The probability that both prizes were won by two people of the same sex is 0.48
Let's call the number of men in the small party "m" and the number of women in the small party "w". The total number of people in the party is "m + w = 10 + 12 = 22".
The number of ways to choose two people of the same sex can be calculated as follows:
The number of ways to choose two men is "C(m,2) = C(10,2) = 45".
The number of ways to choose two women is "C(w,2) = C(12,2) = 66".
The total number of ways to choose two people without replacement is "C(22,2) = 231".
The probability that both prizes were won by two people of the same sex is then given by the sum of the probabilities for two men or two women:
P(same sex) = (C(10,2) / C(22,2)) + (C(12,2) / C(22,2)) = (45/231) + (66/231) = 111/231 = approx. 0.48
So, the probability that both prizes were won by two people of the same sex is approximately 0.48
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The number 345,600 can be expressed as 2^a*3^b*5^b for integers a, b and c. What is the value of the product abc?
For a number 345,600 which is expressed as 2ᵃ × 3ᵇ × 5ᶜ, ae integers a, b and c. Then the value of the product abc is equals to the 54.
We have, a number 345,600, which can be expressed as 2ᵃ × 3ᵇ × 5ᶜ. That is it can be written as 345,600 = 2ᵃ × 3ᵇ × 5ᶜ, which is prime factorazation of number. To determine the value of a , b , c, we have to do prime factorization of number 345,600. Prime factorzation of a number contains all prime factors of a number. So,
345600 = 3456×100 = 576× 6 × 100
= 24² × 2×3 × 10² = ( 2×2×2×3)² × 2× 3×(2× 5)²
= 2⁶ × 3² × 2× 3×2²× 5²
345,600 = 2⁹ × 3³ × 5²
but 345,600 = 2ᵃ × 3ᵇ × 5ᶜ,
=> 2ᵃ × 3ᵇ × 5ᶜ = 2⁹ × 3³ × 5²
On comparing the powers of 2, 3, and 5 in above equation, we get a = 9 , b = 3 , c = 2.
Therefore, the value of product of a, b, and c
= abc = 9×3×2 = 54
Hence, the value of product is 54.
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Complete question:
The number 345,600 can be expressed as 2ᵃ × 3ᵇ × 5ᶜ for integers a, b and c. What is the value of the product abc?
4,400 is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 22 years to the nearest cent
After 22 years the amount in the account will be 12,386.
What is simple interest?Simple interest is an interest amount calculated on the principal amount with certain interest rate. It is given by the formula,
[tex]S.I.=\frac{P*n*r}{100}[/tex]
Where P is the principal amount, n is the number of years, r is the rate of interest.
4,400 is placed in an account i.e., Principal amount, P=4400
With an annual interest rate, r=8.25%
Number of years, n=22 years.
Amount in the account after 12 years will be,
By using simple interest formula,
[tex]S.I.=\frac{P*n*r}{100}[/tex]
= [tex]\frac{4400*8.25*22}{100}[/tex]
=7,986
Interest amount = 7,896.
Total amount after 22 years= interest amount + principal amount
= 7896+4400
= 12,386.
Hence, after 22 years the amount in the account will be 12,386.
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classify the following set of measurements as accurate, precise, both, or neither. checking for consistency in the weight of chocolate chip cookies: 17.27 g, 13.05 g, 19.46 g, 16.92 g
The dimensions listed above are thus neither exact nor precise.
In the given question the chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively and we have to classify the following set of measurements as accurate, precise, both, or neither.
It is the "value" that a buyer is prepared to pay for an object, particularly a used or second-hand car; typically, the "real worth" of any used car is a predetermined price tag after determining its value based on its condition and usage.
The chocolate chip cookies weigh 17.27 g, 13.05 g, 19.46 g, and 16.92 g, respectively. This demonstrates that the weight of chocolate chips is not comparable to their actual worth.
The dimensions listed above are thus neither exact nor precise.
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IV. Long Answer and Analysis (20 points) Do a simple Price Elasticity of Demand Calculation: ; A. If an original price was $5.00 and the amount bought (purchased) was an amount of 50 units (say of good like McDonalds Big Macs). What is the Revenue the producer receives at this point: $________ B. Now the price is lowered to $4.00 and now 200 Big Macs are purchased. What is the new revenue at this point: has it gone up or down?
C. using the formula for Price elasticity of Demand, calculate the actual fraction value of the change In price
If the quantity of big macs demanded falls from 2.0 million to 1.6 million as the price of whoppers falls from $1.40 to $.80, the cross-price elasticity of demand for big macs is 0.4.
What is cross-price elasticity?Cross-price elasticity quantifies how responsive a product's demand is to changes in a related product price. Some products on the market frequently have connections to one another.
This could imply that the demand for a product can be favourably or negatively impacted by a product's price change. The cross elasticity of demand, also known as the cross-price elasticity of demand, in economics quantifies the relationship between the percentage change in the quantity of a commodity sought and the percentage change in the price of another good, ceteris paribus. The cost of milk is one such example. People might switch to 2% milk if full milk prices rise. Similar to how whole milk gets more popular as 2% milk prices go up.
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Evaluate the following expression by drawing the unit circle and the appropriate right triangle. The angle is in radians.
cos(5π/3)
The answer for the angle cos (5π/3) is 1/2.
We know that in the polar coordinate system,
x = r cosθ ; y = r sinθ
Since, we are approximating using a unit circle, therefore, r = 1
As we can see in the graph of unit circle, we take the angle in radians anti-clockwise as 5π/3.
As we want the value of cos(5π/3), we look for the x coordinate.
We get this from the end point of the angle that we have drawn on the unit circle in anti-clockwise motion.
The x co-ordinate is 1/2, hence we get the value of cos(5π/3) as 1/2.
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If two medians of a triangle are congruent, then what is the triangle?
What are the coordinates of R' for the Dilation D(0,5 P) (PQRS)?
The coordinate of R' after dilation of (0.5, P) is at R(- 1.5, - 1.5).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, The coordinate point of R is (1, 1).
Now, After a dilation of 0.5 it would be (1×0.5, 1×05) ⇒ (0.5, 0.5).
Again a dilatation of P(- 3, - 3) would be, - 3[(0.5, 0.5)] ⇒ (- 1.5, - 1.5)
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(4a-5)-(-2a-3) find the difference
Answer: [tex]6a-2[/tex]
Step-by-step explanation:
[tex](4a-5)-(-2a-3)\\=4a-5+2a+3\\=6a-2[/tex]
The difference of (4a-5)-(-2a-3) is 64a^15 = 9a is different to 5
Apply the product rule to 4a^5:
⇒ 4^3(a^5)^3
Raise 4 to the power of 3:
⇒ 64(a^5)^3
Apply the power rule and multiply exponents, (a^m)^n = a^mn:
⇒ 64a^5*3
Multiply 5 by 3:
64a^15
⇒ (4a-5)⇒ = 9a⇒ (-2a-3)⇒ = 5Therefore, The difference of (4a-5)-(-2a-3) is 64a^15 = 9a is different to 5
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Please help me answer this math problem!
Answer:
P(t) = 30t + 4820
In 2009, the moose population will be 5,330 according to the model.
Step-by-step explanation:
4970 - 4820 = 150
150 / 5 = 30
P(t) = 30t + 4820
30 x 17 = 510
510 + 4820 = 5330
Your credit card has a balance of $4500 and an interest rate of 22%. The credit card requires a minimum payment of 3%.
What is your minimum payment?
What is your interest for 1 month?
What is your new balance?
Answer: Your welcome!
Step-by-step explanation:
Your minimum payment would be $135 ($4500 x 0.03 = $135).
Your interest for 1 month would be $99 ($4500 x 0.22 = $990 x 0.1 = $99).
Your new balance would be $4634 ($4500 + $99 - $135 = $4664).
g consider the following sets of vectors. show that each set (i) contains the zero vector, (ii) is closed under addition and scalar multiplication. then find a basis for each set and give the dimension.
(i) A basis for the set is {(2, 3, 4), (3, -2, 1)} and the dimension is 2.
(ii) A basis for the set is {(1, 1, 1, 1), (2, 0, 0, -1)} and the dimension is 2.
(i) {(2, 3, 4), (3, -2, 1)}
(i) The set contains the zero vector (0, 0, 0). It is closed under addition because for any two vectors in the set, the sum of the two vectors is also in the set. It is closed under scalar multiplication because for any vector in the set and any scalar, the scalar multiplied by the vector is also in the set.
A basis for the set is {(2, 3, 4), (3, -2, 1)} and the dimension is 2.
(ii) {(1, 1, 1, 1), (2, 0, 0, -1)}
(ii) The set contains the zero vector (0, 0, 0, 0). It is closed under addition because for any two vectors in the set, the sum of the two vectors is also in the set. It is closed under scalar multiplication because for any vector in the set and any scalar, the scalar multiplied by the vector is also in the set.
A basis for the set is {(1, 1, 1, 1), (2, 0, 0, -1)} and the dimension is 2.
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The complete question is:
Consider the following sets of vectors. show that each set (i) contains the zero vector, (ii) is closed under addition and scalar multiplication. then find a basis for each set and give the dimension.
(i) {(2, 3, 4), (3, -2, 1)}
(ii) {(1, 1, 1, 1), (2, 0, 0, -1)}
Referring to the figure, use the graph to estimate the
roots of the equation: y = x2 - 2x - 8
Answer:
The roots are -2 and 4
Step-by-step explanation:
Using the graph, we can estimate the roots of the equation by seeing where it crosses the x axis.
It appears to cross the x axis at -2 and 4.
The roots are -2 and 4
i need help with this problem lol
Answer:15
Step-by-step explanation:
We know this figure's all angles sum is equal to 180*(n-2)=180*3=540
so,
112+7x+5+6x+2+10x-8+4x+24=540
27x+135=540
27x=405
x=15
1. Cuando Raúl y Esperanza llegaron a una fiesta quedaban 3/10 del pastel, así que se dividieron esa porción en partes iguales. ¿Qué parte del pastel completo le tocó a cada uno?
Answer:
13
Step-by-step explanation:
first multiply then divide and subtract
Evaluate h - 3 for h = 1
The result of the function is h = 1 is equal to -2
Evaluating linear equationsLinear equations are equations that has a leading degree of 1.
Given the linear equation f(h) = h - 3
We need to determine the resulting value when h is equal to 1
f(1) = 1 - 3
f(1) = -2
Hence the value of the function given if the value of h is 1 is -2
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decide whether the function could be linear, exponential, or neither. linear exponential neither correct: your answer is correct. if the function could be linear or exponential, write a possible equation for the function. (if the function is neither, enter neither.) f(x)
Since the ratio of consecutive outputs is not constant, the function is not an exponential function. Hence the function is neither linear nor exponential.
To determine whether the given function is linear, exponential, or neither, first compute the average rate of change of with respect to and then compute the ratio of the consecutive outputs.
If the average rate of change is constant, then the function is linear.
If the ratio of consecutive outputs is constant, then the function is exponential.
x y Average rate of change ratio of consecutive outputs
-1 3 [tex]\frac{\delta y}{\delta x}=[/tex](6-3)/0-(-1)=3 6/3=2
0 6 (12-6)/(1-0)=6 12/6=2
1 12 (18-12)(2-1)=6 3/2
2 18 (30-18)/(3-2)=12 5/3
3 30 - -
Observe the above table, for the given function, the average rate of change from to is , and from to is .
Since the average rate of change is not constant, the function is not a linear function.
Observe the above table, for the given function, the ratio of consecutive outputs from -1 to 0 is 2 from 0 to 1 is 2, and from 2 to 1 is3/2
Since the ratio of consecutive outputs is not constant, the function is not an exponential function.
Hence the function is neither linear nor exponential.
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Let us now consider the Schrödinger Equation for an electron confined to a two dimensional box, 0
and 0
. That is to say, within this rectangle the electron wavefunction behaves as a free particle ( V(x,y)=0
), but the walls are impenetrable so the wavefunction ψ(x,y,t)=0
at the walls.
3.11.1.svg
Figure 1
: A particle in a a×b
2-dimensional box with infinite height can only be found within the box (highlighted). (CC BY-NC; Ümit Kaya)
Extending the (time-independent) Schrödinger equation for a one-dimensional system
−ℏ22md2ψ(x)d x2+V(x)ψ(x)=Eψ(x)(1)
to a two-dimensional system is not difficult
−ℏ22m(∂2ψ(x,y)∂x2+∂2ψ(x,y)∂y2)+V(x,y)ψ(x,y)=Eψ(x,y).(2)
Equation 2
can be simplified for the particle in a 2D box since we know that V(x,y)=0
within the box and V(x,y)=[infinity]
outside the box, ii.e.
V(x,y)=⎧⎩⎨0[infinity][infinity]0≤x≤aand0≤y≤bx<0andx>ay<0andy>b
So Equation 2
becomes
−ℏ22m(∂2ψ(x,y)∂x2+∂2ψ(x,y)∂y2)=Eψ(x,y).(3)
Since the Hamiltonian (i.e. left side of Equation 3
) is the sum of two terms with independent (separate) variables, we try a product wavefunction like in the Separation of Variables approach used to separate time-dependence from the spatial dependence previously. Within this approach we express the 2-D wavefunction as a product of two independent 1-D components
ψ(x,y)=X(x)Y(y).(4)
This ansatz separates Equation 3
into two independent one-dimensional Schrödinger equations
−ℏ22m(d2X(x)dx2)=εxX(x).(5)
−ℏ22m(d2Y(y)dy2)=εyY(y).(6)
where the total energy of the particle is the sum of the energies from each one-dimensional Schrödinger equation
E=εx+εy(7)
The differential equations in Equations 5
and 6
are familiar as they were found for the particle in a 1-D box previously. They have the general solution
X(x)=Axsin(kxx)+Bxcos(kxx)(8)
Y(y)=Aysin(kyy)+Bycos(kyy)(9)
For a particle in a 2D box with impenetrable walls, the time-independent Schrödinger equation can be simplified to equation 3, which is a separable differential equation.
Using the Separation of Variables approach, the 2D wavefunction can be expressed as the product of two independent 1D components, given by equation 4.
The resulting differential equations in equations 5 and 6 have the same form as those found for the particle in a 1D box and their solutions are given by equations 8 and 9. The total energy of the particle is given by equation 7.
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Find the average number from the following numbers. 13, 33, 2, 10, 3.
Answer: 12.2
Step-by-step explanation:=
61/5=12.2
In a study of television viewing habits, it is desired to estimate the average number of hours teenagers spend watching per week. If it is reasonable to assume σ = 3.2 hours, how large a sample is needed so that it will be possible to assert with 95 percent confidence that the sam mean is off by at most 20 minutes?
We need a sample size of at least 397 in order to be 95% confident that the sample mean is within 20 minutes of the true mean.
To calculate the sample size needed, we need to use the formula:
n = (zα/2σ/E)2
where zα/2 is the critical value associated with the desired confidence level (in this case 95%), σ is the standard deviation (3.2 hours in this case), and E is the margin of error (20 minutes in this case).
Thus, n = (1.96*3.2/20)2, which simplifies to 397.
E = 20
σ = 3.2
n = (1.96*3.2/20)2
Therefore, we need a sample size of at least 397 in order to be 95% confident that the sample mean is within 20 minutes of the true mean.
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22\5= how many /10?
44
22
11
Or
10
Answer:
the correct answer is 44
Step-by-step explanation:
22/5 = 4.4
44/ 10 = 4.4
A car drove at 65 miles per
hour for 7 hours. How
many miles are left if the
entire trip is 540 miles?
Answer: 85 miles left
Step-by-step explanation:
65 miles x 7 hours = 455 miles
540 miles - 455 miles = 85 miles
assume that water is poured into a spherical bottle at a constant rate. which of the following graphs best represents the height of water in the bottle as a function of the amount of water in the bottle?
A graph that shows a slow and steady increase at first, followed by a steeper increase as the bottle approaches full capacity, would be the most accurate representation. Without seeing the available graphs, it's difficult to say which one is the best representation.
The best graph to represent the height of water in a spherical bottle as a function of the amount of water in the bottle is a non-linear graph that has a curved shape.
As the volume of water in the bottle increases, the height of the water will also increase, but not at a constant rate. The curve will become steeper as the bottle fills up, because the same amount of water will fill less and less of the remaining space in the bottle. Therefore, a graph that shows a slow and steady increase at first, followed by a steeper increase as the bottle approaches full capacity, would be the most accurate representation.
The height of water in a spherical bottle as a function of the amount of water in the bottle would be represented by a non-linear graph that has a curved shape. As the volume of water in the bottle increases, the height of the water will also increase, but not at a constant rate. The curve will become steeper as the bottle fills up, because the same amount of water will fill less and less of the remaining space in the bottle.
The most correct illustration would be a graph showing a gradual increase at initially, followed by a sharper increase as the bottle nears capacity. It's challenging to determine which graph is the best depiction without seeing the available graphs.
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find an equation of the line with the given slope and containing the given point. write the equation using function notation. slope -7 through (-5,9)
The equation of line with slope as "-7" and passes through point (5,9) in function notation is f(x) = -7x - 26 .
We know that the equation of the line with slope "m = -7" passing through the point (-5, 9) can be found using the point-slope form of the equation of a line : which is ⇒ y - y₁ = m(x - x₁)
where (x₁, y₁) = (-5, 9) is the point and m = -7 is the slope.
On Substituting the values of point and slope , in the equation ,
⇒ y - 9 = -7(x - (-5)) ;
Simplifying the expression further ;
⇒ y - 9 = -7(x + 5) ;
⇒ y - 9 = -7x - 35 ;
Adding 9 to both sides,
⇒ y = -7x - 26
In function notation is f(x) = -7x - 26 .
Therefore, the required equation of the line is f(x) = -7x - 26 .
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Question 5 (1 point)
When budgeting for savings, you should wait until you pay all your bills and
discretionary expenses and then see if you have money left.
True
False
The adage "You should wait until after paying all of your bills and discretionary expenses before budgeting for savings" is accurate.
How do you determine discretionary spending?Consider your disposable income, or the amount of money that remains in your paycheck after taxes. Your discretionary income is the amount that remains after deducting all of your expenses, such as rent or mortgage payments, student loans, utilities, and food. Spending that are not necessary to run a household are categorized as discretionary expenses, including travel and luxury purchases. In other words, the income-earner has the option of paying for these items or services.Think about whether it's a want or a need before deciding whether it's a discretionary spend. Food is necessary, but it doesn't have to come from a restaurant.To learn more about discretionary expense, refer to:
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the charged balloon in (figure 1) expands as it is blown up, increasing in size from the initial to final diameters shown.
The size of a balloon increases as it is blown up because of the pressure of the air inside the balloon is greater than the atmospheric pressure outside.
The change in size of the balloon is determined by the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature and inversely proportional to its volume (PV = nRT). Therefore, when air is added to the balloon and the pressure inside the balloon increases, its volume decreases. We can calculate the final diameter of the balloon, given the initial diameter and the change in pressure. For example, if the initial diameter of the balloon is 10 cm and the change in pressure is 0.5 atmospheres, then the final diameter of the balloon is[tex](10 cm) x [(1 + 0.5)⁰’⁵] = 10.63 cm.[/tex]
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according to a recent pew research center survey, 23% of us adults say they have not read a book in any format in the past 12 months. assume the stated rate of 23% is indeed the correct population proportion value.
This means that out of every 100 US adults, 23 of them have not read a book in the past year. This rate is quite high, considering the vast number of books available to read.
To calculate the number of US adults who have not read a book in the past year, we can use the following equation:
Number of US Adults Who Have Not Read a Book in the Past Year = Total Number of US Adults x Proportion of US Adults Who Have Not Read a Book in the Past Year
First, determine the total number of US adults. For example, let's say that there are 80 million US adults.
Next, multiply the total number of US adults by the proportion of US adults who have not read a book in the past year (0.23). Therefore, 80 million x 0.23 = 18.4 million US adults who have not read a book in the past year.
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Help pls!! I’ll give points and brainliest!!!
An train station has determined that the relationship between the number of passengers on a train and the total weight of luggage stored in the
baggage compartment can be estimated by the least squares regression equation y = 200+ 23x. Predict the weight of luggage for a flight with
57 passengers.
Answer: pounds
The residual sum of squared values is reduced using the least-squares method. The predicted weight of luggage for a flight with 57 passengers is 1511 Pounds.
What is meant by least-squares method?
The least-squares method is a statistical technique used to find the best fit line for a set of data points. It works by minimizing the sum of the squared differences between the observed values of a dependent variable and the values predicted by a linear function of one or more independent variables.
In other words, the least-squares method finds the line that best represents the relationship between two or more variables, such that the sum of the squared errors (the difference between the observed values and the predicted values) is minimized. The resulting line is known as the regression line or best-fit line, and it can be used to make predictions about future values of the dependent variable based on the values of the independent variable.
Based on the given least squares regression equation, we have:
y: the total weight of luggage stored in the baggage compartmentx: the number of passengers on the train200: the intercept term of the regression equation23: the slope of the regression equationTo predict the weight of luggage for a flight with 57 passengers, we simply substitute x = 57 into the regression equation:
y = 200 + 23x
= 200 + 23(57)
= 200 + 1311
= 1511
Therefore, the predicted weight of luggage for a flight with 57 passengers is 1511 pound.
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10. Usando el metodo de la iteracion del punto fijo
¿Para que raiz el porcentaje de error es del
16.1%?
*
(4 puntos)
f (x) = x − (√5x – e^x)comenzando en xo = 0.5
O 1.7278
O 1.7351
O 1.4482
O 0.9226
Answer: Your welcome!
Step-by-step explanation:
O 1.7278
El porcentaje de error del 16.1% se refiere a la raíz de la ecuación f(x) = x - (√5x - e^x), comenzando en xo = 0.5. Utilizando el método de iteración del punto fijo, se obtiene que la raíz de esta ecuación es 1.7278.
Answer:
Step-by-step explanation:
Para encontrar la raíz de la ecuación f(x) = x - (√(5x) - e^x) con un porcentaje de error del 16.1%, podemos utilizar el método de iteración de punto fijo con la siguiente fórmula:
x1 = f(x0) + x0
Donde x0 es el valor inicial, f(x) es la función y x1 es el siguiente valor de la raíz aproximada.
Primero, evaluamos la función en x0 = 0.5:
f(0.5) = 0.5 - (√(5*0.5) - e^0.5) = -0.2749
Luego, usamos la fórmula para encontrar el siguiente valor:
x1 = f(0.5) + 0.5 = 0.2251
Continuamos iterando hasta que el porcentaje de error sea menor o igual al 16.1%. Podemos calcular el porcentaje de error relativo por iteración con la siguiente fórmula:
Error relativo (%) = |(x_nuevo - x_viejo) / x_nuevo| * 100%
donde x_nuevo es el valor actual de la raíz aproximada y x_viejo es el valor anterior de la raíz aproximada.
Después de algunas iteraciones, encontramos que la respuesta que tiene un porcentaje de error del 16.1% es 1.7351.
The qualitative characteristic that means there is agreement between a measure and a real-world phenomenon is:
A) Verifiability.
B) Representational faithfulness.
C) Neutrality.
D) Materiality.
Verifiability is the ability to demonstrate that a measure is in agreement with a real-world phenomenon. It is an important qualitative characteristic of financial reporting.
Verifiability is a qualitative characteristic of financial reporting that refers to the ability to demonstrate that a measure is in agreement with a real-world phenomenon. This means that the financial information presented is accurate and reliable, and that it faithfully reflects the underlying transactions or events that it is supposed to represent. Verifiability is important because it ensures that users of financial statements, such as investors and creditors, are able to make informed and accurate decisions based on the information contained in the statements. This is achieved through the use of external auditors to objectively verify the integrity of financial statements and disclosures. If a measure is not verifiable, it is not considered to be a reliable source of information and should not be used for decision-making. Verifiability is essential for reliable financial reporting.
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