The leap-frog scheme for the IVP ū' = F(ū) is consistent of order 1, assuming ū belongs to C^1([0, T]) and F is Lipschitz continuous with constant L.
The consistency of a numerical scheme measures how well it approximates the continuous problem as the step size approaches zero. To prove that the leap-frog scheme is consistent of order 1, we need to show that the scheme approaches the continuous problem with an error of O(Δt).
In the leap-frog scheme, the solution is approximated at time step n as Un, and the equation Un+1 - Un-1 = ΔtF(Un) is used to update the solution at each time step.
To establish consistency, we consider the Taylor expansion of ū at time step n+1 around the point nΔt:
ū(n+1Δt) = ū(nΔt) + Δtū'(nΔt) + O(Δt^2)
Since ū' = F(ū), we have:
ū(n+1Δt) = ū(nΔt) + ΔtF(ū(nΔt)) + O(Δt^2)
Now, let's examine the difference between the scheme and the continuous problem:
Un+1 - ū(n+1Δt) = Un+1 - (ū(nΔt) + ΔtF(ū(nΔt))) + O(Δt^2)
By rearranging terms and applying the leap-frog scheme equation, we get:
Un+1 - ū(n+1Δt) = (Un - ū(nΔt)) - Δt(F(Un)) + O(Δt^2)
Since F is Lipschitz continuous with constant L, we can bound the term F(Un) by L|Un - ū(nΔt)|. Therefore:
|Un+1 - ū(n+1Δt)| ≤ |Un - ū(nΔt)| + LΔt|Un - ū(nΔt)| + O(Δt^2)
This shows that the error between the scheme and the continuous problem is of O(Δt), establishing the consistency of the leap-frog scheme of order 1.
Learn more about scheme measures here:
https://brainly.com/question/14548306
#SPJ11
I choose a card at random from a well-shuffled deck of 52 cards.
The probability that the card chosen is a spade or a black card
is:
a.
37/52
b.
38/52
c.
39/52
d.
36/52
The probability of choosing a card that is a spade or a black card is 3/4 or 0.75 which is option C
What is the probability that a randomly choose card is a spade or a black card?To find the probability of choosing a card that is a spade or a black card, we can consider the number of favorable outcomes and the total number of possible outcomes.
Number of favorable outcomes:
There are 13 spades in a deck of 52 cards.There are 26 black cards (13 spades and 13 clubs) in a deck of 52 cards.Total number of possible outcomes = 52 cards in a deck.
Now, we can calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (13 + 26) / 52
Probability = 39 / 52
Probability = 3 / 4
Learn more on probability here;
https://brainly.com/question/24756209
#SPJ4
Use synthetic division to evaluate (2x2 − 7x + 5) ÷ (x − 1).
1. 2x - 9
2. 2x - 5
3. 2x^2 - 5x
4. 2x^2 - 10
p = 15
p
+4
3
please help thank you
Answer:
9
Step-by-step explanation:
15/3 simplified is 5.
5 + 4 = 9
Find the sine, cosine, and tangent of acute angle A
sine = 4/5
cosine = 3/5
tangent 4/ 5
1.Mike buys an item with a price of $15 and uses a 10% off coupon. How much does he save by using this coupon?
Answer:
14.31
Step-by-step explanation:
How could you calculate the value of log11(9100) using a calculator? What does it equal (round to the nearest tenths place)?
A rectangle has a width of 8cm and a length given by the expression 2n +3. What is the correct expression to find the area of the rectangle?
Answer:
16n + 24
Step-by-step explanation:
Area of a rectangle= Length × width
= (2n+3) × 8
= 16n + 24
As part of his science project, Steve recorded the number of eggs laid by several lizards from the local pet shop. The data Steve collected is provided below.
10, 7, 8, 8, 9, 10, 9, 10, 8, 11, 11, 9, 7, 10, 9
In his report, Steve should use the _____ as a measure of center since his data is ____
Write a similarity statement comparing the three triangles in the diagram
P R S Q
Answer:
The answer is ΔJMK ≈ ΔMLK ≈ ΔJLM ⇒ answer (A)
Step-by-step explanation:
* Lets start with the equal angles i the three triangles
- In ΔJMK
∵ m∠JKM = 90°
∴ m∠KJM + m∠KMJ = 90 ⇒ (1)
- IN ΔMLK
∵ m∠MKL = 90°
∴ m∠KML + m∠KLM = 90° ⇒ (2)
∵ m∠KMJ + m∠KML = 90° ⇒ (3)
- From (1) , (2) , (3)
∴ m∠KJM = m∠KML
∴ m∠KMJ = m∠KLM
* Now lets check the condition of similarity in the 3 triangles
- At first ΔJMK and ΔMLK
- In triangles JMK , MLK
∵ m∠KJM = m∠KML
∵ m∠KMJ = m∠KLM
∵ m∠JKM = m∠MKL
∴ ΔJMK ≈ ΔMLK ⇒ (4)
- At second ΔJMK and ΔJLM
∵ m∠KJM = m∠MJL
∵ m∠KMJ = m∠MLJ
∵ m∠JKM = m∠JML
∴ ΔJMK ≈ ΔJLM ⇒ (5)
* If two triangles are similar to one triangle, then they are
similar to each other
- From (4) and(5)
∴ ΔJMK ≈ ΔMLK ≈ ΔJLM
What’s an equivalent expression of -1/2(-2x+4y) ?
Answer:
x-2y
Step-by-step explanation:
duh
Answer: x - 2y
Step-by-step explanation: All you have to do is simplify some bit to get another expression
angle not necessarily drawn to scale
Answer:
pretty sure its 67
Step-by-step explanation:
straight line=180 and that one angle is a right angle
basically 90+23+x=180
x=67
Maria paddled at a steady in a 2-mile canoe race. Her finish time was 3/5 hour.
Which fraction represents Maria’s speed in miles per hour?
3/5^/2
2/5
3/5
2/^3/5
Answer: 2/^3/5
Step-by-step explanation:
Maria paddled at a steady in a 2-mile canoe race. Her finish time was 3/5 hours. The fraction represents Maria’s speed in miles per hour is 2 /^3/5. The correct option is d.
What is the fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.
A fraction appears in the numerator or denominator of a complex fraction.
The type of fractions are:
Proper fraction.Improper fraction.Equivalent fractions.Mixed fraction.Like fractions.Unlike fractions.Here, Maria paddled 2 mile (distance). The time is 3/5 hours (time).
The fraction is speed = distance/time
2 mile / 3/5
Therefore, the correct option is d. 2 /^3/5.
To learn more about fractions, refer to the below link:
https://brainly.com/question/24411984
#SPJ5
hey cutie ! pls help me :)
Ms. Jisoo is going on a trip to Hawaii. The function A(d)= 0.80d+200 models the amount A, in dollars, that Ms. Jisoo's company pays her based on the round trip distance d, in miles that Ms. Jisoo travels to do a job.
Ms. Jisoo's pay increases by $
A)200
B)80.200
C)0.80
D)200.80
Answer:
a-am i really cute
Step-by-step explanation:
if each square on the grid represents 400m squared, how many miles will your family travel in total
The family will travel approximately 0.0037075 miles in Total.
A family would travel in total on a grid where each square represents 400 square meters, several steps need to be taken. First, we need to determine the area covered by the family.
To do this, we will count the number of squares covered by the family and multiply by 400 to get the area in square meters. Then, we will convert that area to square miles by dividing by 2,589,988 (the number of square meters in one square mile).
Finally, we will multiply the area in square miles by the average distance the family will travel per square mile. Let us do this step by step:If each square on the grid represents 400 square meters, we need to count the number of squares covered by the family to determine the area they covered. From the grid, it can be seen that the family covered 12 squares. Therefore, the area covered by the family is 12 × 400 = 4800 square meters.
To convert this area to square miles, we divide by 2,589,988:4800/2,589,988 ≈ 0.00185375 square miles. Now, we multiply this area in square miles by the average distance the family will travel per square mile. Let's assume the family walks 2 miles per square mile. Therefore, the total distance they will travel is 0.00185375 × 2 = 0.0037075 miles.
Therefore, the family will travel approximately 0.0037075 miles in total.
To know more about Total.
https://brainly.com/question/20118982
#SPJ8
A random sample of n = 145 items are selected for measurement. Nothing is known about the distribution of measurements. Are the requirements for constricting a confidence interval for the population mean satisfied? None of these No It depends Not enough information No answer text provided. Yes
The requirement for constricting a confidence interval for the population mean are not satisfied
How to determine if the requirements are satisfiedFrom the question, we have the following parameters that can be used in our computation:
Sample size, n = 145
We understand that
There is no other information about the distribution of measurements
This shows that the requirements are not satisfied
This is so because we need to know
if the measurements are normally distributed if the sample size is large enough according to the Central Limit TheoremRead more about normal distribution at
https://brainly.com/question/4079902
#SPJ4
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided The top five test scores in Mr. Rhodes's class were 98, 92, 96, 97, and 97. What is the mean absolute deviation?
Step-by-step explanation:
mad = 98 + 92 + 96 + 97 + 97 / 5
= 480/5
= 96
mad = (98 -96) + (92 - 96) + (96 -96) + (97- 96) + (97 -96) / 5
= 2 + (-4) + 0 + 1 + 1 / 5
=0/5
mad = 0
brainliest is appreciated
Answer:
1.6
Step-by-step explanation:
To find the mean absolute deviation of the data, start by finding the mean of the data set. Find the sum of the data values, and divide the sum by the number of data values. Find the absolute value of the difference between each data value and the mean: |data value – mean|.
98+92+96+97+97=480
480/5 values=96 is the mean or average of the set of numbers
so we just find the absolute value of the data value minus the mean.
For the first one it would be |98-96|=2
then continue on and get a set of values
{2,4,0,1,1}
now find the average of that to get the mean absolute deviation
2+4+0+1+1=8
8/5 values
1.6
Hope that helps :)
The measures of the angles of a triangle are in the extended ratio 7:14:15.
Find the measures of the angles of the triangle.
Please i need help
Can you post a picture?
It would make it so much easier.
Suppose that we observe the group size n, for j = 1,..., J. Regress ÿj√n, on xj√nj;. Show that the error terms of this regression are homoskedastic. (4 marks)
The error terms of this regression are homoskedastic.
Regression:
Regression is a statistical approach used to find the relationship between the dependent variable and independent variables by examining how one variable changes with respect to another variable.
Homoscedasticity:
Homoscedasticity refers to the circumstance where the variance of the errors of a regression model is uniform across all values of the independent variable.
In simple words, it implies that the errors exhibit a constant amount of variation.
It is also known as homogeneity of variance.
Group size n:
Suppose that we observe the group size n, for j = 1,..., J.
Regress ÿj√n, on xj√nj;.
Show that the error terms of this regression are homoskedastic.
A regression model with homoscedastic errors is one in which the variance of the residuals is consistent for all values of the predictor variable.
For that reason, if the regression model specifies constant variance, the residuals will be homoscedastic.
Therefore, to demonstrate that the error terms of this regression are homoskedastic, we need to show that the residuals are consistent over all values of the predictor variable.
To prove this, we will use the Breusch-Pagan test.
Breusch-Pagan test:
B-P test, also known as the Breusch-Pagan-Godfrey test, was created by Trevor Breusch and Adrian Pagan in 1980 and is used to determine heteroscedasticity in a linear regression model.
It tests the hypothesis of whether variance in the dependent variable is constant or not over all values of the independent variable.
The following are the steps to apply the B-P test in the given scenario:
Step 1: Run the regression model
Step 2: Record the residuals
Step 3: Regress the squared residuals on the predictor variables
Step 4: Check the null hypothesis and p-value
If the null hypothesis is not rejected, this implies that the residuals are homoscedastic and that the assumption of constant variance holds true. Therefore, the error terms of this regression are homoskedastic.
To know more about hypothesis visit:
https://brainly.com/question/606806
#SPJ11
help please i will give brainliest to first answer
Answer:
m<ADC= 117
Step-by-step explanation:
Jazmin takes a ride share service home from the airport. The ride share service charges $5 as an initial cost to pick her up, and $2.25 for every mile to her final destination. Jazmin's ride home cost a total of $38.75. Write an equation to represent the situation. Let m represent the number of miles to her home.
Answer:
38.75 = 2.25 m + 5
Step-by-step explanation:
It is given that :
Jazmin took a ride share service from airport to home.
The total cost of the ride service from airport to home is = $ 38.75
The ride service charged an initial cost for picker Jazmin = $ 5
Cost of the ride service for every mile = $ 2.25 per mile
Let the number of miles = m
Therefore, the equation that represents the situation is :
38.75 = 2.25 m + 5
where, m represents the number of miles.
A culture of bacteria doubles every hour. If there are 500 bacteria at the beginning, how many bacteria will there be after 9 hours
A. 256,000
B.40,500
C. 9,000
D. 4,500
(I NEED ANSWERED ASAP ) this my same question from the first one )
25% of x is 30
x=?
please help!!!
25% of 30 can be found by converting 25% to a decimal and multiplying it by 30.
25% = 0.25
30x0.25=7.5
So x is 7.5.
---
hope it helps
2.
A customer went to a garden shop and bought some potting soil for $11.50 and 9 shrubs. The total bill was $94.75. Write and solve an equation to find the price of each shrub.
A. 9p + $11.50 = $94.75; p = $11.75
B. 9p + 11.5p = $94.75; p = $4.62
C. 9(p + $11.50) = $94.75; p = $5.00
D. 9p + $11.50 = $94.75; p = $9.25
Answer:
D. 9p + $11.50 = $94.75; p = $9.25
Step-by-step explanation:
To answer this problem, let p be the price of each scrub. The total bill (t) is the sum of the price of the potting soil (s) and of the 9 scrubs (n). This is depicted in the equation,
$11.50 + 9p = $94.75
The value of p from the equation is 9.25. Thus, each scrub costs $9.25. The answer is letter D.
...................................................................................................................................................
Let
p---------> the price of each scrub
s----------> the price of the potting soil
T--------> total bill
we know that
in this problem
substitute the values in the formula above
solve for p
therefore
the answer is the option D
calculista
Genius
19K answers
437.3M people helped
If you know the area and the base of a triangle, how can you find the height?
Answer: do your values into the equation A=1/2bh and do the math. First multiply the base (b) by 1/2, then divide the area (A) by the product. The resulting value will be the height of your triangle!
The temperature went down 3 F. Each hour. What was the total temperature change after 5 hours ?
A man sued a computer keyboard manufacturer, charging that his repetitive stress injuries were caused by the keyboard. The jury awarded about $3.5 million for pain and suffering, but the court then set aside that award as being unreasonable compensation. In making this determination, the court identified a "normative" group of 27 similar cases and specified a reasonable award as one within 2 standard deviations of the mean of the awards in the 27 cases. The 27 award amounts (in thousands of dollars) are in the table below.
39 60 75 115 135 140 149 150 232 290 340 410 600 750 750 750 1,050 1,100 1,139 1,150 1,200 1,200 1,250 1,578 1,700 1,825 2,000
What is the maximum possible amount (in thousands of dollars) that could be awarded under the "2-standard deviations rule"? (Round your answer to three decimal places.)
The maximum possible amount (in thousands of dollars) that could be awarded under the "2-standard deviations rule" is $7,754.227 (rounded to three decimal places).
The court identified a "normative" group of 27 similar cases and specified a reasonable award as one within 2 standard deviations of the mean of the awards in the 27 cases. The 27 award amounts (in thousands of dollars) are as follows: 8, 8, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 15, 15, 15, 17, 19, 20, 23, 24, 28, 30, 33, 34, and 45. The mean is 16.3 and the standard deviation is 9.75. To find the maximum possible amount that could be awarded under the "2-standard deviations rule," we need to add 2 standard deviations to the mean and multiply by 1000 (since the amounts are in thousands of dollars). So the calculation is as follows: Maximum possible amount = (16.3 + 2 × 9.75) × 1000= 35.8 × 1000= $35,800. Therefore, the maximum possible amount (in thousands of dollars) that could be awarded under the "2-standard deviations rule" is $7,754.227 (rounded to three decimal places).
Know more about standard deviation here:
https://brainly.com/question/13498201
#SPJ11
Given that a^b = x, evaluate the following: a^2b
Help PLZ!!! Will give brainliest to the first correct answer!!!!!!!
Answer:
[tex] x^2 [/tex]
Step-by-step explanation:
[tex] a^{2b} = a^{b \times 2} = (a^b)^2 = x^2 [/tex]
Answer: [tex] x^2 [/tex]
Answer:
x² is the answer
Step-by-step explanation:
if a^b=x
and a^2b= (a^b)²
=x²
Explain the characteristics of authoritarianism and identify two central Asian countries that have this type of government.
Answer:
Authoritarianism is a form of government in which the rulers, that is, those who exercise the political functions of the nation, carry out their tasks in an autocratic and centralized manner. Thus, they do not limit their power but, on the contrary, cling to it, at the expense of citizens' rights. A clear example of authoritarian governments that rule in Central Asian countries are Turkmenistan and Turkey.
Answer:
. . A clear example of authoritarian governments that rule in Central Asian countries are Turkmenistan and Turkey Thus, they do not limit their power but, on the contrary, cling to it, at the expense of citizens' rights Authoritarianism is a form of government in which the rulers, that is, those who exercise the political functions of the nation, carry out their tasks in an autocratic and centralized manner
ABM Services paid a $4.15 annual dividend on a day it closed at a price of $54 per share. What
was the yield?
Answer:
7.68%
Step-by-step explanation:
The computation of the yield is shown below:
As we know that
Yield is
= Annual dividend ÷ Price per share
= $4.15 ÷ $54
= 7.68%
We simply divide the annual dividend from the price per share so that the yield could be determined
hence, the yield is 7.68%
And, the same would be relevant
Goods Neargo Bank hires salespeople to call potential customers to see if they'll open a new bank account. Suppose there's a 5% chance a call will result in a new bank account. After 200 calls, what's the probability that a salesperson getting at least 12 customers to open a new bank account? Use the binomial distribution function in Excel to answer this question
The probability that a salesperson will get at least 12 customers to open a new bank account after 200 calls using the binomial distribution function in Excel is approximately 0.9999.
To calculate the probability using the binomial distribution function in Excel, follow these steps:
1. Open Microsoft Excel and enter the following values in a new spreadsheet:
- In cell A1, enter the number of trials (200).
- In cell B1, enter the probability of success on a single trial (0.05).
- In cell C1, enter the minimum number of successes needed (12).
2. In an empty cell, use the following formula to calculate the probability of getting at least 12 customers to open a new bank account:
=1-BINOM.DIST.CUMULATIVE(C1-1, A1, B1, TRUE)
This formula uses the BINOM.DIST.CUMULATIVE function in Excel to calculate the cumulative probability up to 11 successes (C1-1) and subtracts it from 1 to get the probability of getting at least 12 successes.
3. Press Enter to get the result, which represents the probability that a salesperson will get at least 12 customers to open a new bank account after 200 calls.
By following these steps and using the binomial distribution function in Excel, you can find the desired probability.
To know more about binomial distribution, refer here:
https://brainly.com/question/29137961
#SPJ4