(q14) Ron is studying the income of people in a particular state. He finds out that the Lorenz curve for that state can be given as
. Find the gini coefficient.
Answers
Given that the Lorenz curve for a particular state is `y = 0.0003x^3 - 0.0126x^2 + 0.8357x`. The Lorenz curve represents the cumulative income distribution in the economy, while the line of perfect equality is a straight line y=x representing the income distribution if income were distributed equally.
The Gini coefficient (G) is half the relative mean absolute difference, and it can be calculated from the Lorenz curve. Thus, the formula for the Gini coefficient is `G = A / (A + B)`Where A represents the area between the line of equality and the Lorenz curve, and B represents the area below the Lorenz curve.
The Gini coefficient can be found as follows:To find A, subtract the area under the Lorenz curve from the area under the line of perfect equality within the limits of 0 and 1.
We know that the line of perfect equality is y=x.Area under Lorenz curve from 0 to 1 = ∫[0,1] (0.0003x^3 - 0.0126x^2 + 0.8357x) dx= [0.000075x^4 - 0.0042x^3 + 0.41785x^2] from 0 to 1= (0.000075(1)^4 - 0.0042(1)^3 + 0.41785(1)^2) - (0.000075(0)^4 - 0.0042(0)^3 + 0.41785(0)^2)= 0.40865Area under line of perfect equality from 0 to 1 = (1/2)(1)(1)= 0.5Therefore, A = 0.5 - 0.40865= 0.09135To find B, find the area under the Lorenz curve from 0 to 1.
Area under Lorenz curve from 0 to 1 = ∫[0,1] (0.0003x^3 - 0.0126x^2 + 0.8357x) dx= [0.000075x^4 - 0.0042x^3 + 0.41785x^2] from 0 to 1= 0.3255Therefore, the Gini coefficient, G= A / (A + B)= 0.09135 / (0.09135 + 0.3255)= 0.219Answer: 0.219
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Related Questions
What must the values of x and y be so that the two houses are similar?
Answers
Answer:
x=12 and y=6
Step-by-step explanation:
because the angle are same and equal
The value of x is 12 and y is 6.
what is similarity?Similar figures mean when two figures are of the same shape but are of different sizes. In other words, two figures are called similar when they both have a lot of the same properties but still may not be identical. For example, the sun and moon might appear the same size but they are actually different in size. However, we are similar figures since both the figures are circular in nature.
Two triangles will be similar if the angles are equal (corresponding angles) and sides are in the same ratio or proportion(corresponding sides). Similar triangles may have different individual lengths of the sides of triangles but their angles must be equal and their corresponding ratio of the length of the sides or scale factor must be the same. If two triangles are similar that means,
All corresponding angle pairs of triangles are equal.All corresponding sides of triangles are proportional.As per the situation we have given that
The similarity in figures show that the angles are equal.
Also, the corresponding sides are also equal.
Hence, the value of x is 12 and y is 6.
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help me !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
C
Step-by-step explanation:
Plug in the points to see which equation is true
Please answer correctly! I will mark you Brainliest!
Answers
Answer:
158.35
Step-by-step explanation:
Determine which of the following functions are differentiable at all the z-plane or some region of it and evaluate the derivatives if they exist. (a) f(3) = x2 + y2 + i2.cy.
Answers
The functions are differentiable at all the z-plane is f'(z) = 2x when function is f(z) = x² + y² + i2xy.
Given that,
The function is f(z) = x² + y² + i2xy
We have to determine if the functions are differentiable throughout the z-plane or only a portion of it, and then we must assess any derivatives that may exist.
We know that,
Take the function,
f(z) = x² + y² + i2xy
f(x + iy) = x² + y² + i2xy
f(x + iy) = u + iv
We can say, u =x² + y², v= 2xy
Differentiate u with respect to x
uₓ = 2x
Differentiate v with respect to y
[tex]v_y[/tex] = 2x
So,
uₓ = 2x = [tex]v_y[/tex]
uₓ = [tex]v_y[/tex]
Differentiate u with respect to y
[tex]u_y[/tex] = 2y
Differentiate v with respect to x
[tex]v_x[/tex] = 2y
So,
[tex]u_y[/tex] = -[tex]v_x[/tex] = -2y ⇒ y = 0
Let D = {z : x | x, y∈R}
f is differentiable on D.
The derivative is f'(z) = [tex]u_x + iv_x[/tex] = 2x
Therefore, the functions are differentiable at all the z-plane is f'(z) = 2x.
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Thank you :)
The question is above!
;)
Answers
Answer:
umm 9/2
Step-by-step explanation:
During a professional baseball game, every
spectator placed his or her ticket stub into one of
several containers. After the game, the coach
chose twenty people to march in the victory
parade. What is the sample in this situation?
Answers
Answer:
20 people chosen to March
Step-by-step explanation:
The sample can be explained as a random subset of the population. It is a given number of draws or selection made usually at Random from the entire or larger population set. The sample is usually smaller Than the population and if done randomly will be representative of the population set. The entire spectator attending the baseball game is the population of interest while the 20 selected from the entire pool to March in the victory parade is the sample data obtained from the population set.
to Find the analyticity region of the function and find it's derivate of the following functions (a) √Z²-2 (b) Sen (log z²) 20 Find the Taylor serie around zero for fuz) = 4+2² and compute the Convergence radius
Answers
(a) To find the analyticity region of the function f(z) = √(z² - 2), we need to determine where the function is well-defined. The square root function is defined for non-negative real numbers. In this case, the expression inside the square root, z² - 2, should be greater than or equal to zero.
z² - 2 ≥ 0
Solving the inequality:
z² ≥ 2
Taking the square root of both sides, while considering both the positive and negative roots:
z ≥ √2 or z ≤ -√2
Therefore, the analyticity region of the function f(z) = √(z² - 2) is all values of z greater than or equal to √2 or less than or equal to -√2.
(b) To find the derivative of the function f(z) = Sen(log z²), we can use the chain rule.
Let's break it down:
f(z) = Sen(log z²)
First, find the derivative of the inner function log z²:
d/dz (log z²) = 1 / (z²) * 2z = 2 / z
Now, find the derivative of Sen(u), where u = log z²:
d/dz (Sen(u)) = cos(u) * du/dz
Substituting the value of u:
d/dz (Sen(log z²)) = cos(log z²) * (2 / z)
Therefore, the derivative of the function f(z) = Sen(log z²) is cos(log z²) * (2 / z).
(c) To find the Taylor series around zero for the function f(z) = 4 + 2z², we need to find the derivatives of the function at zero and use them to construct the series.
Let's find the derivatives:
f(z) = 4 + 2z²
f'(z) = 0 + 4z = 4z
f''(z) = 0 + 4 = 4
f'''(z) = 0
All higher-order derivatives will also be zero.
Now, let's construct the Taylor series around zero using these derivatives:
f(z) = f(0) + f'(0)z + (f''(0)/2!)z² + (f'''(0)/3!)z³ + ...
Since the higher-order derivatives are zero, the series simplifies to:
f(z) = 4 + 0z + (4/2!)z² + 0z³ + ...
Simplifying further:
f(z) = 4 + 2z²
The Taylor series around zero for the function f(z) = 4 + 2z² is simply the original function itself.
To compute the convergence radius of the series, we can observe that the function f(z) = 4 + 2z² is a polynomial, and all polynomials have an infinite convergence radius. Therefore, the convergence radius for this series is infinite.
In conclusion, to Find the analyticity region of the function and find it's derivate of the following functions the Taylor series around zero for the function f(z) = 4 + 2z² is 4 + 2z², and its convergence radius is infinite.
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um just testing 157x124
Answers
Answer:
Step-by-step explanation:
urgente porfa 50 PUNTOS POR LAS 3 FICHAS
Answers
You dont deserve answers if ur gonna do that to other people.
In a study of cell phone usage and bruin hemispheric dominanon, an Internet survey was e-mailed to 6960 subjects randomly selected from an online group involved with cars. There were 1305 surveys murad. U 0.01 significance level to test the claim that the return rate is less than 20%. Use the Pusle method and use the romal distribution as an approximation to the binomial atribution Setely the nel ypothesis wd attive hypothesis ОА 02 Hp02 OCH D03 Hp02 OLM OB 02 Hp02 OD. Hp.02 Hp02 OF HH02 The treat statinio iz- Round to two decimal places as needed.) The Punto e Round to the decimal places is needed.) fiecause the value is the significance level the hypothesis. There is evidence to support the claim that the retumisess than 20%
Answers
Therefore, we conclude that there is evidence to support the claim that the return rate is less than 20%. Hence, option D03 Hp02 OLM is the correct answer.
According to the given problem, an internet survey was e-mailed to 6960 subjects randomly selected from an online group involved with cars. The return rate of the survey was 1305.Use the Pusle method and use the romal distribution as an approximation to the binomial distribution to test the claim that the return rate is less than 20% at 0.01 significance level. We are to set the null and alternative hypotheses. The null hypothesis is the claim that we are testing against. The alternative hypothesis is what we conclude when we reject the null hypothesis.We can state the null hypothesis as;H0: p >= 0.20The alternative hypothesis is;Ha: p < 0.20Where p is the population proportion.Now, we calculate the test statistic using the Pusle method, which is given by;P = (1305/6960) = 0.18804q = 1 - p = 0.81196n = 6960The standard deviation can be calculated using the formula;σ = sqrt (n * p * q)σ = sqrt (6960 * 0.18804 * 0.81196)σ = 23.43Now, we calculate the z-score using the formula;z = (x - μ) / σz = (0.20 - 0.18804) / 0.00349z = 3.43Finally, we can calculate the p-value using the z-score table or calculator.The critical value of z at the 0.01 significance level is 2.33. Since our calculated z-score (3.43) is greater than the critical value (2.33), we reject the null hypothesis.Therefore, we conclude that there is evidence to support the claim that the return rate is less than 20%. Hence, option D03 Hp02 OLM is the correct answer.
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An application layer IDS security device uses a Bayes based machine learning algorithm that is: - 99% sensitive, 99% of the time identifies true positive packets with malware payload - 95% specific, 95% of the time identifies true negative packets without malware payload. The IDS performs real time deep Malware Traffic Analysis in a high attack application environment where approximately 60% of the traffic is legitimate and 40% of the traffic contains malware, in which case the device drops the packets with malware. Calculate the probability of false negative packets, which is the worst case scenario and is equivalent to the probability for a successful attack. Note: Conditional Probability (A | B) = Probability (A and B) / Probability (B)
Answers
The probability of false negative packets, which represents the worst-case scenario of a successful attack, can be calculated using the sensitivity and prevalence of malware traffic.
The sensitivity of the IDS, which is the probability of correctly identifying packets with malware, is given as 99%. This means that out of all the packets containing malware, the IDS will correctly identify 99% of them as positive.
The prevalence of malware traffic in the high attack application environment is stated as 40%, meaning that 40% of the traffic contains malware.
To calculate the probability of false negative packets (P(false negative)), we need to determine the probability of the IDS incorrectly identifying packets without malware as negative. Since the specificity of the IDS is not provided, we can assume it to be 100% - 95% = 5%, as specificity and false positive are complements.
P(false negative) = 1 - sensitivity = 1 - 0.99 = 0.01
Therefore, the probability of false negative packets, which represents the worst-case scenario and is equivalent to the probability for a successful attack, is 0.01 or 1%.
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Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric, Frances, Gale), count the number of different ways of choosing 4 people for a committee. Assume no one can hold more than one office and that each person is to hold a different position on the committee.
Answers
There are 35 unique approaches to choosing 4 individuals for a board.
Given a gathering of understudies: G = {Allen, Brenda, Chad, Dorothy, Eric, Frances, Gale}, the undertaking is to count the quantity of various approaches to picking 4 individuals for a panel with the suspicion that nobody can hold more than one office and that every individual is to stand firm on an alternate foothold on the council. There are two primary sorts of mix: With and without repetition, the case here is without repetition, as shown by the formulae "C(n, r)."
The following formula calculates the number of Probability selection options for r items from a set of n items: C(n, r) = n!/(n - r)!r!Where n is the quantity of things in the set, and r is the quantity of things to be chosen from the set. Applying the recipe to the above issue: The group consists of seven students, and we want to select four for the committee. C(7, 4) = 7!/(7 - 4)!4! = (7 × 6 × 5 × 4)/(3 × 2 × 1 × 4) = 35. Answer: 35. Subsequently, there are 35 unique approaches to choosing 4 individuals for a board.
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What is the volume of the figure?
6 cm
3 cm
8 cm
2 cm
A
3 X 2 X 6
B.
6 X 8 2
C.
8 * 2 * 3
D.
3 * 2 * 8 * 6
Answers
Answer:
The given figure is a cuboid
it's volume = length × breadth × height
so the answer should be option (c) 8 × 2 ×3
8m - 5.5 =10.1
Help Please
Answers
Answer:
= 1.95
Step-by-step explanation:
8 − 5.5 + 5.5 = 10.1 + 5.5
8 = 15.6
8 = 15.6
8 8
first 5.5 means 55/10 and 10.1 means101/10 when we change them to fraction.
8m=101/10+55/10=156/10
divide 8 by 8 and we get m
and again divide 156/10 for 8
m=1.95
The slope of a line is 2. The y-intercept of the line is –6. Which statements accurately describe how to graph the function?
Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
Locate the ordered pair (0, –6). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
Locate the ordered pair (–6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
Locate the ordered pair (–6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair on the line. Draw a line through the two points.
Answers
Answer:
Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.
Step-by-step explanation:
(0, -6) is the y-intercept, as x = 0. Moving up 2, and right 1 represents the slope of the function. Going up is positive in the y direction, and going right is positive in the x direction.
Drawing a line through the 2 points gives a sneak peak on the full function to be graphed
PRO GAMER MOVE: function is y = 2x - 6
Answer:
It's A. (Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.)
Hurry!! MATH TEST
Ill make brainlest and pls show work if you can!
Answers
Answer:
option 1
Step-by-step explanation:
if it goes up 6 then it means plus 6
Tamara can mow an acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard? Write an equation to model and solve the problem. Explain the answer in terms of the problem. Show all work.
Answers
Answer:
2 hours
Step-by-step explanation:
Given that P(B AND A) = 0.04 and P(A) = 0.18, what is P(BA)?
Answers
P(BA) is the conditional probability of event B given that event A has occurred approximately 0.04
P(BA), we need to know the individual probabilities of events A and B, as well as the probability of the intersection of events A and B.
P(B AND A) = 0.04
P(A) = 0.18
We can use the formula for the intersection of two events:
P(BA) = P(B AND A) = P(A) × P(B | A)
P(B | A) is the conditional probability of event B given that event A has occurred.
To calculate P(B | A), we can rearrange the formula as:
P(B | A) = P(B AND A) / P(A)
Putting in the given values:
P(B | A) = 0.04 / 0.18 ≈ 0.2222
Now we can calculate P(BA) using the formula:
P(BA) = P(A) × P(B | A)
= 0.18 × 0.2222
≈ 0.04
Therefore, P(BA) is approximately 0.04.
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NO LINKS I will give brainliest, it’s a graph pls answer if you know how. Where are the smart people
Answers
Answer:
The answer for (a) is at the picture
(b) The vertex is (-2,7)
(c) Yes the parabola open downward
(d) -(x+2)^2+7 the turning point is at (-2,7) since it is where the group curves
Step-by-step explanation:
Need help with the answer
Answers
Answer:
volume of cylinder=pi×r²×h
volume of cylinder =3.14×(11ft)²×10ft
volume of cylinder=3799.4ft³
Enter the result as a single logarithm with a coefficient of 1. log9 (12x^4) - logg (5x^) = ____________
Answers
The expression [tex]log9(12x^4) - logg(5x^?)[/tex] can be simplified by combining the logarithms into a single logarithm with a coefficient of 1.
To simplify the expression log9(12x^4) - logg(5x^?), we can apply the logarithmic property of subtraction, which states that loga(b) - loga(c) = loga(b/c). Using this property, we can rewrite the expression as a single logarithm.
First, let's simplify the expression log9(12x^4). Since the base of the logarithm is 9, we can rewrite it as log(12x^4) / log(9).
Next, let's simplify the expression logg(5x^?). Since the base of the logarithm is g, we can rewrite it as log(5x^?) / log(g).
Combining these two expressions, we have:
log(12x^4) / log(9) - log(5x^?) / log(g).
To combine these logarithms into a single logarithm, we need a common base. Let's use the base 10. Applying the logarithmic property of division, we can rewrite the expression as:
log(12x^4) / log(9) - log(5x^?) / log(g) = (log(12x^4) - log(5x^?)) / log(9g).
Finally, we simplify the numerator by applying the logarithmic property of subtraction:
[tex]log(12x^4) - log(5x^?) = log((12x^4) / (5x^?)).[/tex]
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What kind of function is f(x)?
A. Exponential
B. Logarithmic
C. Rational
D. Polynomial
Answers
Determine all possible digit replacements for x so that the first number is divisible by the second. 95,768,24x; 4 What digit will make the first number divisible by 4? (Use a comma to separate answer
Answers
The digit replacements for x in the number 95,768,24x that make it divisible by 4 is either 0, 4, or 8.
To evaluate the digit replacements for x in the number 95,768,24x that make it divisible by 4, we need to determine the possible values for x that satisfy this condition.
For a number to be divisible by 4, the last two digits must be divisible by 4. Therefore, we need to find the values of x that make the number 24x divisible by 4.
The possible values for x that make 24x divisible by 4 are 0, 4, 8. This is because any multiple of 4 ends in 0, 4, 8 when the tens and units place are considered.
Therefore, the possible digit replacements for x are 0, 4, and 8. These values will make the number 95,768,24x divisible by 4.
Hence, the digit that will make the first number divisible by 4 is either 0, 4, or 8.
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Someone help me with this its in the picture!!!
Answers
Answer:
JK < KI < IJ
Step-by-step explanation:
The length of the side of a rectangle corresponds with the size of the angle opposite it.
m<K = 180 - (50 + 44) (sum of triangle)
m<K = 86°
IJ is opposite m<K = 86°
JK is opposite to m<1 = 44°
KI is opposite to m<J = 50°
The bigger the measure of an angle, the larger the side opposite it.
Therefore, form least to greatest, the side lengths of the triangle cam be ordered as follows:
JK < KI < IJ
mDE⌢=129°, and mBC⌢=65°. Find m∠A
Answers
Answer:
mDE⌢=129°, and mBC⌢=65°. Find m∠A
Step-by-step explanation:
Please help me with the three questions on the top ignore the writing
Answers
Answer:
1. (1/4 x 5/4 x 5/4) = 25/64
2. (2/4 x 2/4 x 6/4) = 3/8
3. (1/4 x 1/4 x 4/2) 1/8
Step-by-step explanation:
Thank me later.
A projectile was launched from the ground with a certain initial velocity. The militaries used a radar to determine the vertical coordinate you of the projectile for two moments of time measured in seconds from the moment when the projectile was launched. The radar measurements showed that y(3) = 419 meters, 6) = 679 meters. Calculate the maximum of y() if it is known as follows 1. The projectile was moving along a vertical line 2. The acceleration due to gravity gis 9.81 meter second 3. There is an air resistance proportional to the velocity of the projectile. 4. The value of the empirical coefficient p is a constant 5. Time is measured in seconds, and distances are measured in meters A student solved the problem, rounded-off the numerical value of the maximum of y(t) to THREE significant figures and presented it below (15 points) meters your numerical answer must be written here Also, it is required to answer several additional questions as follows: 1. If p is the value of a positive empirical constant (its value is to be found), is the unknown initial velocity of the projectle, then the formula for the altitude y of the projectile at the moment of timetis given by the formula (1 point): = ロロロロロ 2. If p is the value of a positive empirical constant (its value is to be found) is the unknown initial velocity of the projectile, then the value of the velocity of the projectile at the moment of time is given by the formula (1 point): ( *Y-811.pl 3. The maximum of the altitude was achieved by the projectile when time expressed in seconds and rounded-odfo FOUR significant figures) was qual to (3 points) 9.354 DD0000 10:49 10.89 11 35 11.89 12.48.
Answers
The maximum altitude attained by the projectile is 720 meters. The maximum altitude was achieved by the projectile when time expressed in seconds and rounded off to four significant figures was equal to 10.89 seconds.
The formula for the altitude y of the projectile at the moment of time t is given by the formula: y(t) = [(v_0 / p)g][1 - exp(-pt / m)] + (m / p)g(t / p) where v_0 is the initial velocity of the projectile, p is the empirical constant, g is the acceleration due to gravity, m is the mass of the projectile, and t is the time.
The formula for the velocity of the projectile at the moment of time t is given by the formula: v(t) = (v_0 / p)exp(-pt / m) + (m / p)g.
Any object launched into space with only gravity acting on it is referred to as a projectile. Gravity is the main force affecting a projectile. This doesn't imply that other forces don't affect it; it merely means that their impact is far smaller than that of gravity. A projectile's trajectory is its route after being fired. A projectile is something that is launched or batted, as a baseball.
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Farm workers are employed on a contract-to-contract basis. The contract lengths follow a normal distribution with a mean of 25 weeks and a variance of 36.
Answers
The variance is the average squared deviation of each value from the mean. It calculates how far each value in a group is from the mean, and then it squares the result of each of those calculations. Finally, it averages the sum of the squares to produce a figure that represents how varied the data is from the mean.
The variance formula is as follows:
Var(X) = (Σ (Xi - μ)^2) / (n - 1)
Where, X is a random variable representing the group data, μ is the mean of the group data, Xi is each value in the group data, Σ is the sum of all Xi values, and n is the number of values in the group data.
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According to given information, the probability that a contract will last between 15 and 35 weeks is `0.905`.
To compute the probability that a contract will last between 15 and 35 weeks, we must utilize the standard deviation for the normal distribution.
To solve for the probability of a normal distribution, we use the formula `z = (x - μ) / σ`, where `x` is the value we are looking for, `μ` is the mean, and `σ` is the standard deviation.
We can compute the standard deviation using the variance, which is the square of the standard deviation, which is `σ^2`.
To begin, we first find the standard deviation. `σ = sqrt(36) = 6`.
Next, we will calculate the `z-scores` for 15 and 35.
[tex]`z1 = (15 - 25) / 6 = -10 / 6 = -1.67`[/tex]
and [tex]`z2 = (35 - 25) / 6 = 10 / 6 = 1.67`[/tex].
Now we can use the `Z-table` to find the probabilities that correspond to `z1` and `z2`. We can see that the probability of `z1` is `0.0475` and the probability of `z2` is `0.9525`.
Finally, to obtain the probability that a contract will last between 15 and 35 weeks, we must subtract the probabilities corresponding to `z1` from `z2`.
[tex]`P(15 ≤ X ≤ 35) = P(Z ≤ 1.67) − P(Z ≤ −1.67) = 0.9525 − 0.0475 = 0.905`[/tex].
Therefore, the probability that a contract will last between 15 and 35 weeks is `0.905`.
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Graph y = 2x + 1
Help pleaee
Answers
Answer:
Step-by-step explanation:
Answer:
Answer is linked
Step-by-step explanation:
The equation is in slope-intercept form, which is y = mx + b.
To graph the line, first we have to find the slope, m, and the y- intercept, b.
So, the slope is 2 and the y- intercept is 1.
We can graph this, beginning with the y- intercept, 1. The y- intercept is always on the y axis, so the (x) value will always be zero.
Plot a point at (0, 1).
Next, add more points using the slope. The slope is 2, or [tex]\frac{2}{1}[/tex]. Start at the point we have made on the y axis. The slope equals the [tex]\frac{rise}{run}[/tex]. We can rise 2 units, then run one more unit to the right. If the slope is negative, the run goes to the left. However, in this case, the slope is positive, to it slants to the right.
We end on point (1, 3). We can continue this path infinitely, some other points on the graph could be (2, 5), (3, 7), (4, 9) and (5, 11).
Connect these points to make a line.
The finished line is linked below as well.
I hope this helps :] Good luck ^^
For the functions f(x) = 2x3- 3 and g(x) = 4x + 4, find (fog)(0) and (gºf)(0)
Answers
For the functions f(x) = 2x3- 3 and g(x) = 4x + 4, (gºf)(0) = g(f(0)) = g(-3) = -8.
To find (fog)(0), we need to evaluate the composition of functions f and g at x = 0.
First, we find g(0):
g(0) = 4(0) + 4 = 4.
Next, we substitute g(0) into f:
f(g(0)) = f(4).
Now, we find f(4):
f(4) = 2(4)^3 - 3 = 2(64) - 3 = 128 - 3 = 125.
Therefore, (fog)(0) = f(g(0)) = f(4) = 125.
To find (gºf)(0), we need to evaluate the composition of functions g and f at x = 0.
First, we find f(0):
f(0) = 2(0)^3 - 3 = -3.
Next, we substitute f(0) into g:
g(f(0)) = g(-3).
Now, we find g(-3):
g(-3) = 4(-3) + 4 = -12 + 4 = -8.
Therefore, (gºf)(0) = g(f(0)) = g(-3) = -8.
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