The Gauss Seidel method is the fastest convergence method among Gauss elimination, Gauss Jordan, and Gauss Jacobi methods.
The Gauss-Seidel method is an iterative method used to solve linear systems of equations. It is named after German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel. This method uses the value of each variable as soon as it is updated in each iteration. It starts with an initial guess for the solution and then iteratively refines the solution until a desired level of accuracy is reached.
In contrast, the Gauss elimination method and its variants (Gauss Jordan and Gauss Jacobi) are direct methods that involve the manipulation of the entire matrix at once. While these methods can be faster for smaller systems of equations or when parallelized, they may not converge at all for certain matrices or may require a large number of iterations to reach the desired accuracy. Therefore, in general, the Gauss-Seidel method is preferred for solving linear systems of equations due to its faster convergence rate.
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Shirley is saving money to buy a computer.
• The computer she will buy costs $1,200.00
• She has already saved $300.00
Shirley will save $60.00 per week until she has enough money to buy
the computer.
Answer:
It will take her 15 weeks to have enough money for the computer.
Step-by-step explanation:
$1200 - $300 = $900
900 divided by 60 gives you 15
Therefor, it'll take Shirley 15 weeks to save $1200.
Joshua has 3.95 pounds of candy. He is placing the candy into 5 equal size bags. How much candy will be in each bag?
Find the value of the expression below
when x =3/4
4x² + 8x - 5
Answer:
4x² + 8x - 5
= 4(3/4)² + 8(3/4) - 5
= 4 × 9/16 + 24/4 - 5
= 36/16 + 24/4 - 5
= 9/4 + 6 - 5
= 9/4 +1
= 3.25
Step-by-step explanation:
Hope it helps!!
selects a piece of candy and eats it (so it is NOT replaced!) Then selects a piece of candy and eats it. Find the probability of each event
Question:
There are 30 candies in a box, all identically shaped. 5 are filled with coconut, 10 with caramel, and 15 are solid chocolate.
You randomly select a piece of candy and eat it (so it is NOT replaced!), then select a second piece. Find the probability of each event
(a) The probability of selecting two solid chocolates in a row.
(b) The probability of selecting a caramel and then a coconut candy.
Answer:
[tex](a)[/tex] [tex]P(Chocolates) = \frac{7}{29}[/tex]
[tex](b)[/tex] [tex]P(Caramel\ and\ Coconut) = \frac{5}{87}[/tex]
Step-by-step explanation:
Given
[tex]Coconut = 5[/tex]
[tex]Caramel = 10[/tex]
[tex]Chocolate = 15[/tex]
[tex]Total = 30[/tex]
For probabilities without replacement, 1 is subtracted after the first selection.
So, we have:
Solving (a): Two solid chocolates
This is calculated as:
[tex]P(Chocolates) = P(First\ Chocolate) * P(Second\ Chocolate)[/tex]
[tex]P(Chocolates) = \frac{n(Chocolate)}{Total} * \frac{n(Chocolate) - 1}{Total - 1}[/tex]
[tex]P(Chocolates) = \frac{15}{30} * \frac{15 - 1}{30 - 1}[/tex]
[tex]P(Chocolates) = \frac{15}{30} * \frac{14}{29}[/tex]
[tex]P(Chocolates) = \frac{1}{2} * \frac{14}{29}[/tex]
[tex]P(Chocolates) = \frac{7}{29}[/tex]
Solving (a): Caramel and Coconut
This is calculated as:
[tex]P(Caramel\ and\ Coconut) = P(Caramel) * P(Coconut)[/tex]
[tex]P(Caramel\ and\ Coconut) = \frac{n(Caramel)}{Total} * \frac{n(Coconut)}{Total - 1}[/tex]
[tex]P(Caramel\ and\ Coconut) = \frac{10}{30} * \frac{5}{30- 1}[/tex]
[tex]P(Caramel\ and\ Coconut) = \frac{10}{30} * \frac{5}{29}[/tex]
[tex]P(Caramel\ and\ Coconut) = \frac{1}{3} * \frac{5}{29}[/tex]
[tex]P(Caramel\ and\ Coconut) = \frac{5}{87}[/tex]
the functions y=x^2+ (c/x^2) are all solutions of equation: xy′ 2y=4x^2, (x>0). find the constant c which produces a solution which also satisfies the initial condition y(6)=4. c= ______--
The constant c that produces a solution satisfying the initial condition y(6) = 4 is c = 24.
To find the constant c that satisfies the given equation and the initial condition, we need to substitute the function y = x² + (c/x²) into the differential equation and solve for c. The given equation is xy' * 2y = 4x².
First, we differentiate y with respect to x to find y',
y = x² + (c/x²)
y' = 2x - (2c/x³)
Now we substitute y and y' into the differential equation,
xy' * 2y = 4x²
x(2x - (2c/x³)) * 2(x² + (c/x²)) = 4x²
Simplifying,
2x³ - 2cx + 4c = 4x²
Rearranging,
2x³ - 4x² - 2cx + 4c = 0
Now we substitute x = 6 and y = 4 (from the initial condition y(6) = 4) into the equation,
2(6)³ - 4(6)² - 2(6)c + 4c = 0
432 - 144 - 12c + 4c = 0
288 - 8c = 0
8c = 288
c = 36
Therefore, the constant c that produces a solution satisfying the initial condition y(6) = 4 is c = 36.
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Describe a situation that can be represented by the integer - 6
Answer:
One Chilly Night, Elijah Was Sleeping but Then Woke Up. He Realized It Was 45 Degrees According To the AC Monitor, So He Changed it To 70 Degrees But The Monitor Broke And Changed to -6 DEGREES!!
Step-by-step explanation:
A situation that can be represented by the integer - 6 was envisaged.
What are integers?An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
One day maths teacher decided to take a random test
There were 16 questions each of 4 marks and 1 mark deduction for each wrong answer, with no penalties for non-attempt.
David was so good at guessing. He guessed all the 16 answers out of which 2 were correct and 14 were incorrect.
So, the total marks that David got = 4(2)-1(14) = 8-14 =-6
Thus, a situation that can be represented by the integer - 6 was envisaged.
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The circumference of a circle is 127 cm. What is the area,
in
square centimeters?
Express your answer in terms of Pi.
Tuition for one year at Mount Tusk University is $13,400. Elijah has saved
$1,800 for this year's tuition. His parents have agreed to pay $5,000 this
year, and he earned a football scholarship for $3,500. Elijah hopes to earn
the rest of the money through his work-study job tutoring in the math
center. How much money does Elijah need to earn tutoring? (Enter the
quantity only)
Your answer
Answer:
The answer is 3,100
Step-by-step explanation:
If you subtract the 8,500 from his parents and his football scholarship you get 4,900 and then take the 1,800 from his saved money, You get what he still needs, which is 3,100.
can you guys help me please as much as you can ^^
Answer:
Step-by-step explanation:
m<1 = 50
m<2 = 22
m<3 = 108
m<4 = 50
m<5 = 65
m<6 = 50
m<7 = 43
m<8 = 65
m<9 = 75
m<10 = 18
m<11 = 25
m<12 = 40
m<13 = 115
m<14 = 65
m15 = 115
Find the slope of the line
Answer:
2/3
Step-by-step explanation:
Answer:
Slope = -6
Step-by-step explanation:
This XP set is worth a maximum points 1) As of 5/12/22. 72.7% of the residents of Washington state were fully vaccinated against CV19. Also, the population of our state is about 74 million people. a) Suppose that random samples of size n 50 are selected from this state's population. Let X represent the number people in each sample that are fully vaccinated against CV19 The variable X has an approximately Binomial distribution, with n 50 and D 727 Using the special Binomial formulas, compute the mean and the sigma of Round each value to the nearest tenth b) Refer to part . Which specific values of this variable X are within 3- sigma of its mean value? (OW, what are the common numbers of fully vaccinated people you'd expect to find in samples of this size, given the 72.7% fully vaccinated percentage?) c) Refer to part a. Use your calculator / technology like the "binompat and "binomcd commands on the TI-84) to help answer the following questions Report each probability correct to four decimal places Find the probability that one of these samples has exactly 35 fully vaccinated people in ite find the value of PX - 3571 Is this an unusual event using the 5% probability criterion? 10 Find the probability that one of these samples has 25 or fewer fully vaccinated people in it be find the value of PX $25)) is this an unusual event, using the 5% probability criterion? 30 IP 3: DO %: . $ 4 % 5 . # 3 $ 4 % 5 & 7 6 > 0 00 9 E R T T Y U 0 P D F G H J I KL < < C V B N M 1
Random samples of size 50 are taken from this population, and the number of fully vaccinated individuals in each sample, represented by the variable X, follows an approximately binomial distribution with n = 50 and p = 0.727.
(a) Using the binomial formulas, the mean (μ) of X is calculated as np, which is 50 * 0.727 = 36.4, rounded to the nearest tenth. The standard deviation (σ) is given by the square root of np(1-p), which becomes √(50 * 0.727 * 0.273) ≈ 4.1.(b) To determine the values within 3 sigma of the mean, we calculate 3 times the standard deviation (3σ) and find the range around the mean: 36.4 ± 3 * 4.1, resulting in the range of approximately 24.1 to 48.7. Therefore, the common numbers of fully vaccinated people expected in samples of this size, given the 72.7% vaccination rate, would fall within this range.(c) By using appropriate commands on a calculator or technology, the following probabilities can be determined:
The probability of one sample having exactly 35 fully vaccinated people is obtained from the binomial distribution as P(X = 35), which can be calculated using the binompdf command.
The value of P(X ≤ 25) can be found using the binomcdf command, representing the probability of having 25 or fewer fully vaccinated people in a sample. The probabilities should be reported to four decimal places for accuracy.
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MATH PLEASE HELP!! HELP BADLY NEEDED....
simplify each of the following.
5.1.
[tex]2 sin(90 - x ) - cos(360 - x)[/tex]
Step-by-step explanation:
[tex]2 \sin(90 - x) - \cos(360 - x) [/tex]
[tex]2 \cos(x) - \cos(x) [/tex]
[tex] \cos(x) [/tex]
If you give me right answer will cashapp money
Answer:
x=8
Step-by-step explanation:
The ratio of the sides is 7:14=1:2. So, the ratio of DF:XZ is 1:2. DF=2x-5, and XZ=22. This makes the ratio. 2x-5:22=1:2. That means 2x-5 is half of 22, which is 11. We can solve from there.
2x-5=11Add 5, 2x=16Divide by 2, x=8Check your work:
2(8)-5=1116-5=1111=11what two number have an absolute value of 12?
Answer:
The absolute value of 12, is 12...
Step-by-step explanation:
Answer:
-12
Step-by-step explanation:
In a survey of 3203 adults, 1447 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. Interpret the results. A 99% confidence interval for the population proportion is ??
Answer:
(0.4291, 0.4743)
Step-by-step explanation:
Using the relation :
p ± Zcritical * Sqrt[(p(1-p)) / n]
P = x / n =. 1447 / 3203 = 0.4517
1 - p = 0.5483
Zcritical at 99% = 2.575
Sqrt[(p(1-p)) / n] = sqrt(0.4517(0.5483)) / 3203) = 0.008793
p ± Zcritical * 0.008793
Lower boundary = 0.4517 - (2.575 * 0.008793) = 0.4291
Upper boundary = 0.4517 + (2.575 * 0.008793) = 0.4743
(0.4291, 0.4743)
A bakery made 55 boxes of rolls. Each box holds 12 rolls. How many rolls were made in all?
Make an equation to represent the problem. Drag numbers and symbols to the lines.
55
12
+
X
Construct an equation for a function with a zero at -2 and a double zero at 3.
Step-by-step explanation:
feeling the compa
Como te amo mucho
Suppose you place a $35 bet on a horse with a 2:7 odds against winnning. Determine the winning payout for this horse.
The winning payout for the horse is $45
To determine the winning payout for the horse, you need to use the following formula:
Odds against winning: B / (A + B)
Betting amount: X Payout: X + (X * B / A)where A is the denominator of the odds and B is the numerator of the odds.
Here, the odds against winning are 2:7.
So, the denominator (A) is 7 and the numerator (B) is 2.
The betting amount is $35.
Plugging these values into the formula:
Payout = 35 + (35 * 2 / 7)
Payout = $45.
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Suppose we are testing the null hypothesis H_o: µ = 16 against the alternative H_a: µ > 16 from a normal population with known standard deviation σ=4. A sample of size 324 is taken. We use the usual z statistic as our test statistic. Using the sample, a z value of 2.34 is calculated. (Remember z has a standard normal distribution.)
a) What is the p value for this test? ______
b) Would the null value have been rejected if this was a 2% level test?
OY
ON
c) Would the null value have been rejected if this was a 1% level test?
OY
ON
d) What was the value of x calculated from our sample? _______
a) The p- value is 0.0094.
b) True
c) Yes
To calculate the p-value for the test, we can use the standard normal distribution table or a statistical calculator.
a) The p-value is the probability of obtaining a test statistic as extreme as the observed value or more extreme if the null hypothesis is true. Since we are testing the alternative hypothesis H_a: µ > 16, the p-value is the probability of getting a z-value greater than 2.34.
Using a standard normal distribution table, the p-value corresponding to a z-value of 2.34 is 0.0094.
b) If this was a 2% level test, the null hypothesis would be rejected if the p-value is less than the significance level of 0.02.
Since the p-value (0.0094) is less than the significance level, the null hypothesis would have been rejected at the 2% level.
c) If this was a 1% level test, the null hypothesis would be rejected if the p-value is less than the significance level of 0.01.
Since the p-value (0.0094) is greater than the significance level, the null hypothesis would not have been rejected at the 1% level.
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Jasmine scored a 85 on the last math test. The class average was a 76 with a standard deviation of 4.5. So, XN(76,4,5) Jasmine's Z-score is This tells you that 85 is standard deviations to the left or right) of the mean, 14. The number of problems on all math exams are normal distributed. What is the probability a randomly selected math exam has fewer than 15 questions if the mean is 20 questions with a standard deviation of 2.5? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary. A city has around 890 thousand people. There are 123 parks in this city. What is the number of parks per capita in this city? Write your answer in scientific notation.
Jasmine's Z-score is 2. The number of parks per capita in the city is [tex]1.38 * 10^-4[/tex] in scientific notation.
To calculate Jasmine's Z-score, we can use the formula:
Z = (X - μ) / σ
where X is the individual score (85), μ is the mean (76), and σ is the standard deviation (4.5).
Z = (85 - 76) / 4.5
Z = 9 / 4.5
Z = 2
Since Jasmine's Z-score is 2, this tells us that her score of 85 is 2 standard deviations to the right of the mean.
Now let's calculate the probability of randomly selecting a math exam with fewer than 15 questions using the mean of 20 and a standard deviation of 2.5.
To apply the empirical rule, we need to determine how many standard deviations 15 is away from the mean.
Z = (X - μ) / σ
Z = (15 - 20) / 2.5
Z = -5 / 2.5
Z = -2
Since 15 is 2 standard deviations to the left of the mean, we can use the empirical rule to estimate the probability.
According to the empirical rule:
The data is within one standard deviation of the mean for about 68% of the time.
The data is within 2 standard deviations of the mean for about 95% of the time.
99.7% of the data are contained within a 3 standard deviation range around the mean.
Since 15 is beyond 2 standard deviations to the left, the probability of randomly selecting a math exam with fewer than 15 questions would be very close to 0. In this case, we can assume it's effectively 0%.
Now let's calculate the number of parks per capita in the city with 890,000 people and 123 parks.
Number of parks per capita = Number of parks / Population
Number of parks per capita = 123 / 890,000
To write the answer in scientific notation, we can express 890,000 as 8.9 x 10^5:
Number of parks per capita =[tex]123 / (8.9 * 10^5)[/tex]
Calculating the result:
Number of parks per capita =[tex]1.38 * 10^-4[/tex]
Therefore, the number of parks per capita in the city is[tex]1.38 * 10^-4[/tex] in scientific notation.
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Dani has only 1/2 of a cup of baking mix. She needs 3/4 of a cup for one batch of muffins. Which solution method shows how much of a batch of muffins Dani can make?
Answer:
Step-by-step explanation:
Dani has only 1/2 of a cup of baking mix. She needs 3/4 of a cup for one batch of muffins. Which solution method shows how much of a batch of muffins Dani can make?
If 25% of a number is 65 and 60% of the same number is 156, find 35% of that number.
Answer:
35% of that number is 91.
Step-by-step explanation:
we need to first find 25% of what number equals 65.
65×100÷25 = 260
Then, if you use the same method again, 60% of 260 would be 156.
We know "that" number is 260, and all we need to do is find 35% of it.
35% of 260 = 91
Hope this helped :)
maths equation : solve (2 - x)² < 4/25
Answer:
8/5 < x < 12/5
Step-by-step explanation:
(2 - x)² < 4/25
2 - x < ±2/5
2 - x < 2/5
-x < -8/5
x > 8/5
2 - x > -2/5
-x > -12/5
x < 12/5
Therefore, your answer is 8/5 < x < 12/5
Which would be the next step? Does anyone know? Please, help.
Answer:
∠DAB = ∠DBA
Then AD=DB from above statement
Mikel is trying to save for college expenses. He has a job, but can only afford to put $20 per month aside. He has 4 years until he will need to pay for college. How much will he have saved by the end of 4 years?
Answer:
960
20 times 12 moths to get 240 then multiply that by 4 years and get 960 .
Step-by-step explanation:
sorry if wrong ]
have a good day /night
may i pleae have a branlliest .
20 x 12=240 x 4 =960
Answer:
960
Step-by-step explanation:
What is the value of the output when the
input is 18?
Answer:
Any number less than greater than or equal to 18
Step-by-step explanation:
I give brainiest!!!!!
Answer:
c. 4
Step-by-step explanation:
yan sagot
using the equation y=x , what would be the value of y if the value of x is 2
Answer:
y = 2
Step-by-step explanation:
y = x
x = 2
Plug in the given value.
y = (2)
This is already simplified.
Therefore, when x = 2, y = 2.
Hope this helps!
Will give crown for the RIGHT answer please do not mess around or give me weird links
Answer:
28
Step-by-step explanation: