Given that X₁, X₂, ..., Xₙ are iid according to a uniform continuous distribution over the open interval (0,0+1).
Now, we have to find a sufficient statistics for 8.Let T = ∑Xᵢ, then T ~ U(n*0,n).Thus, T is a sufficient statistic for θ.Hence, T is a sufficient statistics for 8.
Given that X₁, X₂, ..., Xₙ are iid according to a uniform continuous distribution over the open interval (0,0+1).
We have to find a minimally sufficient statistics for
Let T = (X(n), X(1)), where X(n) = max{X₁,X₂, .... Xₙ} and X(1) = min{X₁,X₂, .... Xₙ}.As Xᵢ follows uniform distribution, so T can take any value in [0, 1].
Let Y = nX(n)/(1-X(n)), thenY = (nX(n))/(1-X(n)) = (nX(n))/(X(n)-X(1)) = 1/[(X(n)-X(1))/n].Now, 0 < X(1) ≤ X(n) < 1. Therefore, 0 < (X(n)-X(1))/n ≤ 1/n. Then, Y takes values in [0,∞).Thus, Y is a one-to-one function of T.
Hence, T is a minimally sufficient statistics for 8.
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A sample of 20 students who have taken a statistics exam at ZZ University, shows a mean = = 72 and variance s² 16 at the exam grades. Assume that grades are distributed normally, find a %98 confidence interval for the variance of all student's grades.
A 98% confidence interval for the variance of all student's grades is [9.41, 31.41].
The degrees of freedom (df) are (n - 1) = (20 - 1) = 19.
A confidence interval is given by the formula: $[{\chi }_{\frac{\alpha }{2},(n-1)}^{2}\frac{s^{2}}{d_f},\ { \chi }_{1-\frac{\alpha }{2},(n-1)}^{2}\frac{s^{2}}{d_f}]$ where ${\chi }_{\frac{\alpha }{2},(n-1)}^{2}$ is the lower percentile of the chi-square distribution with (n - 1) degrees of freedom, ${ \chi }_{1-\frac{\alpha }{2},(n-1)}^{2}$ is the upper percentile of the chi-square distribution with (n - 1) degrees of freedom, and s² is the sample variance.
Lower percentile (L.P) = ${\chi }_{\frac{\alpha }{2},(n-1)}^{2}\frac{s^{2}}{d_f}$
Upper percentile (U.P) = ${ \chi }_{1-\frac{\alpha }{2},(n-1)}^{2}\frac{s^{2}}{d_f}$
Now, α = 0.02, n = 20, s² = 16, and df = 19.
Lower percentile:L.P = ${\chi }_{\frac{\alpha }{2},(n-1)}^{2}\frac{s^{2}}{d_f} = { \chi }_{\frac{0.02}{2},19}^{2}\frac{16}{19} = 9.410$
Upper percentile:U.P = ${ \chi }_{1-\frac{\alpha }{2},(n-1)}^{2}\frac{s^{2}}{d_f} = { \chi }_{1-\frac{0.02}{2},19}^{2}\frac{16}{19} = 31.410$
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The 98% confidence interval for the variance of all student's grades is (10.12, 30.29). Hence, option A is the correct answer.
Given data are: The sample size, n is 20, the mean of the sample is 72 and the variance of the sample, s² is 16.
Option A is the correct answer.
Step-by-step explanation: Given, Sample size, n = 20
Mean of the sample, [tex]\bar x = 72[/tex]
Variance of the sample, [tex]s^{2} =16[/tex].
We have to find a 98% confidence interval for the variance of all student's grades.
Assumption: Grades are distributed normally.
So, the formula for the confidence interval for the variance is: [tex]((n-1)s^{2} / \chi^{2} \alpha /2, (n-1)s^{2} / \chi^{2} 1-\alpha /2)[/tex]
Where, [tex]\alpha = 1-0.98[/tex]
= 0.02
n-1 = 19
Degrees of freedom [tex]\chi^{2}\alpha /2[/tex] and [tex]\chi^{2}²1-\alpha /2[/tex] are the critical values of chi-square distribution with (n-1) degrees of freedom.
From the chi-square distribution table, we can find the values of [tex]\chi^{2}\alpha /2[/tex] and [tex]\chi^{2}²1-\alpha /2[/tex] such that the area between these values is 0.98.
Here, [tex]\alpha = 0.02[/tex] (as 98% confidence interval)
[tex]\alpha /2 = 0.02/2[/tex]
= 0.01
Using the above values, we get,
[tex]\chi^{2}0.01/2,19 = 8.907[/tex] and
[tex]\chi^{2}1-0.01/2,19 = 32.852[/tex]
Now, using the formula of confidence interval for the variance, we get,
[tex]((n-1)s^{2} / \chi^{2} \alpha /2, (n-1)s^{2} / \chi^{2} 1-\alpha /2)=((20-1) \times 16 / 32.852, (20-1) \times 16 / 8.907)[/tex]
We get, (10.12, 30.29).
Therefore, the 98% confidence interval for the variance of all student's grades is (10.12, 30.29). Hence, option A is the correct answer.
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(q8) Find the volume of the solid obtained by rotating the region bounded by
, and the x-axis about the y axis.
The correct option is:d.9/2 pie units cubbed. The given region is obtained by rotating the curve y = x2 – 3 about the x-axis, which can be represented as:y = x² - 3
We have to rotate this curve around the y-axis. The required volume can be obtained by integrating the area of the circular cross-sections formed after rotating the curve.The radius of each circular cross-section at any value of x is equal to the perpendicular distance between the curve and the y-axis, which is x.
Thus, the area of each circular cross-section can be represented as:A = π(x²)The limits of integration can be found by equating y = x² - 3 to 0, which is:0 = x² - 3x = ± √3
Thus, the volume of the solid obtained by rotating the region bounded by y = x² - 3 and the x-axis about the y-axis is given by:V = ∫-√3^√3 π(x²) dxV = π ∫-√3^√3 (x²) dx.
By using the formula for integration, we get:V = π [(x³)/3] -√3^√3V = π [(√3³ - (-√3)³)/3]V = π (18/3)V = 6π.Therefore, the volume of the solid obtained by rotating the region bounded by y = x² - 3 and the x-axis about the y-axis is 6π units cubed. Hence, the correct option is:d.9/2 [tex]\pi[/tex]units cubbed.
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The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.9 grams with a standard deviation of 0.2 grams.
For parts (a) through (c), enter your responses as a decimal with 4 decimal places.
a) What is the probability that a randomly chosen mouse has a mass of less than 20.74 grams?
b) What is the probability that a randomly chosen mouse has a mass of more than 21.14 grams?
c) What proportion of mice have a mass between 20.8 and 21.04 grams?
d) 10% of all mice have a mass of less than grams.?
Given: The mass of a species of mouse commonly found in houses is normally distributed with a mean of 20.9 grams with a standard deviation of 0.2 grams.
a) The probability that a randomly chosen mouse has a mass of less than 20.74 grams is 0.2119.
b) The probability that a randomly chosen mouse has a mass of more than 21.14 grams is 0.1151.
c) The proportion of mice have a mass between 20.8 and 21.04 grams is 0.4495.
d) 10% of all mice have a mass of less than 21.15632 grams.
(a) The probability that a randomly chosen mouse has a mass of less than 20.74 grams.
Z = (X - μ)/σ, where X = 20.74, μ = 20.9, σ = 0.2.
Z = (20.74 - 20.9)/0.2Z
= -0.8P(X < 20.74)
= P(Z < -0.8)
Using standard normal distribution table, P(Z < -0.8) = 0.2119.
Thus, the required probability is 0.2119.
(b) The probability that a randomly chosen mouse has a mass of more than 21.14 grams.
Z = (X - μ)/σ, where X = 21.14, μ = 20.9, σ = 0.2.
Z = (21.14 - 20.9)/0.2
Z= 1.2
P(X > 21.14) = P(Z > 1.2)
Using standard normal distribution table, P(Z > 1.2) = 0.1151.
Thus, the required probability is 0.1151.
(c) To find the proportion of mice have a mass between 20.8 and 21.04 grams.
Z_1 = (X1 - μ)/σ
= (20.8 - 20.9)/0.2
= -0.5
Z_2 = (X2 - μ)/σ
= (21.04 - 20.9)/0.2
= 0.7
P(20.8 < X < 21.04) = P(-0.5 < Z < 0.7)
= P(Z < 0.7) - P(Z < -0.5)
Using standard normal distribution table,
P(Z < 0.7) = 0.7580
P(Z < -0.5) = 0.3085
Therefore, P(-0.5 < Z < 0.7) = P(Z < 0.7) - P(Z < -0.5)
= 0.7580 - 0.3085
= 0.4495
Thus, the required probability is 0.4495.
(d) 10% of all mice have a mass of less than grams.
Let the mass be X.
We have to find X such that P(X < k) = 0.1
Z = (X - μ)/σ, where μ = 20.9, σ = 0.2.
P(X < k) = P(Z < (k - μ)/σ)
0.1 = P(Z < (k - 20.9)/0.2)
0.1 = P(Z < 5k - 104.5)
Using standard normal distribution table, we get
5k - 104.5 = -1.2816k
k= 21.15632
Thus, 10% of all mice have a mass of less than 21.15632 grams.
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Select the correct answer.
If f(t)
- 6 and 9(3)
22 (
+ 3), find g(x) < f(x).
OA. 5/2 - 3232
- 1867
OB. 75
3VI3
18va
OC. 5
6vr
OD.
5
3.13 – 180

A
see attached for explanation
I hope it helps
I have two questions
1.) what are 3 equivalent ratios for 5/45
2.) what are 3 equivalent ratios for 3/5
For a, b, c, d € Z, prove that a - c|ab + cd if and only if a - cl ad + bc. 2. (a) What are the possible remainders when 12 + 16 + 20 is divided by 11? (b) Prove for every n € Z that 121 + n2 +16n+20
(a) The possible remainders when 12 + 16 + 20 is divided by 11 are 8 and 19.
(b) For every integer n, the expression 121 + n^2 + 16n + 20 is always divisible by 11.
In the first statement, we are asked to prove that a - c divides ab + cd if and only if a - c divides ad + bc. To prove this, we can use the property of divisibility. If a - c divides ab + cd, then there exists an integer k such that ab + cd = (a - c)k. Similarly, if a - c divides ad + bc, there exists an integer m such that ad + bc = (a - c)m. By rearranging the terms, we can express k and m in terms of a, b, c, and d. By substituting these expressions into the equation ab + cd = (a - c)k, we can show that ab + cd = (a - c)(ad + bc)m. Thus, proving the equivalence.
In the second statement, we are asked about the possible remainders when 12 + 16 + 20 is divided by 11. To find the remainder, we can calculate the sum as 48 and then divide it by 11. The quotient is 4 with a remainder of 4. Hence, 12 + 16 + 20 leaves a remainder of 4 when divided by 11.
To prove that 121 + n^2 + 16n + 20 is divisible by 11 for every integer n, we can use algebraic manipulation. By factoring the expression as (n + 4)(n + 4) + 16(n + 4), we can rewrite it as (n + 4)^2 + 16(n + 4). Now, we notice that both terms have a common factor of (n + 4). Factoring it out, we get (n + 4)(n + 4 + 16). This simplifies to (n + 4)(n + 20). Since both factors contain n + 4, we can conclude that the expression is divisible by 11 for any integer n.
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Two counters are selected at random from a bag containing 5 red counters and 3 blue counters.
Find the expected number of red counters selected.
Answer:
1.4
Step-by-step explanation:
Probability of selecting a red counter :
Number of red counter / total number of counters
5 / (5 + 3) = 5 /8 = 0.625
Probability of selecting a blue counter = 0.375
Let number of red counters :
0, 1 or 2
0 red counters :
Expected value = x * p(x)
0 + (0.625*1) + (0.390625 * 2)
0 + 0.625 + 0.78125 = 1.40625
Expected number of red counters = 1.4
What is the compound ratio of 3:4 and 4:5?
Electron A is fired horizontally with speed 1.00 Mm/s into a region where a vertical magnetic field exists. Electron B is fired along the same path with speed 2.00 Mm/s.
(i) Which electron has a larger magnetic force exerted on it?
A does.
B does.
The forces have the same nonzero magnitude.
The forces are both zero.
(ii) Which electron has a path that curves more sharply?
A does.
B does.
The particles follow the same curved path.
The particles continue to go straight.
a)The force on electron B doubles the force acting on electron A
The correct answer is (b)
b)The path radius for electron A is half that of electron B .
The correct option is (a)
Magnetic ForceMoving charges are sources of the magnetic field and also recipients of the magnetic interaction. Stationary charges interact with the electric field but are not influenced by the magnetic field. The magnetic force acting on a moving charge is proportional to the value of the charge, to its velocity, and the absolute value of the magnetic field. The absolute value of the force also depends on the relative direction of the magnetic field and the velocity.
The magnetic force acting on the electron equals:
[tex]F_A =ev_A(B).....(1)\\\\F_B =ev_B(B).....(2)[/tex]
proportional to the vector product between the velocity and the magnetic field. The magnetic field and the velocity vectors are perpendicular, consequently, the absolute value of the vector product reduces to the product of the absolute values,
[tex]|F_A| =e|v_A||B|\\\\|F_B| =e|v_B||B|[/tex]
The only difference between the forces strives in the value of the velocities. The velocity of electron B is twice that of electron A . Therefore, the force on electron B doubles the force acting on electron A
The correct answer is (b)
b) To analyze the orbit of the electrons due to the magnetic force let us use Newton's second law. The magnetic force is always perpendicular to the velocity not changing its absolute value but only its direction. The acceleration resulting from the force is centripetal. In scalar form
[tex]F_A =ev_A(B)=ma_c_A\\\\F_B =ev_B(B)=ma_c_B[/tex]
Substituting the centripetal acceleration in terms of the velocities and the radiuses,
[tex]ev_AB=m\frac{v^2_A}{R_A} \\\\ev_BB=m\frac{v^2_B}{R_B}[/tex]
Solving for the radius,
[tex]R_A=\frac{mv_A}{eB} \\\\R_B=\frac{mv_B}{eB}[/tex]
The orbital radius is directly proportional to the velocity of the electron. As a result the path radius for electron A is half that of electron B .
The correct option is (a)
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What is the area, in square inches of a rectangle will the dimensions with 7/8 3/16 in the diagram below?
Answer:
1 1/16
Step-by-step explanation:
you you have to add 7/8 + 3/16 to get the answer of one whole and 1/16
The equation for the rollercoaster before is f(x)=-0.2x^2-2x
Find the vertex algebraically
Hint: x=-b/2a
??? The answer is not able to be found for the fact that there are 3 numbers all coming from x.
Glenn needs to cut pieces of ribbon that are each 1 meter long to make ribbon key chains. If he has 6 pieces of ribbon that are each 1 dekameter long, how many 1−meter pieces of ribbon can he cut?
Answer: 60
Step-by-step explanation:
5x-2y=15
2x+6y=-11
solve by substitution or equal values method
Answer:
Point form -
[tex](2-\frac{5}{2})[/tex]
Equation form -
[tex]x=2, y=-\frac{5}{2}[/tex]
Step-by-step explanation:
if you have any questions feel free to ask
Complete the following similarity statement for the figure below.
Answer:
Triangle JKLM ~ Triangle STUV
What is the simplified form of the following expression? Assume y does not equal 0. 3 square root 12x^2 over 16y
Answer:
Ok y does not = 0 (They say this because is y=0 it would be undefined anything divided by 0 is undefined)
[tex](3\sqrt{12x^2})/16y\\[/tex]
Answer: [tex](3x\sqrt{3})/8y[/tex]
pleaaaaseeeeeee help!!!!!!!!!!!!!!!!!!!!!
brainliest and 20 points
Answer:
x=0
Step-by-step explanation:
Answer:
Short answer: Empty set ∅
if x is less than -1 then it can't be greater than 1
is the equation y = x ^2 + 3 a function?
Answer: Yes it is
Step-by-step explanation:
Answer:
Yes it is. Succese to The homework
Lydia is a childbirth assistant. The first year of her career, she attended the births of 2 babies. Every year after that, the number of births Lydia attended has been double that of the previous year. After 6 years of working as a childbirth assistant, how many births has she attended in total?
Answer:24 or 4
Step-by-step explanation:
2x2=4 4x6=24 24 or 4
find a vector function, r(t), that represents the curve of intersection of the two surfaces. the paraboloid z = 2x2 y2 and the parabolic cylinder y = 3x2
To find the vector function that represents the curve of intersection between the paraboloid z = 2x^2y^2 and the parabolic cylinder y = 3x^2, we can parameterize the curve using a parameter t. The vector function r(t) will consist of x(t), y(t), and z(t), where each component is expressed in terms of t.
First, we need to find the relationship between x and y by setting the equation of the parabolic cylinder equal to the y-coordinate of the paraboloid. Substituting y = 3x^2 into z = 2x^2y^2, we get z = 2x^2(3x^2)^2 = 18x^6.
Now, we can express x and z in terms of t. Let's set x(t) = t, which allows us to write z(t) = 18t^6. The y-component can be obtained by substituting x(t) into the equation of the parabolic cylinder: y(t) = 3(t^2).
Finally, we can combine the x(t), y(t), and z(t) components to form the vector function r(t) = (x(t), y(t), z(t)). In this case, r(t) = (t, 3t^2, 18t^6) represents the curve of intersection between the two surfaces.
Note that this vector function parameterizes the curve and allows us to describe various points on the curve by plugging in different values of t.
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The Kickers soccer team has 4 strikers, 6 midfielders, 7 full backs and 2 goalies. How many ways can they field a 2/4/4 team?
There are 3150 ways the Kickers soccer team can field a 2/4/4 team.
To determine the number of ways the Kickers soccer team can field a 2/4/4 team, we need to consider the different positions and the number of players available in each position.
For a 2/4/4 team, we have:
2 strikers
4 midfielders
4 full-backs
2 goalies
To calculate the number of ways, we can multiply the number of choices for each position:
Number of ways = Number of choices for strikers [tex]\times[/tex] Number of choices for midfielders [tex]\times[/tex] Number of choices for full-backs [tex]\times[/tex] Number of choices for goalies.
For the strikers, there are 4 available players, and we need to choose 2 of them.
This can be calculated using the combination formula, denoted as C(n, r):
Number of choices for strikers = C(4, 2) = 4! / (2! [tex]\times[/tex] (4-2)!) = 6
For the midfielders, there are 6 available players, and we need to choose 4 of them:
Number of choices for midfielders = C(6, 4) = 6! / (4! [tex]\times[/tex] (6-4)!) = 15
Similarly, for the full-backs, there are 7 available players, and we need to choose 4 of them:
Number of choices for full-backs = C(7, 4) = 7! / (4! [tex]\times[/tex] (7-4)!) = 35
Finally, for the goalies, there are 2 available players, and we need to choose 2 of them:
Number of choices for goalies = C(2, 2) = 1
Now, we can multiply all the choices together:
Number of ways [tex]= 6 \times15 \times 35 \times 1 = 3150[/tex]
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Create 5 geometric sequences
Answer:
Below.
Step-by-step explanation:
The formula for a GS is:
a1, a1r, a1 r^2, a1r^3 .....
Examples are:
1. First term a1 =2 and common ratio r = 3, the first 4 terms are:
2, 2*3, 2*3^2, 2*3^3
= 2, 6, 18, 54
2. a1 = 1 , r = 0.5:
1, 0.5, 0.25, 0.125 .....
3. a1 = -4, r = -2:-
-4, 8, -16, 32 ...
4. a1 = 0.1, r = -3:
0.1, -0.3, 0.9, -2.7 .....
5. a1 = 2, r = 1/3:
2, 2/3, 2/9, 2/27 .....
Three coffees and two muffins cost a total of $7. Two
coffees and four muffins cost $8.
Let x = cost of coffees
Let y = cost of muffins
how do i write this in a system of linear equations?
Step-by-step explanation:
3 coffees + 2 muffins = $7
therefore,
[tex]3x + 2y = 7[/tex]
2 coffees + 4 muffins = $8
therefore,
[tex]2x + 4y = 8[/tex]
Answer:
i think in every coast we're adding two shillings in the first sentence the total was 5 and we paid $7 and in the second sentence the total was 8 dollars meaning we added to shillings.
Step-by-step explanation:
in my school we are taughtthat we shouldn't mix goats with sheeps so we this the same way we can't mix x and y so in my opinion I guess you can say x + y =to that amount of money at the end you paid if it's 8 dollars or 7 dollars. we can say x represents the coffees and y represents the muffins that's how I get it I hope you want to be angry with me. for example 3 + 2 equals to 7 .3 + 2 is 5 so we'll carry five to the other side of equals where we will make it be minus so we'll say 7 - 5 where will get 2
Construct a confidence interval for p₁-P2 at the given level of confidence. x₁ =354. n₁ =545, x2 #406, n₂ = 596, 95% confidence The researchers are % confident the difference between the two population proportions. P₁ P2, is between and (Use ascending order. Type an integer or decimal rounded to three decimal places as needed).
To find the confidence interval for p1 - p2 at a given level of confidence 95%, with x1 = 354, n1 = 545, x2 = 406, n2 = 596, we need to first calculate the point estimate for the difference in proportions:
$$\hat{p_1} = \frac{x_1} {n_1} = \frac {354}{545} \approx. 0.6495$$$$\hat{p_2} = \frac{x_2} {n_2} = \frac {406}{596} \approx. 0.6822$$
Therefore, the point estimate of the difference in proportions is: $$\hat{p_1} - \hat{p_2} = 0.6495 - 0.6822 \approx. -0.0327$$. Now, we can use the formula for the confidence interval for the difference in proportions:
$$\text{Confidence interval} = (\hat{p_1} - \hat{p_2}) \pm z_{\alpha/2} \sqrt{\frac{\hat{p_1}(1 - \hat{p_1})}{n_1} + \frac{\hat{p_2}(1 - \hat{p_2})}{n_2}}$$where z_{\alpha/2} is the z-score for the level of confidence 95% (or 0.95), which is approximately 1.96
Using this information, the confidence interval for p1 - p2 at a 95% level of confidence is: $$(0.6495 - 0.6822) \pm 1.96 \sqrt {\frac {0.6495(1 - 0.6495)}{545} + \frac {0.6822(1 - 0.6822)}{596}}$$$$\approx. -0.0327 \pm 0.0472$$
Therefore, we can conclude that the researchers are 95% confident the difference between the two population proportions, P1 - P2, is between -0.080 and -0.004 (using ascending order and rounding to three decimal places as needed).
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Suppose that you used technology to find the least-squares regression line from a table of values for two variables and the results were displayed as follows.
m = -0.03576 b = 42.17093 r^2 = 0.8914 r = -0.9438
What can we say about the relationship between the two variables?
Since the r-value is quite close to -1 (only 0.0562 away), we can conclude that the two variables are strongly negatively associated. This implies that when one variable increases, the other variable decreases.
In statistics, the correlation coefficient is used to quantify the linear relationship between two variables. The r-value ranges from -1 to 1, indicating the degree to which the variables are positively or negatively associated.
The r-value measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1.
The closer the r-value is to -1, the stronger and more negative the correlation is.
The closer the r-value is to 1, the stronger and more positive the correlation is.
A value of 0 indicates that there is no linear relationship between the variables.In this case, the r-value is -0.9438.
Because the r-value is negative, the two variables are negatively associated. The closer the r-value is to -1, the stronger the negative association is.
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Performance Task: Super Survey Simulator
A performance task is a learning activity that asks students to perform to demonstrate their knowledge, understanding and proficiency.
What is a performance task?Your information is incomplete. Therefore, an overview will be given. A performance task measure whether a student can apply his or her knowledge to make sense of a new phenomenon.
It should be noted that performance tasks yield a tangible product and performance that serve as evidence of learning.
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Complete the remainder of the table for the given function rule: y = 2x + 4
Answer:
eight.
Step-by-step explanation:
2(6) ÷ 3
12÷3
4+4
8
What is the solution to the initial value problem J²u(x, t) D.E.: J²u(x, t) Ət² = dx² I.C.: [u(x,0) = e-x² ut (x,0) = 0 Ans. u(x,t) = [e−(z−¹)² + e¯(x+t)²]. [infinity] < x
The solution to the given initial value problem is u(x,t) = [e−(z−¹)² + e¯(x+t)²]. [infinity] < x
Given Differential equation is J²u(x, t) Ət² = dx²I.
C is u(x,0) = e-x² and ut (x,0) = 0
We need to find the solution to the given initial value problem. The general solution to the given Differential equation is
u(x,t) = f1(x − t) + f2(x + t)
where f1 and f2 are arbitrary functions. We need to find the particular solution that satisfies the given initial conditions. Given intial condition,
u(x,0) = e-x² …………(1)
ut (x,0) = 0…………(2)
Let us find the value of f1(x) and f2(x) using the given intial condition,
From equation (1)u(x,0) = f1(x) + f2(x) = e-x²
Now, Differentiating f1(x) + f2(x) = e-x² w.r.t x, we getf1'(x) + f2'(x) = -2x ………..(3)
From equation (2)
ut (x,0) = f1'(x) + f2'(x) = 0
On solving the above two equations, we get
f1'(x) = x, f1(x) = ½x² + C1
and
f2'(x) = -x, f2(x) = ½x² + C2
Now, the particular solution is
u(x,t) = ½(x − t)² + C1 + ½(x + t)² + C2
u(x,t) = (x² + t² + C1 + C2)………….(4)
Using the initial condition u(x,0) = e-x² in equation (4)
e-x² = x² + C1 + C2
Now, we know that for large value of x, the term e-x² becomes negligible. So, C1 + C2 = 0 ⇒ C2 = -C1
Substituting C2 = -C1 in equation (4), we get
u(x,t) = [e−(z−¹)² + e¯(x+t)²]. [infinity] < x
The solution to the given initial value problem is u(x,t) = [e−(z−¹)² + e¯(x+t)²]. [infinity] < x.
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Suppose that the average screen time for all students at this middle school is 2 hours, with a standard deviation of 0.6 hours. A random sample of 36 students turns out to have an average of 2.2 hours? Calculate a standardized score for this sample average.
The calculated value of the standardized score for this sample average is 2
How to calculate a standardized score for this sample average.From the question, we have the following parameters that can be used in our computation:
Population mean = 2
Population standard deviation = 0.6
Sample size = 36
Sample mean = 2.2
The standardized score for this sample average can be calculated using
z = (Score - Sample mean)/(Sample standard deviation)
Where
Standard deviation = Population standard deviation/√n
So, we have
Standard deviation = 0.6/√36
Evaluate
Standard deviation = 0.1
So, we have
z = (2.2 - 2)/0.1
Evaluate
z = 2
Hence, the standardized score for this sample average is 2
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Find the maximum heigh reached by the rocket
y=-16x^2+146x+137
Answer:
Step-by-step explanation:
se gana 10000 y 2
Let f(x) = 2x–8 and g(x) = x + 2. Find f(g(x)) and g(f(x)).
Answer:
g(f(x)) = 2x - 6
f(g(x)) = 2x - 4
Step-by-step explanation:
g(f(x)) = 2x - 8 + 2
g(f(x)) = 2x - 6
f(g(x)) = 2(x + 2) - 8
f(g(x)) = 2x - 4
Answer: g ( 2 x − 8 ) = 2 x− 6
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