MLE (20 points) The probability density function of the Pareto distribution is given by f(x;α,β)=αxα+1βα​, with x≥β and α,β>0.

The finance charge on the average daily balance for this credit card over the 1-month period is approximately $84.31.

To calculate the finance charge on the average daily balance for this credit card over a 1-month period, let's break down the information provided.

The balance for the first 3 days is given as $150 (initial balance) minus a $50 purchase, which equals $100.

Next, we need to calculate the balance for the remaining days:

Days 4-20: The balance remains constant at $200 for 17 days, so the total balance for these days is 17 \(\times\) $200 = $3,400.

Days 21-30: The balance is $50 due to a $150 payment made.

To calculate the finance charge on the average daily balance, we need to determine the total balance for the entire 30-day period.

Summing up the balances for each period:

Balance for the first 3 days: $100

Balance for days 4-20: $3,400

Balance for days 21-30: $50

Total balance for the 30-day period: $100 + $3,400 + $50 = $3,550

Now, to calculate the finance charge, we multiply the total balance by the monthly interest rate.

The monthly interest rate can be found by dividing the annual percentage rate (APR) by 12.

Monthly interest rate = 28.5% / 12 = 0.02375

Finance charge = Total balance \(\times\) Monthly interest rate = $3,550 \(\times\)0.02375 ≈ $84.3125

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Based on the given informations, the change in y as t changes from 1 to 6 is approximately 3.870. Therefore the correct option is (A).

To find the change in y as t changes from 1 to 6, we need to integrate the given function with respect to t over the interval [1, 6] and then find the difference between the values of the integral at the two endpoints.

∫₁⁶ 6e\(.^{(-0.08(t-5)^2)}\)  dt

We can use the substitution u = t - 5 to simplify the integral:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\)  du

Unfortunately, there is no closed-form solution for this integral. We can use numerical integration methods, such as Simpson's rule or the trapezoidal rule, to approximate the integral. Using Simpson's rule with a step size of 1, we get:

∫₋₄¹ 6e\(.^{(-0.08u^2)}\) du ≈ 3.870

Therefore, the change in y as t changes from 1 to 6 is approximately 3.870, which corresponds to option (A).

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Answer:

50.2 is the answer as the answer came in point

The remaining side is 16.9 and remaining angles are 83.1 and 34.9.

The cosine formula to find the side of the triangle is given by:

c = √[a² + b² – 2ab cos C] Where a,b and c are the sides of the triangle.

Given:

m∠B = 62°, a = 11, and c = 19

Now, b² = a² + c² - 2ac cos B.

b = √ a² + c² - 2ac cos B

b = √ 11² + 19² - 2x 11  x 19 cos 62

b= 16.9

Now. a/ sin A = b/ sin B= c/ sin C

So, <C = arc sin ( c sin B /b)

<C = arc sin ( 19 sin 62 /16.9)

<C = 83.1

and, <A = arc sin ( a sin B /b)

<A = arc sin ( 11 sin 62 /16.9)

<A = 34.9

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Answer:

y=-5/2x-9

Step-by-step explanation:

I hope this helps

Answer:

A person with $-40 is in more debt

Step-by-step explanation:

The person with $-40 has borrowed or spent money from their credit card more than the person who is in debt for $-30.

Answer:$-40

Step-by-step explanation:

A person with negative 40 dollars has 40 dollars missing, a person with -30 dollars only has 30 dollars missing. So the person with -$40 is missing more money and therefore, is in more debt.

Answer: 10

Step-by-step explanation:

| –10 | = 10

Because that's the number of spaces it's from 0. :-)

the answer is D

Hopefully this helps you!

Answer:

5/4

Step-by-step explanation:

The formula for slope is [ y2-y1/x2-x1 ]. Use the given values to solve.

-6-9/-8-4

-15/-12

5/4

Best of Luck!

Answer:

5 / 4

Step-by-step explanation:

Part A: The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: The point (8, 2) is not included in the solution area.

Part C: The point (3, 1) represents one feasible solution that meets the constraints of the problem.

Part A: The graph of the system of inequalities consists of two lines and a shaded region. The line x + 3y = 8 is a solid line because it includes the equality symbol, indicating that points on the line are included in the solution set. The line x + y = 2 is also a solid line. The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: To determine if the point (8, 2) is included in the solution area, we substitute the x and y values into the inequalities:

8 + 3(2) ≤ 8

8 + 6 ≤ 8

14 ≤ 8 (False)

Since the inequality is not satisfied, the point (8, 2) is not included in the solution area.

Part C: Let's choose a point in the solution set, such as (3, 1). This point satisfies both inequalities: x + 3y ≤ 8 and x + y ≥ 2. In the context of the real-world scenario, this means that Michelle can buy 3 servings of dry food (x = 3) and 1 serving of wet food (y = 1) with her $8 budget. This combination of dog food allows her to feed at least two dogs at the animal shelter while staying within her budget. The point (3, 1) represents one feasible solution that meets the constraints of the problem.

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The perimeter of one face of the cube is given by the option (A) a/4.


The surface area of a cube is given by the formula 6a^2, where a is the length of one side of the cube. In the given expression 6(a/4)^2, we can simplify it as follows:
6(a/4)^2 = 6(a^2/16) = (6/16) * a^2 = 3/8 * a^2

We know that the perimeter of a square is equal to 4 times the length of one side. In this case, we have a cube, and each face of the cube is a square. Therefore, the perimeter of one face of the cube is 4 times the length of one side.

Hence, the correct option is (A) a/4, as it represents the perimeter of one face of the cube.

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Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.

In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.

For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:

Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

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Franklin wrote his autobiography for a number of reasons: to "remember" and relive his life, perhaps more perfectly, as he said at the beginning; to provide some genealogical anecdotes to his son; to bow before his friends To their flattery, he owes society an account of his life.

Benjamin Franklin was an American polymath author, scientist, inventor, statesman, diplomat, printer, publisher, forger, and political philosopher. Among the leading intellectuals of the time, Franklin was one of the founding fathers of the United States, the drafter and signer of the American Declaration of Independence, and the first postmaster of the United States.

As a scientist, he was an important figure in American Enlightenment history and physics as he studied electricity and mapped and named the Gulf Stream. As an inventor, he is known for the lightning bolt, bifocal glasses, and the Franklin stove, among others. He founded many civic organizations, including the Library Company, Philadelphia's First Fire Department, and the University of Pennsylvania. Franklin earned the title of "First American" for his early and tireless efforts to unify the colonies and for his work in London as a writer and spokesperson for several colonies. As the first United States Ambassador to France, he exemplified America's rise to power.

Franklin defined the American spirit as the combination of practical values ​​of economy, industry, education, community spirit, self-government, and opposition to political and religious authoritarianism with the values ​​of science and tolerance. clarification. In the words of historian Henry Steele Commager, "In Franklin it was possible to combine the virtues of faultless Puritanism, the lightness of Enlightenment without enthusiasm." Franklin has been called "the most able and influential American inventor in this type of society". America will become.

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Using trigonometric identity, cos(A-B) is:

\(cos (A-B) = \frac{2\sqrt{8}\ + \sqrt{5}}{9}\)

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

If sin A = 1/3 and A terminates in Quadrant 1. All trigonometric functions in Quadrant 1  are positive

sin A = 1/3 (sine = opposite/hypotenuse)

adjacent = √(3² - 1²)

               = √8 units

cosine = adjacent/hypotenuse. Thus,

\(cos A = \frac{\sqrt{8} }{3}\)

If cos B = 2/3 and B terminates in Quadrant 4.

opposite = √(3² - 2²)

                = √5

In  Quadrant 4, sine is negative. Thus:

\(sin B = \frac{\sqrt{5} }{3}\)

We have:

cos(A-B) = cosA CosB + sinA sinB

\(cos (A-B) = \frac{\sqrt{8} }{3} * \frac{2}{3} + \left \frac{1}{3} * \frac{\sqrt{5} }{3}\)

\(cos (A-B) = \frac{2\sqrt{8} }{9} + \left\frac{\sqrt{5} }{9}\)

\(cos (A-B) = \frac{2\sqrt{8}\ + \sqrt{5}}{9}\)

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Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is  1 - 1/k².

In statistics, Standard deviation is a measure of the variation of a set of values.

σ = standard deviation of population

N = number of observation of population

X = mean

μ = population mean

We know that Chebyshev's theorem states that for a large class of distributions, no more than 1/k² of the distribution will be k standard deviations away from the mean.

This means that 1 - 1/k² of the distribution will be within k standard deviations from the mean.

Lets k = 1.8, the amount of the distribution that is within 1.8 standard deviations from the mean is;

1 - 1/1.8² = 0.6914

= 69.14%

Hence, Chebyshev's theorem says that for any set of observations, the proportion of values that lie within k standard deviations of the mean is  1 - 1/k².

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A sample statistic handles the parameter it is intended to estimate so when target population and indeed the sampled population are equal.

Data gathering, organization, analysis, interpretation, as well as presentation are all topics covered in the field of statistics. It is customary to start with a statistical population or perhaps a statistical model to be investigated when using statistics to solve a scientific, industrial, or social problem.

To sum up, the five reasons to studying statistics are to be able to do research efficiently, to read and assess journal articles, to even further develop critical thinking and analytical skills, to behave as an informed consumer, and to be aware of when you need to seek outside statistical support.

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Answer:

a. -24w^6/y^7z^3

Step-by-step explanation:

i hope this helps :)

Answer:

A = 600 ft²

Step-by-step explanation:

Area of a triangle = (1/2) · b · h

↓ plugging in the given values (noting that the base is actually at the top of the triangle)

A = (1/2) · 40 · 30

↓ multiplying

A = 20 · 30

A = 600 ft²

Step-by-step explanation:

See image:

( the picture is cut off , so I cannot tell the units....If each square is 10 feet then it would be

 600 ft^2)

Answer:

Roger

Step-by-step explanation:

Since he is attending more shows, he will benefit. He will save a net amount of $40

Answer:

roger

Step-by-step explanation:

1.

Assume that the first prism have dimension l, w and h. Therefore its volume is:

Now, the second prism after applying the scale factor has dimensions 59.5l, 59.5w and 59.5h, hence its volume will be:

Therefore, the scale factor for the volume is 210,644.9.

2.

The are of the base of a rectangular prism is given by:

hence, in this case we have:

Therefore the area of the base is 50 squared units.

Answer:

The answer should be 12.5%

The equation will be 4x = 3 and the fraction of the butter stick that each friend will use is x = 3/4.

So, the equation will be:

Then, the equation is:

3 sticks equally shared by 4 friends:

Therefore, the equation will be 4x = 3 and the fraction of the butter stick that each friend will use is x = 3/4.

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 By multiplying matrices B and A, we obtain the product BA. Using BA, we can solve the system of equations y + 2z = 7, x - y = 3, and 2x + 3y + 4z = 17.the values of x, y, and z are -1, 2, and 1 respectively

To find the product BA, we multiply matrix B with matrix A. The resulting matrix will have the same number of rows as B and the same number of columns as A. The product BA will be used to solve the given system of equations.
The product BA can be computed by multiplying each row of matrix B by each column of matrix A and summing the results. The resulting matrix will be:
Now, we can use the product BA to solve the system of equations:
-10x - 10y + 6z = 7,
3x - 8y + 2z = 3,
-6x - 16y + 15z = 17.

1 -1 2
2 3 1
0 4 2
We can rewrite this system of equations as:
-10x - 10y + 6z = 7,
3x - 8y + 2z = 3,
-6x - 16y + 15z = 17.
By comparing the coefficients of x, y, and z in the system of equations with the entries in the matrix BA, we can determine the values of x, y, and z.
Solving the system of equations using matrix BA, we get:
x = -1,
y = 2,
z = 1.
Therefore, the values of x, y, and z are -1, 2, and 1 respectively.

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The complete question is:
Given A=
⎣2 2 -4|
|-4 2 -4|
|2 -1 5|
, B=
⎣1 -1 0|
⎢2 3 4|
⎢0 1 2|
, find BA and use this to solve the system of equations y+2z=7, x−y=3, 2x+3y+4z=17.

Answer:

N = 34

Step-by-step explanation:

METHOD I

(hit and trial)

The given two ratios have to be equal.

This means, 24 : N must break down to 12 : 17 after dividing it by some common factor.

The common factor here is 2.

Since,

12 × 2 = 24

17 × 2 = 34

\( \boxed{\mathsf{ \underline{N \: must \: be \: 34}}}\)

(after dividing the first ratio by 2(common factor) we get the second ratio. Meaning that they become equivalent as required by the question).

METHOD II

(mathematical approach)

Ratios can be written in form of fractions as:

\( \boxed{ \mathsf{ \frac{24}{N} = \frac{12}{17} }}\)

Cross multiplying:

\( \implies \mathsf{24 \times 17 = 12 \times N }\)

taking 12 to the denominator:

\( \implies \mathsf{ \frac{24 \times 17 }{12} = N }\)

24 and 12 gets canceled and 2 takes up their spot

(why?

=> 24 ÷ 12 = 2)

\( \implies \mathsf{2 \times 17 = N } \)

\( \implies \mathsf{2 \times 17 = N } \)

\( \implies \mathsf{ N = 34 } \)

\( \implies \mathsf{ N = 34} \)

The calculation that is not a way to find a fraction of 5/8 is:

1 - 0.125.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

The terms are classified as follows:

Hence the numeric value of the fraction 5/8 presented in this problem is given as follows:

5/8 = 0.625.

The calculation that is not a way to find the fraction of 5/8 is the only expression that has a different value than 5/8.

The expression with a different value is of:

1 - 0.125 = 0.875.

As the value of 0.875 is different than the value of 0.625 equivalent to the fraction of 5/8.

The complete problem is given by the image at the end of the answer.

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Chemical equations must be balanced to satisfy the law of conservation of mass. Coefficients can be adjusted to balance the number of atoms, but changing subscripts would alter the compound's identity.

To balance the equation CH4 + O2 → CO2 + H2O, we need to ensure that the number of atoms of each element is the same on both sides of the equation.

Balancing chemical equations is necessary because they represent the law of conservation of mass. According to this law, matter is neither created nor destroyed in a chemical reaction. Therefore, the total number of atoms of each element must be the same on both sides of the equation to maintain this fundamental principle.

Coefficients are used in chemical equations to balance the equation by adjusting the number of molecules or atoms of each substance involved. Coefficients are written in front of the chemical formula and represent the number of moles or molecules of that substance. By changing the coefficients, we can adjust the ratio of reactants and products to ensure that the number of atoms of each element is balanced.

On the other hand, subscripts within a chemical formula cannot be changed when balancing an equation. Subscripts represent the number of atoms of each element within a molecule and are specific to that compound. Changing the subscripts would alter the chemical formula itself, resulting in a different substance with different properties. Therefore, we must work with the existing subscripts and only adjust the coefficients to balance the equation.

In summary, balancing chemical equations ensures that the law of conservation of mass is upheld, and the same number of atoms of each element is present on both sides of the equation. Coefficients are used to adjust the number of molecules or moles, while subscripts within the chemical formula remain fixed as they represent the unique composition of each compound.

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The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.

The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.

However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.

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Answer:

a = 93°, b = 120°, c = 150°

Step-by-step explanation:

b + 36 = 78 × 2 => b + 36 = 156 => b = 120°

87 × 2 - b = the minor arc between a and 78

=> 174 - 120 = 54

54 + b + 36 + c = 360

=> 54 + 120 + 36 + c = 360

=> c = 150°

(c + 36) ÷ 2 = a

=> (150 + 36) ÷ 2 = a

=> a = 93°