The Airy differential equation is a second-order linear ordinary differential equation given by Fourier Transform:
-d^2u/dx^2 = x*u
To find a bounded solution to this equation, we can use the Fourier transform. The Fourier transform of a function f(x) is given by:
F(ω) = ∫ f(x) e^(-iωx) dx
Using the Fourier transform, we can convert the differential equation into an algebraic equation in terms of the Fourier transform F(ω):
-ω^2 F(ω) = ∫ x*u(x) e^(-iωx) dx
We can rewrite the integral on the right-hand side using integration by parts:
∫ x*u(x) e^(-iωx) dx = -∫ u(x) d/dx(e^(-iωx) dx)
= -iω∫ u(x) e^(-iωx) dx + [u(x) e^(-iωx)]^∞_0
Since we are looking for a bounded solution, the term [u(x) e^(-iωx)]^∞_0 must be equal to zero. Therefore, we have:
ω^2 F(ω) = iω∫ u(x) e^(-iωx) dx
We can then solve for the Fourier transform F(ω):
F(ω) = i/ω ∫ u(x) e^(-iωx) dx
Finally, we can take the inverse Fourier transform to find the solution u(x):
u(x) = (1/2π) ∫ F(ω) e^(iωx) dω
Substituting the expression for F(ω), we have:
u(x) = i/(2πω) ∫ ∫ u(y) e^(-iω(y-x)) dy dω
This gives us an integral formula for a bounded solution to the Airy differential equation in terms of the Fourier transform.
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A sample of 66 observations will be taken from an infinite population. the population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is:_________.
Using the normal distribution, the probability that the sample proportion will be less than 0.1768 is of 0.9222 = 92.22%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].For this problem, the proportion and the sample size are given by:
p = 0.12, n = 66.
Hence the mean and the standard error are:
[tex]\mu = p = 0.12[/tex].[tex]s = \sqrt{\frac{0.12(0.88)}{66}} = 0.04[/tex]The probability that the sample proportion will be less than 0.1768 is the p-value of Z when X = 0.1768, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.1768 - 0.12}{0.04}[/tex]
Z = 1.42
Z = 1.42 has a p-value of 0.9222.
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The length of time needed to complete a certain test is normally distributed with mean 44 minutes and standard deviation 8 minutes. Find the probability that it will take less than 34 minutes to complete the test.
The probability that it willtake less than 34 minutes to complete the test is 0.1056
Given mean of 44 minutes and standard deviation of 8 minutes.
We have to find the probability that it will take less than 34 minutes to complete the test.
The probability lies between 0 and 1. The formula to calculate probability is number of items divided by total items but it can also be found through z test calculations.
We are using z test to find the probability.
Z=X-μ/σ
Where μ is sample mean and
σ= standard deviation
Z is z value
First we will find the p value from 34 to 44.
Z=34-44/8
=-10/8
=-1.25
P value for X<34=P(Z<-1.25)
=0.5-0.3944
=0.1056.
Hence the probability that it will take less than 34 minutes is 0.1056.
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There were only 86 confirmed cases of Measles in the year 2000. In 2019, there was a reported 1,350 % increase in confirmed
cases of Measles. How many cases were there in 2019?
Answer:
1161 confirmed cases
Step-by-step explanation:
In 2000 the number of cases was 86
Percent means out of a hundred, so if we divide 1350 by 100 we get 13.5.
So, we must multiply 13.5 and 86 to get the amount of cases in 2019.
13.5*86 = 1161 confirmed cases in 2019
Kady and Scott both invest £800.
Kady invests in an account that gives 15.2% compound interest per annum.
Scott invests in an account that gives 15.9% simple interest per annum.
After how many years is Kady's investment worth more than Scott's?
Answer:we smoking fredoooooooooo
Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answer: No, they are not similar
Step-by-step explanation:
Similar triangles are triangles with congruent angles.
33° ≠ 32°
These triangles are not similar.
(pls help me with this)
4. The points C and D are (4, 5) and (p, q) respectively,
a) Write down, in terms of p and q, the coordinates of the midpoint of CD.
b) Given that the midpoint of CD is (7, 1), find the coordinates of D.
A. The coordinates of the midpoint of CD in terms of p and q is [(4 + p) / 2 , (5 + q) / 2]
B. The coordinates of D, Given that the midpoint of CD is (7, 1) is (10 , -3)
A. How to determine the mid pointCoordinate of C = (4, 5)Coordinate of D = (p, q)Mid point =?Mid point = (X , Y)
X = (x₁ + x₂) / 2
X = (4 + p) / 2
Y = (y₁ + y₂) / 2
Y = (5 + q) / 2
Thus,
Mid point = (X , Y)
Mid point = [(4 + p) / 2 , (5 + q) / 2]
B. How to determine the coordinates of DMid point = (7, 1)Coordinates of D =?Mid point = (7, 1) = (X , Y)
X = (4 + p) / 2
7 = (4 + p) / 2
Cross multiply
7 × 2 = 4 + p
14 = 4 + p
Collect like terms
p = 14 - 4
p = 10
Y = (5 + q) / 2
1 = (5 + q) / 2
Cross multiply
1 × 2 = 5 + q
2 = 5 + q
Collect like terms
q = 2 - 5
q = -3
Coordinates of D = (p, q)
Coordinates of D = (10 , -3)
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Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?
The final step in solving the inequality is to divide through by -2 and flip the sign
Solving InequalitiesFrom the question, we are to determine the final step in solving the inequality
The given inequality and the steps for solving are
Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
The final step will be to divide both sides of the inequalities by -2 and then flip the sign
That is,
–6 < –2x
Divide both sides by -2 and flip the sign
3 > x
OR
x < 3
Hence, the final step in solving the inequality is to divide through by -2 and flip the sign
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The centreville city council conducts a survey to find out how many people would be willing to donate money to update the town's library. they randomly select 200 people for the survey, and 80 people say they would donate. if 9,800 people live in centreville, about how many people would likely donate?
a. 122
b. 280
c. 3,920
d. 5,880
(C) 3,920 people would likely donate.
What is the percentage?
A percentage (from Latin per centum "by a hundred") is a number or ratio stated as a fraction of 100 in mathematics. It is frequently symbolized with the percent sign, " percent ". A % is a dimensionless (pure) number; it does not have a unit of measurement.To find about how many people would likely donate:
First, find 80 is what percent of 200.
∴ [tex]\frac{80}{200} * 100 = 40%[/tex]
So, 80 is 40% of 200.
Centreville population is 9,800.
Now, take out 40% of 9,800.
[tex]\frac{x}{9,800} *100 = 40\\\frac{x}{98} =40\\98*40 = 3,920[/tex]
Therefore, (C) 3,920 people would likely donate.
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When positive integer x is divided by positive integer y, the remainder is 9. If = 96.12, what is the value of y ? 96 75 48 25 12
Y= 75.
Lets try to solve it,
When positive integer x is divided by positive integer y, the remainder is 9
=> x=qy+9;
=> x/y=96.12
=>x=96y+0.12y (so q above equals to 96);
=>0.12y=9
=> y=75.
Hence the value of y would be 75.
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To study the population of consumer perceptions of new technology, sampling of the population is preferred over surveying the entire population because ______.
Because It is quicker and fast.
Sampling:
Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population. The methodology used to sample from a larger population depends on the type of analysis being performed, but it may include simple random sampling or systematic sampling.
Sampling is the selection of a subset of the population of interest in a research study. In the vast majority of research endeavors, the participation of an entire population of interest is not possible, so a smaller group is relied upon for data collection.
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Can someone please help with this question. 20 points up for grabs!!
Based on the railway timetable given, the time the first train reaches Oakengates is 0815.
The time taken to reach Shrewsbury from Telford Central is 22 minutes.
What does the train timetable show?Oakengates is 2 minutes away from Telford Central so when a train leaves the latter and arrives at 0815, this is the first train to Oakengates.
If one left Telford Central at 0852, they would reach Shrewsbury at 0914 to make it:
= 0914 - 0852
= 22 minutes
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A 14 oz bag of flour costs $2.95 and a 28 oz bag of flour costs $6.20. What is the price per ounce of the 14 oz bag of flour?
The price per ounce of the 14 Oz bag of flour is; ¢21.1.
What is the price per ounce of the 14 oz bag of flour?Since it follows from the task content that the 14 Oz bag of flour sells for $2.95 which is equivalent to ¢295 since $1 = ¢100.
It follows that the price per ounce of the 14oz bag of flour is; = ¢295/14 = ¢21.1
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PLSSS HELP
Refer to your answers to the questions from Part 2 of Project 1.
A parabola goes through (negative 3, 3) & (1, negative 1). A point is below the parabola at (negative 3, 2). A line above the parabola goes through (negative 3, 4) & (0, 4). A point on the parabola is labeled (x, y).
What is the correct standard form of the equation of the parabola?
Enter your answer below. Be sure to show each step of your work.
The correct standard form of the equation of the parabola is:
[tex](x+3)^{2}[/tex]= 4(y - 3).
What is a parabola?An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix). An essential curve of the coordinate geometry's conic sections is the parabola.
For the given question,
Vertex of parabola is (-3,3)
Thus, the equation of the parabola is:
[tex](x-h)^{2}=4(y-k)[/tex]
[tex](x+3)^{2}[/tex]= 4(y-3)
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write the equation of a line this is parallel to y=0.5x-4 and that passes through the point (9,-6).
Answer:
[tex]y=0.5x-10.5[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line we need to find is 0.5.
Substituting into point-slope form and converting to slope-intercept form,
[tex]y+6=0.5(x-9) \\ \\ y+6=0.5x-4.5 \\ \\ y=0.5x-10.5[/tex]
How much did Alexa make in 5.5 hours?
Using a proportional relationship, it is found that Alexa makes $146.45 in 5.5 hours.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
The constant in this problem is:
k = 213.6/8 = 427.2/16 = 827.7/31 = 26.7.
Hence her earnings for x hours of work is:
y = 26.7x.
For 5.5 hours of work, her earnings are:
y = 26.7(5.5) = $146.45.
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Compare the measures of the different angles of elevation and depression that are labeled in the diagram. Which statements are true? Check all that apply.
x > y
v > x
w = y
y < v
v = w
x < w
The statements that are true about the angle include:
x > y
w = y
y < v
How to illustrate the information?From the information, the first has legs 529m and 229m. Then tan x = 529/229. Also tan y = 529/347.
It can be seen that tan x is greater than tan y. Angles x, v, y, and w are alternate angles. Therefore, the correct options are A, C, avd D.
A weather balloon is 529 meters above the ground. Two weather stations, A and B, monitor the balloon’s progress. Compare the measures of the different angles of elevation and depression that are labeled in the diagram. Which statements are true
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Find n if GCF(n, 40)= 10 and LCM (n, 40)= 280
Answer:
70
Step-by-step explanation:
GCF(x,y)*LCM(x,y)=xy
10*280=40n
2800=40n
70=n
n=70
Please help me on this thanks, I got the right answer but I still don’t understand
His present age is 13 years.
How to solve words problems ?The words problem can be solved as follows:
let
his present age = x
Therefore,
3(x + 5) = 54
Hence,
3(x + 5) = 54
3x + 15 = 54
subtract 15 from both sides
3x + 15 - 15 = 54 - 15
3x = 39
divide both sides by 3
3x / 3 = 39 / 3
x = 13
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If a skydiver jumps out of an airplane and falls at 212 mph, what is the skydiver's velocity and speed?
The skydiver is falling at a speed of 212 miles per hour.
The speed of the skydiver is 212 mph.
What are Speed and Velocity?
Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, whereas velocity is a vector, speed is a scalar quantity.
Given:
If a skydiver jumps out of a plane and plummets to the ground while falling at 212 mph.
To Find:
Speed and acceleration of the skydiver.
Velocity is the speed with a direction, whereas speed is only a number with a speed unit at the end.
While velocity refers to the speed and direction of an object's movement, speed refers to the time rate at which an object moves along a path.
212 miles per hour is the descending velocity of the skydiver.
At 212 miles per hour, the skydiver is moving.
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Tickets for a concert were \$5$5dollar sign, 5 for each child and \$8$8dollar sign, 8 for each adult.
Answer:
What exactly is the question
Step-by-step explanation:
There's no clear question.
Which fractions are equal to 2/3?
Check all that are true.
1
3
6
9
4
6
1
6
3
2
Answer:
It's the correct answer
PLEASE MARK AS BRAINLIEST
Step-by-step explanation:
Equivalent fractions of 2/3 : 4/6 , 6/9 , 8/12 ,
THX
Don't forget to mark me as brainliest
Help please you don’t know how much this means to me
[tex]db {}^{2} - ab {}^{2} = ab {}^{2} - ae {}^{2} \\ db {}^{2} = 2ab {}^{2} - ae {}^{2} \\ (ac + bc) {}^{2} = 2ab {}^{2} - ae {}^{2} \\ ac {}^{2} + bc {}^{2} + 2ac.bc = 2ab {}^{2} - ae {}^{2} \\ 2ac.bc = ab {}^{2} - ae {}^{2} [/tex]
[tex]2ac.bc = ab {}^{2} - (ac {}^{} - ce) {}^{2} \\ 2ac.bc = ab {}^{2} - ac {}^{2} + 2ac.ce - ce {}^{2} \\ 2ac.bc = ab {}^{2} - ac {}^{2} - cb {}^{2} + 2ac.ce \\ but \: ab {}^{2} - ac {}^{2} - cb {}^{2} = 0 \\ 2ac.bc = 2ac.ce \\ bc = ce \\ which \: is \: true[/tex]
NEED HELP ASAP
Which of the following correctly demonstrates how to factor x² - y²?
A.(x - y)²
B.(x-y)(x+y)
C.(x+y)(x+y)
D.2(x - y)
Answer:
B.(x-y)(x+y)
Step-by-step explanation:
The factor of x² - y² can be represented by,
A.(x - y)²
INCORRECT:
Translated to (x - y)(x - y) as the exponent says it multiplied by it self
(x - y)(x - y) = x²- 2xy + y² which doesn't match
B.(x-y)(x+y)
Correct!
x times x = x²
-y times y = -y²
x² - y²
C.(x+y)(x+y)
INCORRECT
x times x = x²
y times y = y²
x² + y² which doesn't match as y positive here
D.2(x - y)
INCORRECT
distribute 2 so 2x - 2y which isn't the original
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Find the volume of the composite figure. Round to the nearest tenth if necessary.
The volume of the given composite solid is 375 m³
Volume of composite solidFrom the question, we are to determine the volume of the composite solid
The volume of the composite solid = Volume of the cuboid + Volume of the triangular prism
Thus,
Volume of the composite solid = (5 × 5 × 13) + 1/2(5 × 4 × 5)
Volume of the composite solid = 325 + 50
Volume of the composite solid = 375 m³
Hence, the volume of the given composite solid is 375 m³
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It cost $1031 for a camping trip. You have to pay $231
to park for the entire trip and $200 per day for the
camping site.
Create the equation below to represent this situation.
The equation that represent this situation is as follows:
1031 = 231 + 200d
How to find the equation that represent the situation?It cost $1031 for a camping trip.
You have to pay $231 to park for the entire trip and $200 per day for the
camping site.
Therefore,
let
d = days on the camping site.
Therefore, the equation that represent this situation is as follows:
1031 = 231 + 200d
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WILL MAKE BRAINLIEST!!
Find the correct angle measure for angle b in each figure.
_1. 52°
_2. 27°
_3. 32°
_4. 98°
A group of Advanced Open Water Divers plans to make two dives. The first dive is on a reef in 22 metres of water for 20 minutes. The group then remains on the surface for 1 hour. The second dive is on a wreck in 16 metres of water, with a planned bottom time of 30 minutes. What will be the ending pressure group after the second dive
The ending pressure group after the second dive is R.
According to the statement
We have given that the
The first dive is on a reef in 22 metres of water for 20 minutes and The second dive is on a wreck in 16 metres of water, with a planned bottom time of 30 minutes.
And we have to find the pressure group after second dive.
So, For this purpose, we know that the
Recreational scuba diving (R) – this diving has prescribed limits, including a depth no greater than 130 fsw, using only compressed air, and never requiring a decompression stop.
From the above situation, we could note that there was a prescribed limit 18m/60ft of water with a bottom time of 30 minutes.
And due to its the ending pressure becomes R.
So, The ending pressure group after the second dive is R.
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Lunch costs $6.90. How much change will
Hector get from $20.00?
Answer: 22
Step-by-step explanation:
Write an expression that can be used to produce vector b from vector a, and explain how you determined that expression.
The explanation regarding the vector is illustrated below.
How to illustrate the information?It should be noted that vector A with components a, b, c, can be written as (a, b, c) or in terms of unit vectors as ai + bj + ck.
In this case, the letters I, j, and k are the standard symbols for the unit vectors in the x, y, and z directions.
Therefore, if A = (3,4,5( you can write A = 3i + 4j + 5k.
If B = (1, 1, 1), you can write B = I + j + k.
Then A - B is the vector whose component are the difference in each components.
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Kenny wants to fill his attic with insulation. If the insulation costs $16.75 per cubic yard, how much would it cost to fill Kenny's entire attic?
9 yd
3 yd
5 yd
4 yd
A. $904.500
B. $938.00
OC. $1,038.50
D. $1,155.75
The total cost to fill Kenny's entire attic given the cost per cubic yards is $904.50; option A
Triangular prismCost of insulation = $16.75 per cubic yard[tex]V = 1/4h \sqrt{ { - a}^{4} + 2 {ab}^{2} } + 2 {ac}^{2} - {b}^{4} + 2 {bc}^{2} - {c}^{4} [/tex]
= 1/4×9 √-4⁴ + 2(4×5)² + 2(4×3)² - 5⁴ + 2(5×3)² - 3⁴
= 9/4√256 + 2(20)² + 2(12)² - 3125 + 2(15)²- 81
= 9/4√256 + 2(400) + 3(144) - 3125 + 2(225) - 81
= 9/4√256 + 800 + 432 - 3125 + 450 - 81
= 9/4√-1268
= 54 cubic yard
Total cost to fill Kenny's entire attic = 54 × $16.75
= $904.50
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