\)

\(\implies \ln\dfrac{561}{155}=0.1T\)

\(\implies T=10\ln\dfrac{561}{155}\)

\(\implies T=12.86295789...\)

Answer:

\(\huge\boxed{\sf 8/3\ pages}\)

Step-by-step explanation:

3 minutes = 8 pages

Dividing both sides by 3

1 minute = 8/3 pages

So, The color printer prints 8/3 pages or 2.67 pages per minute.

Hope this helped!

3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

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\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

____________________________________

\( \large \tt Solution \: : \)

\(\qquad \tt \rightarrow \: 6(3x - 7) = 2\)

Step 1 -

\(\qquad \tt \rightarrow \: 18x - 42 = 2\)

[ distributive property ]

Step 2 -

\(\qquad \tt \rightarrow \: 18x = 2 + 42\)

\(\qquad \tt \rightarrow \: 18x = 44\)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

d) Step 1: 18x - 42 = 2

Step 2: 18x = 44

Step-by-step explanation:

Given equation,

→ 6(3x - 7) = 2

Now the value of x will be,

→ 6(3x - 7) = 2

→ 6(3x) - 6(7) = 2

→ 18x - 42 = 2

→ 18x = 2 + 42

→ 18x = 44

→ x = 44/18

→ [ x = 22/9 ]

Hence, value of x is 22/9.

Answer:

Step-by-step explanation:

Hello!

The researcher developed a treatment to teach social skills to youth offenders. To test if the treatment is effective in increasing empathy compared to the standard treatment she randomly selected a group of 9 offenders and applied the new treatment and to another group of 9 randomly selected youth offenders, she applied the standard treatment. (Note: the data corresponds to two samples of 9 units each, so I've used those sizes to conduct the test)

At the end of the treatment, she administers BES to measure their empathy levels. Her claim is that the offenders that received the new treatment will have higher BES scores than those who received the standard treatment.

1) Using the records obtained for both groups, she  intends to conduct an independent t-test to analyze her claim.

X₁: BES results of a youth offender treated with the new treatment.

X₂: BES results of a youth offender treated with the standard treatment.

H₀: μ₁ = μ₂

H₁: μ₁ ≠ μ₂

α:0.05

test statistic

\(t_{H_0}= -0.32\)

p-value: 0.7517

The p-value is greater than the significance level so the decision is to not reject the null hypothesis. This means that at a 5% significance level you can conclude that there is no difference between the mean BES scores of the youth offenders treated with the new treatment and the mean BES score of  the youth offenders treated with the standard treatment. The new treatment doesn't increase the levels of social empathy of the youth offenders.

I hope this helps

(Box plot in attachment)

The solution for the linear system will be , x(t) = 4 c₁e^t +  4 c₂e^t and

y(t) = -c₂e^t + c₂(1 - t)e^t .

The solution is given by ,

matrix | x y | = c₁ .v . e^λt  + c₂( w + v.t ) e^λt

Given that the matrix has repeated eigenvalue with eigenvector  generalized  vectors ,

λ = 1 with eigenvector v = [ 4 , -1 ] and  generalized  vectors w =[ 0,1 ].

then the solution will be,

c₁ [ 4 , 1 ] e^t +  c₂[ 0 , 1] + [ 4 , -1 ] )e^t

therefore,

x(t) = 4 c₁e^t +  4 c₂e^t

y(t) = -c₂e^t + c₂(1 - t)e^t

Matrixes represent linear maps and allow for explicit linear algebra operations. As a result, matrices play an important role in linear algebra, and most characteristics and operations in abstract linear algebra may be represented in terms of matrices.

Matrix multiplication, for example, depicts the combination of linear maps.

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