(a) The limit of (3x² - 2x + 5)/(6x + 7) as x approaches 143 is approximately 70.42. (b) The limit of sin(2x - 1)² as x approaches infinity does not exist (DNE). (c) The limit of (2x² - 9)/x as x approaches infinity is infinity.
To find the limit, substitute the value of 143 into the expression:
(3(143)² - 2(143) + 5)/(6(143) + 7) = (3(20449) - 286 + 5)/(860 + 7) = (61347 - 286 + 5)/(867) = 61066/867 = 70.42 (approx).
As x approaches infinity, the function sin(2x - 1) oscillates between -1 and 1. When squared, the function does not converge to a specific value but keeps oscillating between 0 and 1. Therefore, the limit does not exist.
Dividing every term in the numerator and denominator by x, we get (2x²/x - 9/x) = 2x - 9/x. As x approaches infinity, the second term, 9/x, approaches 0 since the denominator grows infinitely. Therefore, the limit simplifies to infinity.
Learn more about limits here: brainly.com/question/12211820
#SPJ11
Please state the following definitions: A. Classical Probability
B. Relative frequency probability C. Subjective probability
Subjective probability does not rely on statistical data or mathematical calculations but rather on the individual's assessment of the likelihood of an event based on their own subjective reasoning and intuition. It is often used in situations where objective data or precise calculations are not available or applicable.
A. Classical Probability:
Classical probability, also known as "a priori" or "theoretical" probability, is based on the assumption that all outcomes of an experiment are equally likely. It is used for situations where the outcomes can be determined through theoretical analysis or prior knowledge of the underlying probability distribution. In classical probability, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
B. Relative Frequency Probability:
Relative frequency probability, also known as "empirical" or "experimental" probability, is based on observations and data from repeated experiments or occurrences of an event. It involves determining the probability of an event by observing the relative frequency of its occurrence in a large number of trials. The relative frequency of an event is calculated by dividing the number of times the event occurs by the total number of trials or observations.
C. Subjective Probability:
Subjective probability, also known as "personal" or "belief" probability, is based on an individual's personal judgment or belief about the likelihood of an event occurring. It takes into account subjective factors such as personal experiences, opinions, and biases. Subjective probability does not rely on statistical data or mathematical calculations but rather on the individual's assessment of the likelihood of an event based on their own subjective reasoning and intuition. It is often used in situations where objective data or precise calculations are not available or applicable.
Learn more about probability here
https://brainly.com/question/25839839
#SPJ11
Previous Problem Problem List Next Problem (1 point) Find the length L of the curve R(t)e cos(3t) i + e* sin(3)j + 3ek over the interval (2,5) L-
In this question, we have to find the length of the curve R(t)e cos(3t) i + e* sin(3)j + 3ek over the interval (2,5).
We have the formula for arc length L which is:
L = ∫(b, a) √((dx/dt)²+(dy/dt)²+(dz/dt)²) dt. Where b and a are the upper and lower limits of t.
The parametric equation of the given curve is r(t) = R(t)cos(3t)i + R(t)sin(3t)j + 3R(t)k.
So, we will have to calculate the first derivative of the curve. Let's take the first derivative of the equation r(t):
r'(t) = (-R(t)sin(3t) + 3R'(t)cos(3t))i + (R(t)cos(3t) + 3R'(t)sin(3t))j + 3R'(t)k.
Now, we will calculate the magnitude of r'(t):
|r'(t)| = √((-R(t)sin(3t) + 3R'(t)cos(3t))²+(R(t)cos(3t) + 3R'(t)sin(3t))²+(3R'(t))²).
Substitute the value of R(t) = t in the above equation.|r'(t)| = √(t² + 9t²) = √10t² = √10t.
Substitute the limits of t in the above equation.|r'(t)| = ∫(5, 2) √10t dt = √10 ∫(5, 2) t dt = √10 [(t²/2)] (5, 2) = √10 [(25/2)-(4/2)] = √10 [21/2].
The length L of the curve R(t)e cos(3t) i + e* sin(3)j + 3ek over the interval (2,5) is √10 [21/2].
To know more about parametric equation visit:
brainly.com/question/30286426
#SPJ11
Do Men Talk Less Than Women? The accompanying table gives results from a study of the words spoken in a day by men and women, and the original data are in Data Set 17 in Appendix B (based on "Are Women Really More Talkative Than Men?" by Mehl et al., Science, Vol. 317, No. 5834). Use a 0.01 significance level to test the claim that the mean number of words spoken in a day by men is less than that for women. Calculate Test Statistic and state reject or fail to reject Null Hypothesis. Men n1=180μ1=15668.5 s=8632.5 Women n2=210μ2=16215s=7301.2 t=0.676 fail to reject Null Hypothesis. t=0.676 reject Null Hypothesis. t=−0.676 reject Null Hypothesis. t=.0.676 fail to reject Null Hypothesis.
The calculated test statistic (-0.676) does not fall in the critical region, we fail to reject the null hypothesis.
To test the claim that the mean number of words spoken in a day by men is less than that for women, we can conduct a one-tailed independent samples t-test. The null hypothesis (H0) states that there is no significant difference between the mean number of words spoken by men and women, while the alternative hypothesis (H1) states that the mean number of words spoken by men is less than that for women.
The given information includes the sample sizes (n1 = 180 for men, n2 = 210 for women), the sample means (μ1 = 15668.5 for men, μ2 = 16215 for women), the sample standard deviations (s = 8632.5 for men, s = 7301.2 for women), and a significance level of 0.01.
To calculate the test statistic, we can use the formula for the t-test:
t = (μ1 - μ2) / sqrt((s1^2/n1) + (s2^2/n2))
Substituting the given values, we get:
t = (15668.5 - 16215) / sqrt((8632.5^2/180) + (7301.2^2/210))
t ≈ -0.676
Comparing the calculated test statistic (-0.676) with the critical value at a 0.01 significance level for a one-tailed test, we find that the critical value is greater than -0.676.
Thus, based on the given information, we conclude that there is not enough evidence to support the claim that the mean number of words spoken in a day by men is less than that for women.
For more such questions on test statistic
https://brainly.com/question/29576929
#SPJ8
Let Y1 and Y2 be independent random variables with Yi∽N(0,1). Let [X1X2]=[μ1μ2]+C[Y1Y2] where C:2×2=[12δ2δ1]−21. Derive the probability density function (pdf) of [X1X2].
The probability density function (pdf) of [X1X2] is fX(x1,x2) = (1/(2π(1 - 4δ²))) * exp[-((x1 - μ1)² + (x2 - μ2)² - 2δ(x1 - μ1)(x2 - μ2))/2]
How to derive probability density functionThis given transformation [X1X2]=[μ1μ2]+C[Y1Y2] can be written as;
X = μ + CY
where
X = [X1 X2]ᵀ,
Y = [Y1 Y2]ᵀ,
μ = [μ1 μ2]ᵀ, and
C = [1 2δ; 2δ 1]⁻¹.
The Jacobian of the transformation is given in this form;
J = det(dX/dY) = det(C) = (1 - 4δ²)⁻¹
Remember, Y1 and Y2 are independent and normally distributed with mean 0 and variance 1.Their joint pdf is written as
fY(y1,y2) = (1/(2π)) × exp(-(y1² + y2²)/2)
when we use the transformation formula for joint pdfs, we have;
fX(x1,x2) = fY(y1,y2) × |J| = (1/(2π(1 - 4δ²))) × exp(-Q/2)
where Q = (x1 - μ1)² + (x2 - μ2)² - 2δ(x1 - μ1)(x2 - μ2).
This is the pdf of a bivariate normal distribution with mean μ and covariance matrix Σ,
where:
μ = [μ1 μ2]ᵀ
Σ = [1 δ; δ 1-4δ²]
Hence, the joint pdf of X1 and X2 is:
fX(x1,x2) = (1/(2π(1 - 4δ²))) × exp[-((x1 - μ1)² + (x2 - μ2)² - 2δ(x1 - μ1)(x2 - μ2))/2] which is the probability density function (pdf) of [X1 X2]ᵀ.
Learn more on probability density function on https://brainly.com/question/15714810
#SPJ4
Measures of variability match-up There are multiple ways to refer to or describe a variance or a standard deviation of either a population or a sample. Likewise, each measure has multiple appropriate equations or symbols. The first table consists of alternative ways of referring to each of these measures. The second table consists of equations or symbols for each of these measures. Alternative Description a. Square root of the average squared distance from u b. Mean squared deviation from M c. Mean squared deviation from u d. Standard distance from M
Each measure has different appropriate equations or symbols and multiple alternative ways of referring to or describing a variance or a standard deviation of either a population or a sample.
Measures of variability are used to explain how far apart data is dispersed from the central tendency.
There are a variety of variability measures that can be used to explain the extent to which the data set is spread out. Variance, standard deviation, range, and interquartile range are examples of variability measures that can be used to define variability.
The variance is the square of the standard deviation, and it is the most commonly used measure of variability. The range is a measure of the variability between the largest and smallest values in a set of data.
The interquartile range is another measure of variability that focuses on the middle 50% of data.
The four alternatives for the Measures of Variability are as follows:a. The square root of the average squared distance from u is also known as Standard deviation.
Standard deviation is calculated by taking the square root of the variance.b. Mean squared deviation from M refers to the variance in statistics.
In the population, it is calculated as σ² and in a sample, it is calculated as s².c.
Mean squared deviation from u is referred to as mean deviation or mean absolute deviation. It is the sum of the differences between the mean of the observations and the absolute value of each observation divided by the total number of observations.d.
The standard distance from M is known as Z-score. It is calculated by subtracting the mean from the observation and then dividing the result by the standard deviation.
The four equations or symbols for the Measures of Variability are as follows:
a. Standard deviation (s) = √ Σ(x-µ)² / Nb. Variance (s²) = Σ(x-µ)² / N or Σ(x-µ)² / (N-1) if it is a samplec.
Mean Deviation (MD) = Σ|X - µ| / Nd. Z-score = (X - µ) / σ, where X is the raw score, µ is the population mean, and σ is the standard deviation.In conclusion, variability measures like variance, standard deviation, range, and interquartile range are used to define variability.
Each measure has different appropriate equations or symbols and multiple alternative ways of referring to or describing a variance or a standard deviation of either a population or a sample.
To know more about standard deviation visit;
https://brainly.com/question/475676
#SPJ11
Variance (σ² or s²), represents the mean squared deviation from the mean. Standard deviation (σ or s), which is the square root of the variance, measures how far data values are from their mean and provides the overall variation or the spread of data.
Explanation:In measures of variability, we often refer to variance or standard deviation. To start, variance is denoted by the symbol σ² for population variance and s² for sample variance. It is considered as the mean squared deviation from the mean, where for a set of data (x), a deviation can be represented as x - µ (for population data) or x - x (for sample data).
Standard Deviation meanwhile, is represented by σ for population standard deviation and s for sample standard deviation. It equates to the square root of the variance. As such, you can think of the standard deviation as a special average of the deviations, which measures how far data values are from their mean. The standard deviation provides us an understanding of the overall variation or the spread of data in a dataset.
Learn more about Measures of Variability here:https://brainly.com/question/31636027
#SPJ12
Analyze the scenario and complete the following:
Complete the discrete probability distribution for the given
variable.
Calculate the expected value and variance of the discrete
probability distribut
The expected value of the number of heads is 1.5, and the variance is 1.25.
The probability of getting 0 heads is 1/8, because there is only 1 way to get 0 heads in 3 coin flips (all tails). The probability of getting 1 head is 3/8, because there are 3 ways to get 1 head in 3 coin flips (HT, TH, TT). The probability of getting 2 heads is 3/8, because there are 3 ways to get 2 heads in 3 coin flips (HHT, HTH, THH). The probability of getting 3 heads is 1/8, because there is only 1 way to get 3 heads in 3 coin flips (HHH).
The discrete probability distribution for the number of heads in 3 coin flips is:
Heads | Probability
-------|---------
0 | 1/8
1 | 3/8
2 | 3/8
3 | 1/8
The expected value of the number of heads is calculated by multiplying the probability of each outcome by the value of that outcome, and then adding all of the products together. In this case, the expected value is:
E = (1/8)(0) + (3/8)(1) + (3/8)(2) + (1/8)(3) = 1.5
The variance of the number of heads is calculated by subtracting the square of the expected value from each outcome, multiplying the result by the probability of that outcome, and then adding all of the products together. In this case, the variance is:
Var = (1/8)(0 - 1.5)^2 + (3/8)(1 - 1.5)^2 + (3/8)(2 - 1.5)^2 + (1/8)(3 - 1.5)^2 = 1.25
Learn more about variance here:
brainly.com/question/31432390
#SPJ11
The average score of 100 students taking a statistics final was 70 with a standard deviation of 7 . Assuming a normal distribution, what test score separates the top 25 N of the students from the lower 75% of students? 7525 7000 7469 6531
This means that students who have scored 65.282 or lower are in the lower 75% of students, and students who have scored above 65.282 are in the top 25% of students. Therefore, the test score that separates the top 25% of the students from the lower 75% of students is approximately 65.28.
We are given the following information: Average score of 100 students = 70Standard Deviation of 100 students = 7Now we have to find out the test score that separates the top 25% of the students from the lower 75%.
The normal distribution curve is given as: Normal distribution curve As per the Empirical Rule, in a normal distribution curve, If μ is the mean and σ is the standard deviation, then, About 68% of the data falls within μ ± σAbout 95% of the data falls within μ ± 2σAbout 99.7% of the data falls within μ ± 3σNow, let's calculate the μ + σ.Z score for the top 25% of the students is given as:
Z = -0.674Z = (x - μ)/σ-0.674 = (x - 70)/7x - 70 = -4.718x = 70 - 4.718x = 65.282.
To know more about standard deviation visit:-
https://brainly.com/question/4456025
#SPJ11
A trueffalse test has 110 questions. A passing grade is 61% or more correct answers.
a. What is the probability that a person will guess correctly on one true/false question? b. What is the probability that a person will guess incorrectly on one question? c. Find the approximate probability that a person who is just guessing will pass the test. d. If a similar test were given with multiple-choice questions with four choices for each
In a true/false test with 110 questions, a passing grade is defined as scoring 61% or more correct answers. The probability of guessing correctly on a true/false question is 0.5, as there are two possible outcomes (true or false) and guessing is essentially a random chance.
a. The probability of guessing correctly on a true/false question is 0.5, as there are two possible outcomes (true or false) and guessing is essentially a random chance.
b. Similarly, the probability of guessing incorrectly on a true/false question is also 0.5, since the probability of guessing correctly is equal to the probability of guessing incorrectly.
c. To determine the approximate probability of passing the test when guessing, we need to consider the passing grade requirement of 61% or more correct answers. Since each question has a 50% chance of being answered correctly or incorrectly, we can use the binomial distribution to calculate the probability of getting at least 61% of the questions correct.
d. If the test format changes to multiple-choice questions with four choices each, the probability of guessing correctly on any given question becomes 0.25, while the probability of guessing incorrectly becomes 0.75. The calculation for the approximate probability of passing the test would need to be adjusted using these new probabilities.
To know more about probability, click here: brainly.com/question/31828911
#SPJ11
Find the probability that the waiting time is between 10 and 22 minutes. The probability that the waiting time is between 10 and 22 minutes is ____
The probability that the waiting time is between 10 and 22 minutes is 0.9836.
The probability that the waiting time is between 10 and 22 minutes is calculated by using the Normal distribution function.
Let us consider that the given waiting times follow a normal distribution with a mean of 16 minutes and a standard deviation of 2.5 minutes.
The z-score for 10 minutes is calculated below. z-score for 10 minutes= (10 - 16) / 2.5= - 2.4The z-score for 22 minutes is calculated as below.
z-score for 22 minutes= (22 - 16) / 2.5= 2.4
Therefore, the probability of waiting time being between 10 and 22 minutes can be calculated as below.
The probability of waiting time is between 10 and 22 minutes= P(-2.4 < z < 2.4)By referring to the standard normal distribution table, we get the value of 0.9918 for a z-score of 2.4.
Similarly, we get the value of 0.0082 for a z-score of - 2.4.
Now, we can calculate the probability as below.
Probability of waiting time is between 10 and 22 minutes= P(-2.4 < z < 2.4)= 0.9918 - 0.0082= 0.9836
Therefore, the probability that the waiting time is between 10 and 22 minutes is 0.9836.
To learn about probability here;
https://brainly.com/question/30449584
#SPJ11
Discussion Topic
Businesses are structured to make money. That's part of what defines success for a
business. Company leaders strive to generate as much profit as possible by increasing
revenue while decreasing costs.
It costs the company money to provide benefits to employees, such as insurance. And
yet companies often provide health and dental insurance for their employees. They also
pay for insurance to help employees who become injured or disabled.
Given the costs associated with insurance, why do companies provide insurance plans
to employees?
Overall, providing Insurance plans can be a win-win situation for both companies and their employees.
Companies provide insurance plans to employees for a number of reasons. One of the main reasons is to attract and retain talented employees. Offering health and dental insurance, as well as insurance to help employees who become injured or disabled, is a way for companies to demonstrate that they value their employees and are willing to invest in their well-being and long-term success.
Providing insurance plans can also help companies to reduce turnover and the associated costs of recruiting and training new employees. When employees have access to quality healthcare and other insurance benefits, they are more likely to stay with their current employer, rather than seeking opportunities elsewhere.
In addition, providing insurance plans can help companies to improve employee productivity and overall job satisfaction. When employees have access to healthcare and other benefits, they are more likely to be healthy, happy, and engaged in their work. This can lead to higher levels of productivity and better outcomes for the company as a whole.
Despite the costs associated with providing insurance plans, many companies see it as a necessary investment in their employees and their long-term success. By offering insurance plans, companies can attract and retain talented employees, reduce turnover, and improve productivity and job satisfaction. Overall, providing insurance plans can be a win-win situation for both companies and their employees.
For more questions on Insurance .
https://brainly.com/question/29064772
#SPJ8
Hu leaves school to walk home. His friend, Jasmine, notices 0.2 hours later that Hu forgot his phone at the school. So Jasmine rides her bike to catch up to Hu and give him the phone. If Hu walks at 2.7 mph and Jasmine rides her bike at 11.6 mph, find how long (in hours) she will have to ride her bike until she catches up to him. Round your answer to 3 places after the decimal point (if necessary) and do NOT type any units (such as "hours") in the answer box. Time for Jasmine to catch up to Hu: hours
To find the time it takes for Jasmine to catch up to Hu, we can set up a distance equation based on their respective speeds.
Let's assume that the time it takes for Jasmine to catch up to Hu is represented by t (in hours). In the 0.2 hours that Jasmine waits before starting, Hu has already walked a distance of 2.7 mph * 0.2 hours = 0.54 miles. Now, let's consider the distance traveled by both Jasmine and Hu when they meet. Since Jasmine catches up to Hu, the distance traveled by Jasmine on her bike must be equal to the distance Hu has already walked, plus the distance both of them will travel together. The distance traveled by Jasmine on her bike is given by the formula: distance = speed * time. So the distance traveled by Jasmine on her bike is 11.6 mph * t. Therefore, we can set up the equation: 0.54 miles + 11.6 mph * t = 2.7 mph * t. To solve for t, we can rearrange the equation: 11.6 mph * t - 2.7 mph * t = 0.54 miles. 8.9 mph * t = 0.54 miles. Now, we can solve for t: t = 0.54 miles / 8.9 mph. Using the given values and rounding to 3 decimal places, we find: t ≈ 0.061 hours.
Therefore, Jasmine will have to ride her bike for approximately 0.061 hours (or 3.66 minutes) until she catches up to Hu.
To learn more about equation click here: brainly.com/question/29657983
#SPJ11
2 points Find the area bounded by the curve 2x² + 4x + y - 0 and the line y + x = 0 a. 1.000 b. 1.125 c. 1.525 d. 1.823 e. NONE OF THE ABOVE O A B O E TU Evaluate sec²20d0 a. 00.33 b. 0.5 c. 0.67 d. 0.25 e. NONE OF THE ABOVE O A B O 2 points
The area bounded by the curve 2x² + 4x + y = 0 and the line y + x = 0 is 1.525.
To find the area bounded by the curve and the line, we need to determine the intersection points. We start by solving the system of equations formed by the curve and the line:
2x² + 4x + y = 0
y + x = 0
From the second equation, we have y = -x. Substituting this into the first equation:
2x² + 4x - x = 0
2x² + 3x = 0
Factoring out x, we get:
x(2x + 3) = 0
This equation has two solutions: x = 0 and x = -3/2. Substituting these values back into the line equation, we find the corresponding y-values: y = 0 and y = 3/2.
The bounded area is the integral of the curve between these intersection points:
A = ∫[0, -3/2] (2x² + 4x + y) dx
Evaluating this integral, we find the bounded area to be 1.525.
Therefore, the answer is c. 1.525.
Learn more about finding the area here: brainly.com/question/29213222
#SPJ11
Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=15. Find the probability that a randomly selected adult has an 1Q between 90 and 120 . Click to view page 1 of the table. Click to view. page 2 of the table. The probability that a randomly selected adult has an IQ between 90 and 120 is (Type an integer or decimal rounded to four decimal places as needed.)
The probability that a randomly selected adult has an IQ between 90 and 120 is 0.6826 (rounded to four decimal places).
Given information:
Mean of IQ score, μ = 105
Standard deviation of IQ score, σ = 15
We need to find the probability that a randomly selected adult has an IQ between 90 and 120.
Using standard normal distribution,
we can write: Z = (X - μ) / σ
where Z is the standard score of X.
X
= IQ score
= 90 and 120
σ = 15
μ = 105Z1
= (90 - 105) / 15
= -1Z2
= (120 - 105) / 15
= 1
Probability of having IQ between 90 and 120= P(-1 < Z < 1)
Using standard normal table, we can find that P(-1 < Z < 1) is 0.6826. (rounded to four decimal places)
Therefore, the probability that a randomly selected adult has an IQ between 90 and 120 is 0.6826 (rounded to four decimal places).
Learn more about the normal distribution from the given link-
https://brainly.com/question/4079902
#SPJ11
A motor insurance company uses a no claim discount (NCD) system with four levels of discount listed as below: Level Discount (%)
0 0
1 25
2 30
3 40
A claims free year results in a transition to the next higher discount level or stays at the maximum discount level in the following year. On the other hand, claiming in a year results in moving down to the next lower discount level or stays at the zero-discount level in the following year. The probability of no claims in a year can be assumed to be equal to p in all years. (a) Write down the transition probability matrix P in terms of p, for the Markov chain with the given discount levels as the state space. (b) Determine the stationary distribution in terms of x, where x= p / 1−p ( 9 marks) (c) If the premium paid by a policyholder at level 0 is RM1,000, write down the average premium paid per policyholder per year in terms of x. (d) Assume further that a policyholder either makes no claims or only one claim in a year, and the average claim size is RM2,500, write down the average profit per policyholder per year that the insurance company makes in the long run. (e) Suppose that p=0.8. (i) Calculate the average premium paid per policyholder per year and the average profit per policyholder per year that the insurance company makes in the long run. (ii) Calculate the probability that a policyholder who starts at level 0 will be at the maximum NCD level after two years. (1 mark)
(a) Transition probability matrix, P is:P = [tex]\[\begin{bmatrix}1-p & p & 0 & 0\\1-p & 0 & p & 0\\1-p & 0 & 0 & p\\p & 0 & 0 & 1-p\end{bmatrix}\][/tex]This is obtained because the probability of no claims in a year is equal to p in all years.
(b) The stationary distribution is[tex]:x = \[p/(1-p)\]The stationary distribution is \[\pi =[1-x,{\text{ }}x/(1+0.25x),\text{ }0.25x\text{ }/(1+0.25x),\text{ }0.25x\text{ }/(1+0.25x)]\][/tex]
(c) Average premium paid per policyholder per year, in terms of x is:
[tex]P = 1000 \[/(1+0.25x+0.25x+0.25x^2)\][/tex]
(d) The average profit per policyholder per year that the insurance company makes in the long run is:50 + 0.3*2500 - P for Level 1;70 + 0.4*2500 - P for Level 2; where, 50, 70 are the probability of being at Level 0 and Level 3, respectively. And, P is the average premium paid per policyholder per year.
(e)
(i) The average premium paid per policyholder per year is given by:P = 1000/(1+0.25*4) = RM 607.14 The average profit per policyholder per year that the insurance company makes in the long run is:[tex](50 + 0.3*2500 - 607.14) \* (1-0.8)^\[infinity\] + (70 + 0.4*2500 - 607.14) \* 0.8/(1-0.8) = RM 5.3571[/tex]
(ii) The probability that a policyholder who starts at Level 0 will be at the maximum NCD level after two years is given by the following formula:[tex]\[\pi _3^2 =(0.25x)/(1+0.25x)\]Substituting x = 4, we get:\[\pi _3^2 =1/5\][/tex]
Hence, the probability that a policyholder who starts at Level 0 will be at the maximum NCD level after two years is 1/5.
To know more about stationary distribution visit :
https://brainly.com/question/32616973
#SPJ11
claim that the pass completion percentages have changed? Complete parts (a) through (e) beiow (a) Identify the claim and state H0 and Ha : What is the claim? A. The pass complesion peroentages have decressed. B. The pass completion percentages thave increased. C. The pass completion percentages have changed. D. The pass compietion percentages have not changed. Let μd be the hypothesized mean of the cifferences in the pass complesco percentages (freshman= sophiomorel. Then dis the sangie mean of the differences. What are H0 and Ha ? A. H0:H0=0 B. H0:Ha≥0 H3=Hd=0 Ha+Hedd<0 Ha=μa0
Options A, B, and D are not accurate. Option C ("The pass completion percentages have changed") correctly captures the claim being made
The claim being made is that the pass completion percentages have changed. The null hypothesis (H0) states that there is no change in the pass completion percentages, while the alternative hypothesis (Ha) states that there is a change. The correct answer for H0 and Ha is:
H0: μd = 0 (There is no change in the pass completion percentages)
Ha: μd ≠ 0 (There is a change in the pass completion percentages)
The claim is not about a specific direction of change (increase or decrease), but rather that a change has occurred. Therefore, options A, B, and D are not accurate.
Option C ("The pass completion percentages have changed") correctly captures the claim being made. The hypothesis statements H0 and Ha reflect the idea that the mean of the differences (μd) is being hypothesized to be equal to zero under the null hypothesis, while the alternative hypothesis allows for any non-zero difference.
To learn more about null hypothesis click here: brainly.com/question/29387900
#SPJ11
PLEASE I NEED THIS NOW!!
Find the area of the region.
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y = sin(x), y = 3x, x = π/2, x = π
To find the area of the region enclosed by the given curves, we integrate with respect to y.
To obtain the limits of integration, we set the two equations of y equal to one another and solve for x as follows:
sin(x) = 3x
Let's use numerical methods to solve for x. Newton's method may be used. Let's rewrite sin(x) = 3x as follows:
f(x) = sin(x) - 3x
We may find the value of x that satisfies this equation by finding the root of this function.
Using Newton's method, let's say we start with an initial guess of x1 = 1.
We apply the following recurrence equation to this guess:x_(n+1) = x_n - f(x_n)/f'(x_n) where f'(x_n) is the derivative of f(x) with respect to x and is defined as:
f'(x_n) = cos(x_n) - 3
The first few iterations of Newton's method are:
x2 = 0.5582818494 x3 = 0.4330296021 x4 = 0.4547655586 x5 = 0.4544582153 x6 = 0.4544580617 x7 = 0.4544580617 x8 = 0.4544580617
Once the value of x is known, we can find the area of the region enclosed by the given curves by integrating from x = 0 to x = x, where x is the value we found above. We integrate with respect to y, which gives us the following expression for the area of the region enclosed by the given curves:
We integrate with respect to y and obtain the following expression:
The region enclosed by the given curves is shown in the graph below. Since the curve y = sin(x) is below the curve y = 3x, we integrate with respect to y. The area of the region enclosed by the given curves is approximately 0.354156883 square units.
To know more about integrate visit:
brainly.com/question/31744185
#SPJ11
What hypothesis test should be used to test H₁: 0²2 O One-sample test of means O One-sample test of proportions One-sample test of variances ○ Two-sample test of means (independent samples) O Two-sample test of means (paired samples) O Two-sample test of proportions O Two-sample test of variances > 1
The answer is , Option ( b), the hypothesis test to determine whether the variance of the body weight measurements is equal to 22 or not can be done using a One-sample test of variances.
The hypothesis test that should be used to test H₁: σ² = 22 is One-sample test of variances.
A hypothesis test is a statistical test that examines two contradictory hypotheses about a population:
the null hypothesis and the alternative hypothesis.
The null hypothesis is a statement of the status quo, whereas the alternative hypothesis is a claim about the population that the analyst is attempting to demonstrate.
In the scenario where H₁: σ² = 22, the analyst will use a one-sample test of variances.
This hypothesis test is used to determine whether the sample variance is equal to the hypothesized variance value or if it is significantly different.
The variance is an essential measure of variability for numerical data.
If the variance of the population is unknown, it can be estimated using a sample's variance.
An example of a One-sample test of variances
In a study conducted to determine the variations in body weight measurements across several individual populations, a random sample of 50 individuals from population A is selected to determine the variability of body weight measurements of the population.
The hypothesis test to determine whether the variance of the body weight measurements is equal to 22 or not can be done using a One-sample test of variances.
To know more about Alternative hypothesis visit:
https://brainly.in/question/3231387
#SPJ11
The hypothesis test that should be used to test H₁: σ² = 0² is a one-sample test of variances.
A hypothesis test is a statistical tool that is used to determine if the outcomes of a study or experiment can be attributed to chance or if they are significant and have practical importance.
It is a statistical inference approach that examines two hypotheses: the null hypothesis (H₀) and the alternative hypothesis (H₁).
A one-sample test of variances is used to test the variance of a population. It is used to determine if the variance of the sample is equal to the variance of the population.
The null hypothesis states that the variance of the sample is equal to the variance of the population, while the alternative hypothesis states that they are not equal.
Hence, the hypothesis test that should be used to test H₁: σ² = 0² is a one-sample test of variances.
To know more about hypothesis test, visit:
https://brainly.com/question/17099835
#SPJ11
Within the stock market system, when the value of a stock increases it is represented as a (+) positive growth. When the value of a stock decreases, it is represented as a ( −) negative growth. On Tuesday, the value of a stock was $23.19 per share. On Wednesday, the value of the tock was $22.98 per share. On Thursday, the value of the stock was $23.03 per share. Ihat was the average growth of the stock over the three days?
To find the growth percentage between the days: Wednesday and Tuesday, Thursday and Wednesday, we will use the formula:
Growth = (Difference / Original Price) × 100%
Growth is defined to be the measure of how much a thing or a company or a country is improving and developing. Positive growth is defined as an increase while Negative growth is defined as a decrease. When it comes to stock market, growth is defined on whether the price of the stocks increased or decreased.
On Wednesday:
Growth = [(22.98 − 23.19) / 23.19] × 100%
Growth = (−0.0091) × 100%
Growth = −0.91%
On Thursday:
Growth = [(23.03 − 22.98) / 22.98] × 100%
Growth = 0.0022 × 100%
Growth = 0.22%
Therefore, the average growth over the three days
= (−0.91 + 0.22) / 2
= −0.345 or −0.35% (rounded to two decimal places).
Answer: The average growth of the stock over the three days is -0.35%.
Learn more about growth: https://brainly.com/question/29795656
#SPJ11
The mean hourly rate charged by attorneys in Lafayette, LA is $150 with a standard deviation of $25. What is the probability that an attorney charges more than 210/hour. Assume that hourly rates charged by attorneys are normally distributed. 0 Select one: a. 0.9918 b. 0.0082 c. 0.5082 d. 0.4918
The correct answer is b. 0.0082.
To calculate the probability that an attorney charges more than $210 per hour, we can use the Z-score and the standard normal distribution.
First, we need to calculate the Z-score, which measures the number of standard deviations a value is from the mean. The formula for the Z-score is:
Z = (X - μ) / σ
where X is the value we want to calculate the probability for, μ is the mean, and σ is the standard deviation.
In this case, X = $210, μ = $150, and σ = $25.
Z = (210 - 150) / 25 = 2.4
Next, we need to find the area under the standard normal distribution curve for a Z-score of 2.4, representing the probability that an attorney charges more than $210 per hour. We can look up this value in a standard normal distribution table or use a calculator.
The probability is approximately 0.0082.
Therefore, the correct answer is b. 0.0082.
Learn more about attorney charges here:
https://brainly.com/question/13917726
#SPJ11
Consider the function f(x) = cos x - 3x +1. Since f(0)f () <0. f(x) has a root in [o. If we use Newton-Raphson method, with xo = 0.5, what is x₂? (Answer must be in 8 decimal places)
The problem states that the function f(x) = cos(x) - 3x + 1 has a root in the interval [0, and asks to find the value of x₂ using the Newton-Raphson method with an initial guess of xo = 0.5. The solution is expected to be rounded to 8 decimal places.
To apply the Newton-Raphson method, we start with an initial guess of x₀ = 0.5. The iterative formula for Newton's method is given by the equation xₙ₊₁ = xₙ - f(xₙ) / f'(xₙ), where f(x) is the function and f'(x) is its derivative.
First, we calculate f(x₀) and f'(x₀). Plugging in x₀ = 0.5 into the function f(x), we get f(x₀) = cos(0.5) - 3(0.5) + 1 ≈ -1.52137971. Next, we find f'(x) by differentiating f(x) with respect to x, which gives f'(x) = -sin(x) - 3.
Now, we can apply the Newton-Raphson formula to find x₁:
x₁ = x₀ - f(x₀) / f'(x₀) = 0.5 - (-1.52137971) / (-sin(0.5) - 3).
Continuing this process, we iterate using the value of x₁ to find x₂:
x₂ = x₁ - f(x₁) / f'(x₁).
By performing the above calculations iteratively, rounding to 8 decimal places after each iteration, we can find the value of x₂ using the Newton-Raphson method.
Note: Since the problem does not provide the specific number of iterations required, the process can be repeated until the desired level of accuracy is achieved.
Therefore, by applying the Newton-Raphson method, we can find the value of x₂, which satisfies f(x) = 0, to the specified precision of 8 decimal places.
To learn more about interval click here:
brainly.com/question/11051767
#SPJ11
Which of the following represents the shell height if the shell method will be used to find the volume of solid of revolution by rotating the region bounded by x=5, y=-x+1 and y=0 about the y-axis? X-1 y-5 X-4 Dy+4 x+6 (F) none of these B
The correct answer is (F) none of these. The shell method cannot be used to find the volume of the solid of revolution in this case because the region is not bounded by a vertical axis.
The shell method is a method for finding the volume of a solid of revolution by rotating a thin strip of the region around an axis. The volume of the shell is given by the formula: V = 2πrh
where:
r is the distance from the axis of rotation to the edge of the shell
h is the thickness of the shell
In this case, the axis of rotation is the y-axis. The region is bounded by x = 5, y = -x + 1, and y = 0. However, the region is not bounded by a vertical axis. This means that the shell method cannot be used to find the volume of the solid of revolution.
If the region were bounded by a vertical axis, then the shell height would be equal to the difference between the upper and lower boundaries of the region. In this case, the upper boundary of the region is y = -x + 1 and the lower boundary is y = 0. Therefore, the shell height would be equal to -x + 1 - 0 = -x + 1.
However, since the region is not bounded by a vertical axis, the shell height cannot be determined. Therefore, the correct answer is (F) none of these.
To know more about formula click here
brainly.com/question/30098455
#SPJ11
An annuity immediate has semi-annual payments of 1,000 for 25 years at a rate of 6%, convertible quarterly. Find the present value.
The present value of the annuity immediate is approximately $12,542.23
To find the present value of an annuity immediate with semi-annual payments of $1,000 for 25 years at a rate of 6% convertible quarterly, we can use the present value of an annuity formula:
PV = P * [(1 - (1 + r)^(-nt)) / r]
Where:
PV = Present Value
P = Payment per period
r = Interest rate per period
n = Number of periods per year
t = Total number of years
In this case, the payment per period is $1,000, the interest rate per period is 6% divided by 4 (since it's convertible quarterly), the number of periods per year is 4 (quarterly payments), and the total number of years is 25.
Substituting these values into the formula:
PV = 1000 * [(1 - (1 + 0.06/4)^(-4*25)) / (0.06/4)]
Using a calculator, we can evaluate the expression inside the brackets and divide by (0.06/4) to find that the present value is approximately $12,542.23.
Therefore, The present value of the annuity immediate is approximately $12,542.23.
Learn more about annuity here:
https://brainly.com/question/14908942
#SPJ11
Consider the set N of positive integers to be the universal set. Sets H, T, E, and P are defined to the right. Determine whether or not the sets H' and P' are disjoint. Are H' and P' disjoint? O A. Yes, because there is at least one prime number that is greater than or equal to 100. O B. No, because there are no composite numbers less than or equal to 100. O C. No, because there is at least one composite number that is less than or equal to 100. O D. Yes, because there are no prime numbers greater than or equal to 100. H = {NEN|n> 100} T = {nEN| n<1,000} E = {nEN n is even} P = {nEN n is prime}
Answer:To find out whether the sets H' and P' are disjoint or not, we first need to find out the complement of each set H and P. The complement of set H will be all the positive integers less than or equal to 100, and the complement of set P will be all the composite numbers less than or equal to 100.
So, H' = {NEN|n ≤ 100} P' = {nEN n is composite ≤ 100}We know that a set is disjoint if its intersection with the other set is empty.
Therefore, we need to find out whether H' and P' have any common elements.
We know that the composite numbers are the product of prime numbers.
So, if we can find any prime number less than or equal to 100, then there will be a composite number less than or equal to 100, which will be in the set P'.
And, we know that there are many prime numbers less than or equal to 100, such as 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
So, there are composite numbers less than or equal to 100, which will be in set P'.
Hence, H' and P' are not disjoint.Answer: C. No, because there is at least one composite number that is less than or equal to 100.
To know more about disjoint visit:
https://brainly.com/question/29272324
#SPJ11
Two triangular pens are built against a barn. Four hundred ten meters of fencing are to be used for the three sides and the diagonal dividing fence (see figure). What dimensions maximize the area of the pen? Let A be the area of the pen. What is the objective function in terms of the length of the side of the pen perpendicular to the barn, x. A= (Type an expression.)
The objective function in terms of the length of the side of the pen perpendicular to the barn, `x` is given by the area equation `A` as: A = `(1/8)((820 - x)^2)`
The dimensions that maximize the area of the pen are, length of the side perpendicular to the barn `x = 102.5 m` and length of the side parallel to the barn `y = 205 m`.
Objective function in terms of the length of the side of the pen perpendicular to the barn, x.
The objective is to find an expression for the area A of the pen in terms of one variable.
Let's solve for the value of `y` first.
410 = 2y + x + d ... (1)
where d is the diagonal fence and is also the hypotenuse of the right triangles.
Then d = `sqrt(x^2 + y^2)`410 = 2y + x + `sqrt(x^2 + y^2)`
Let's isolate the square root term on one side of the equation as follows:`sqrt(x^2 + y^2)` = 410 - 2y - x
Squaring both sides, we get:`
x^2 + y^2 = 168100 - 820x + 4y^2 - 1640y + 4xy`
We can now express y in terms of x as follows:4y = `2x - 410 + sqrt(x^2 + y^2)` => 4y = `2x - 410 + sqrt(x^2 + (168100 - 820x + 4y^2 - 1640y + 4xy))`
Simplifying further, we get:4y^2 - (1640 + 4x)y + (2x^2 - 820x + 168100 - x^2) + 168100 - 168100 = 0
Thus, we have a quadratic equation: 4y^2 - (1640 + 4x)y + (x - 205)^2 = 0
The area `A` of the triangular pen is given by: A = (1/2)xy
Solving the quadratic equation using the quadratic formula and substituting for `y` in the above expression for `A`, we get: A = `(1/8)((820 - x)^2)`
Therefore, the objective function in terms of the length of the side of the pen perpendicular to the barn, `x` is given by the area equation `A` as: A = `(1/8)((820 - x)^2)`.
Learn more about function here:
https://brainly.com/question/30721594
#SPJ11
The market price of a stock is $48.15 and it just paid $5.79
dividend. The dividend is expected to grow at 3.79% forever. What
is the required rate of return for the stock?
Given: The market price of a stock = $48.15, Dividend just paid = $5.79, Expected growth rate of dividend = 3.79%To find: Required rate of return for the stock Let's assume the required rate of return is "r" According to the constant growth model of dividends,
The present value of future dividends can be calculated as follows, PV of future dividends = D / (r-g)where D = dividend just paid = $5.79g = expected growth rate of dividend = 3.79%Now, let's substitute the given values, PV of future dividends = 5.79 / (r - 3.79%)As per the problem, the market price of the stock is $48.15. This means that the present value of all future dividends is equal to the current stock price. So we can set up the following equation, PV of future dividends = 48.15Substituting the value of the present value of future dividends in the above equation,5.79 / (r - 3.79%) = 48.15Solving for r, we get,r = 12.29%Hence, the required rate of return for the stock is 12.29%.
To know more about calculated visit:
https://brainly.com/question/30781060
#SPJ11
From previous studies, it is concluded that 79% of workers got their job through college. A researcher claims it has decreased and decides to survey 100 adults. Test the researcher's claim at the α=0.05α=0.05 significance level.
Preliminary:
Is it safe to assume that n≤0.05n≤0.05 of all subjects in the population?
Yes
No
Verify nˆp(1−ˆp)≥10.np^(1-p^)≥10. Round your answer to one decimal place.
nˆp(1−ˆp)=np^(1-p^)=
Test the claim:
Express the null and alternative hypotheses in symbolic form for this claim.
H0:H0:
Ha:Ha:
Use the following codes to enter the following symbols:
≥≥ enter >=
≤≤ enter <=
≠≠ enter !=
After surveying 100 adult Americans, the researcher finds that 61 workers got their job through college. Compute the test statistic. Round to two decimal places.
z=z=
What is the pp -value? Round to 4 decimals.
p=p=
Make a decision based on α=0.05α=0.05 significance level.
Reject the null hypothesis.
Do not reject the null hypothesis.
What is the conclusion?
There is not sufficient evidence to support the claim that 79% of workers got their job through college has decreased.
There is sufficient evidence to support the claim that 79% of workers got their job through college has decreased.
Based on the given sample data and conducting a hypothesis test at the α = 0.05 significance level, the conclusion is that there is not sufficient evidence to support the claim that 79% of workers got their job through college has decreased.
Since the population proportion (p) is given as 0.79 and the sample size (n) is 100, we need to verify if n'p(1-p') ≥ 10.
Calculating n'p(1-p'):
n'p(1-p') = 100 * 0.79 * (1-0.79) ≈ 16.74
Since n'p(1-p') is greater than or equal to 10, it is safe to assume that n ≤ 0.05 of all subjects in the population.
Test the claim:
Null hypothesis [tex](H_0)[/tex]: p = 0.79 (The proportion of workers who got their job through college is 79%)
Alternative hypothesis [tex](H_a)[/tex]: p < 0.79 (The proportion of workers who got their job through college has decreased)
Calculating the test statistic (z-score):
[tex]z = (n'p - np) / \sqrt{np(1-p)}\\ = (61 - 100 * 0.79) / \sqrt{100 * 0.79 * (1-0.79)}[/tex]
≈ -1.37
Calculating the p-value:
Using a standard normal distribution table or a calculator, the p-value corresponding to a z-score of -1.37 is approximately 0.0853.
Since the p-value (0.0853) is greater than the significance level (0.05), we do not reject the null hypothesis.
The conclusion is that there is not sufficient evidence to support the claim that 79% of workers got their job through college has decreased based on the sample data at the α = 0.05 significance level.
To know more about hypothesis test, refer here:
https://brainly.com/question/17099835
#SPJ4
Let f be continuous on [0, 7] and differentiable on (0,7). If f(0) = 10 and f'(x) ≥ 14 for all x, what is the smallest possible value for f(7)?
The smallest possible value for f(7) is 108.
Given that f is continuous on [0, 7] and differentiable on (0, 7), and f(0) = 10 with f'(x) ≥ 14 for all x, we need to find the smallest possible value for f(7).
From the given conditions, we know that f'(x) ≥ 14 for all x, which implies that f(x) is increasing on the interval [0, 7].
To find the smallest possible value for f(7), we consider the case where f(x) is a straight line, given by f(x) = mx + c, where m represents the slope and c represents the constant term.
Since f(0) = 10, we have f(x) - f(0) ≥ 14(x - 0), applying the Mean Value Theorem.
This simplifies to f(x) ≥ 14x + 10.
For x = 7, we have f(7) ≥ 14(7) + 10 = 98 + 10 = 108.
Therefore, the smallest possible value for f(7) is 108.
In summary, we used the Mean Value Theorem to establish the inequality f(x) - f(0) ≥ 14(x - 0) and obtained f(x) ≥ 14x + 10. By considering the straight line equation, we determined that the smallest possible value for f(7) is 108.
To know more about Mean Value Theorem, click here
https://brainly.com/question/30403137
#SPJ11
Find k such that the function is a probability density function over the given interval. Then write the probability density function. f(x)=k; [-3, 4] ○A. 17/1;1(x) = 1/7/2 O 7' B. 7; f(x) = 7 1 1 ○c. - ; f(x) = -33 C. OD. -3; f(x) = -3
The value of k that makes f(x) a probability density function over the interval [-3, 4] is k = 1/7. The corresponding probability density function is f(x) = 1/7.
To determine the value of k such that the function f(x) = k is a probability density function over the interval [-3, 4], we need to ensure that the integral of f(x) over the interval is equal to 1. We can calculate this integral and solve for k to find the appropriate value.
A probability density function (PDF) must satisfy two conditions: it must be non-negative for all x, and the integral of the PDF over its entire range must equal 1. In this case, we have the function f(x) = k over the interval [-3, 4].
To find the value of k, we need to calculate the integral of f(x) over the interval [-3, 4] and set it equal to 1. The integral is given by:
∫[from -3 to 4] k dx
Integrating k with respect to x over this interval, we get:
kx [from -3 to 4] = 1
Substituting the limits of integration, we have:
k(4 - (-3)) = 1
k(7) = 1
Solving for k, we find:
k = 1/7
Therefore, the value of k that makes f(x) a probability density function over the interval [-3, 4] is k = 1/7. The corresponding probability density function is f(x) = 1/7.
To learn more about probability click here: brainly.com/question/31039386
#SPJ11
Use R programming
2. Normal distribution
For values of a ∈(14,22) plot the true value of P(X ≥a) and the Markovs bound on the same plot (x-axis
will be (14,22)) when X ∼N(μ = 18,σ = 1.5).
For values of k ∈(0,5) plot the true value of P(|X −μX|≥k) and the Chebychev’s bound, on the same plot
(x-axis will be (0,5)) when X ∼N(μ = 18,σ = 1.5).
I have already made the function for the two bounds which were
>markov<-function(a,mu)
{
op<-mu/a
op
}
>chebychev<-function(k,sig2)
{
op<-sig2/(k^{2})
op
}
In summary, for a given range of values of "a" (14 to 22), we need to plot the true value of P(X ≥ a) and the Markov's bound on the same plot.
Additionally, for a range of values of "k" (0 to 5), we need to plot the true value of P(|X − μX| ≥ k) and the Chebyshev's bound on the same plot. The probability distributions are based on a normal distribution with a mean (μ) of 18 and a standard deviation (σ) of 1.5.
To plot the true value of P(X ≥ a), we calculate the probability using the cumulative distribution function (CDF) of the normal distribution. Similarly, for P(|X − μX| ≥ k), we use the CDF to calculate the true probability. For the Markov's bound, we apply the formula mu/a, where mu is the mean of the distribution and a is the threshold value. For Chebyshev's bound, the formula is sigma^2/(k^2), where sigma is the standard deviation and k is the threshold value.
By plotting the true probabilities and the corresponding bounds, we can visualize the relationship between the actual probabilities and the theoretical bounds. This allows us to assess the accuracy of the bounds in approximating the true probabilities and gain insights into the behavior of the distribution within the specified ranges of "a" and "k".
To learn more about Markov's bound refer:
https://brainly.com/question/32592118
#SPJ11
use simplex method to maximize the objective function, subject to the given constraints.
19. Objective function: 20. Objective function: z=x 1 +x 2 z=6x 1 +8x 2 Constraints: Constraints: 3x 1 +x 2 ≤432 20x 1 +40x 2 ≤200 x 1 +4x 2 ≤628 30x 1+42x 2 ≤228 x 1 ,x 2 ≥0 x 1 ,x 2 ≥0
The simplex method is continued.The pivot is selected from row 1 and column 2. The row minimum is obtained from the ratio of RHS and the corresponding coefficient of the column. The optimal value of the objective function is 4056.
Simplex method is an algorithm to solve the linear programming problems. It is an iterative method to approach the solution. The simplex method helps to find the values of the variables in the constraints so that the optimal value of the objective function is achieved.
To maximize the objective function z,Subject to constraints: 3x1 + x2 ≤ 43220x1 + 40x2 ≤ 200x1 + 4x2 ≤ 62830x1 + 42x2 ≤ 228Also, x1 and x2 should be greater than or equal to 0. For the first iteration, we select the pivot element, which is 20 from the first row and first column. The column minimum is found from the ratio of RHS and the corresponding coefficient of the column.
The minimum value is obtained from the 3rd row and its corresponding column, which is 31.4. The new pivot is obtained from row 3 and column 1. The row operations are performed to get the new simplex tableau.
The optimality condition is not yet satisfied. There is still scope for improvement. Hence, the simplex method is continued.The pivot is selected from row 1 and column 2. The row minimum is obtained from the ratio of RHS and the corresponding coefficient of the column. The minimum value is obtained from the 3rd row and its corresponding column, which is 78. The new pivot is obtained from row 3 and column 2. The row operations are performed to get the new simplex tableau.
To know more about function visit :
https://brainly.com/question/30594198
#SPJ11
