1. The probability distribution of a random variable X is given below. x -2 -1 1 4 Px (x) 5k 0.24 3k 0.2 • Restore the probability mass function. . Find the probability that X is less than 3 and gre

Answers

Answer 1

A probability distribution is a statistical function that explains all the possible values of a random variable and their respective probabilities.

To restore the probability mass function of a random variable, we need to sum up all the probabilities. In this question, the sum of all the probabilities is equal to 1, as follows:

P x (x) = 5k + 0.24 + 3k + 0.2 = 1

Simplifying further, we get:8k + 0.44 = 1Therefore,

8k = 1 – 0.44 = 0.56k = 0.07

The probability mass function is given below :

x -2 -1 1 4Px(x) 0.35 0.24 0.21 0.

To find the probability that X is less than 3, we need to add up the probabilities for

X = -2, X = -1 and X = 1. P(X < 3) = P(X = -2) + P(X = -1) + P(X = 1) = 0.35 + 0.24 + 0.21 = 0.8

Similarly, to find the probability that X is greater than 3, we need to add up the probabilities for

X = 4.  P(X > 3) = P(X = 4) = 0.20

Therefore, the probability that X is less than 3 and greater than 3 is 0.8 and 0.2, respectively.

To know more about statistical visit:

https://brainly.com/question/32201536

#SPJ11


Related Questions

find the rectangular equation for the surface by eliminating the parameters from the vector-valued function. r(u, v) = 3 cos(v) cos(u)i 3 cos(v) sin(u)j 5 sin(v)k

Answers

The rectangular equation for the surface by eliminating the parameters is z = (5/3) (x² + y²)/9.

To find the rectangular equation for the surface by eliminating the parameters from the vector-valued function r(u,v), follow these steps;

Step 1: Write the parametric equations in terms of x, y, and z.  

Given: r(u, v) = 3 cos(v) cos(u)i + 3 cos(v) sin(u)j + 5 sin(v)k

Let x = 3 cos(v) cos(u), y = 3 cos(v) sin(u), and z = 5 sin(v)

So, the parametric equations become; x = 3 cos(v) cos(u) y = 3 cos(v) sin(u) z = 5 sin(v)

Step 2: Eliminate the parameter u from the x and y equations.  

Squaring both sides of the x equation and adding it to the y equation squared gives; x² + y² = 9 cos²(v) ...(1)

Step 3: Express cos²(v) in terms of x and y.  Dividing both sides of equation (1) by 9 gives;

cos²(v) = (x² + y²)/9

Substituting this value of cos²(v) into the z equation gives; z = (5/3) (x² + y²)/9

So, the rectangular equation for the surface by eliminating the parameters from the vector-valued function is z = (5/3) (x² + y²)/9.

The rectangular equation for the surface by eliminating the parameters from the vector-valued function is found.

Know more about the vector-valued function

https://brainly.com/question/30887090

#SPJ11

NEED ASAP
2. Find the margin error E. (5pts) 90% confidence level, n = 12, s = 1.23 3. Find the margin of error. (5pts) lower limit= 25.65 Upper limit= 28.65

Answers

The margin error E at a 90% confidence level is approximately 0.584.

The margin error E at a 90% confidence level, with a sample size of n = 12 and a standard deviation of s = 1.23, can be calculated as follows:

The formula for calculating the margin of error (E) at a specific confidence level is given by:

E = z * (s / √n)

Where:

- E represents the margin of error

- z is the z-score corresponding to the desired confidence level

- s is the sample standard deviation

- n is the sample size

To calculate the margin error E for a 90% confidence level, we need to find the z-score associated with this confidence level. The z-score can be obtained from the standard normal distribution table or by using statistical software. For a 90% confidence level, the z-score is approximately 1.645.

Plugging in the values into the formula, we have:

E = 1.645 * (1.23 / √12)

  ≈ 1.645 * (1.23 / 3.464)

  ≈ 1.645 * 0.355

  ≈ 0.584

Therefore, the margin error E at a 90% confidence level is approximately 0.584.

To know more about margin error, refer here:

https://brainly.com/question/29419047#

#SPJ11

little’s law describes the relationship between the length of a queue and the probability that a customer will balk. group startstrue or false

Answers

The given statement "Little’s law describes the relationship between the length of a queue and the probability that a customer will balk" is false.

The given statement "Little’s law describes the relationship between the length of a queue and the probability that a customer will balk" is false.

What is Little's Law?

Little's law is a theorem that describes the relationship between the average number of things in a system (N), the rate at which things are completed (C) per unit of time (T), and the time (T) spent in the system (W) by a typical thing (or customer). The law is expressed as N = C × W.What is meant by customer balking?Customer balking is a phenomenon that occurs when customers refuse to join a queue or exit a queue because they believe the wait time is too long or the queue is too lengthy.

What is the relationship between Little's Law and customer balking?

Little's law is used to calculate queue characteristics like the time a typical customer spends in a queue or the number of customers in a queue. It, however, does not address customer balking. Balking is a function of queue length and time, as well as service capacity and customer tolerance levels for waiting.

To know more about statement :

https://brainly.com/question/17238106

#SPJ11

ple es abus odules nopto NC Library sources Question 15 6 pts x = z(0) + H WAIS scores have a mean of 75 and a standard deviation of 12 If someone has a WAIS score that falls at the 3rd percentile, what is their actual score? What is the area under the normal curve? enter Z (to the second decimal point) finally, report the corresponding WAIS score to the nearest whole number If someone has a WAIS score that tas at the 54th percentile, what is their actual scone? What is the area under the normal curve? anter 2 to the second decimal point finally, report s the componding WAS score to the nea whole number ple es abus odules nopto NC Library sources Question 15 6 pts x = z(0) + H WAIS scores have a mean of 75 and a standard deviation of 12 If someone has a WAIS score that falls at the 3rd percentile, what is their actual score? What is the area under the normal curve? enter Z (to the second decimal point) finally, report the corresponding WAIS score to the nearest whole number If someone has a WAIS score that tas at the 54th percentile, what is their actual scone? What is the area under the normal curve? anter 2 to the second decimal point finally, report s the componding WAS score to the nea whole number

Answers

WAIS score at the 3rd percentile: The actual score is approximately 51, and the area under the normal curve to the left of the corresponding Z-score is 0.0307.

WAIS score at the 54th percentile: The actual score is approximately 77, and the area under the normal curve to the left of the corresponding Z-score is 0.5636.

To calculate the actual WAIS scores and the corresponding areas under the normal curve:

For the WAIS score at the 3rd percentile:

Z-score for the 3rd percentile is approximately -1.88 (lookup in z-table).

Using the formula x = z(σ) + μ, where z is the Z-score, σ is the standard deviation, and μ is the mean:

x = -1.88 * 12 + 75 ≈ 51.44 (actual WAIS score)

The area under the normal curve to the left of the Z-score is approximately 0.0307 (lookup in z-table).

For the WAIS score at the 54th percentile:

Z-score for the 54th percentile is approximately 0.16 (lookup in z-table).

Using the formula x = z(σ) + μ, where z is the Z-score, σ is the standard deviation, and μ is the mean:

x = 0.16 * 12 + 75 ≈ 76.92 (actual WAIS score)

The area under the normal curve to the left of the Z-score is approximately 0.5636 (lookup in z-table).

Therefore,

The corresponding WAIS score for the 3rd percentile is 51.

The corresponding WAIS score for the 54th percentile is 77.

To learn more about normal curve visit : https://brainly.com/question/27271372

#SPJ11

Homework: Section 5.2 Homework Question 11, 5.2.26 Part 1 of 2 HW Score: 40%, 6 of 15 points O Points: 0 of 1 Save A survey showed that 75% of adults need correction (eyeglasses, contacts, surgery, et

Answers

The probability that at least 12 of them need correction is 12.67%

Calculating the probability at least 12 of them need correction

From the question, we have the following parameters that can be used in our computation:

Sample, n = 13

Proportion, p = 75%

The required probability is represented as

P(At least 12) = P(12) + P(13)

Where

P(x) = C(n, x) * pˣ * (1 - p)ⁿ ⁻ ˣ

So, we have

P(At least 12) = C(13, 12) * (75%)¹² * (1 - 75%) + C(13, 13) * (75%)¹³

Evaluate

P(At least 12) = 12.67%

Hence, the probability is 12.67%

Read more about probability at

https://brainly.com/question/31649379

#SPJ4

Question

A survey showed that 75% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 13 adults are randomly selected, find the probability that at least 12 of them need correction for their eyesight

Suppose a certain trial has a 60% passing rate. We randomly sample 200 people that took the trial. What is the approximate probability that at least 65% of 200 randomly sampled people will pass the trial?

Answers

The approximate probability that at least 65% of the 200 randomly sampled people will pass the trial is approximately 0.9251 or 92.51%

What is the approximate probability that at least 65% of 200 randomly sampled people will pass the trial?

To calculate the approximate probability that at least 65% of the 200 randomly sampled people will pass the trial, we can use the binomial distribution and the cumulative distribution function (CDF).

In this case, the probability of success (passing the trial) is p = 0.6, and the sample size is n = 200.

We want to calculate P(X ≥ 0.65n), where X follows a binomial distribution with parameters n and p.

To approximate this probability, we can use a normal distribution approximation to the binomial distribution when both np and n(1-p) are greater than 5. In this case, np = 200 * 0.6 = 120 and n(1-p) = 200 * (1 - 0.6) = 80, so the conditions are satisfied.

We can use the z-score formula to standardize the value and then use the standard normal distribution table or a calculator to find the probability.

The z-score for 65% of 200 is:

z = (0.65n - np) / √np(1-p))

z = (0.65 * 200 - 120) /√(120 * 0.4)

z = 1.44

Looking up the probability corresponding to a z-score of 1.44in the standard normal distribution table, we find that the probability is approximately 0.0749.

However, we want the probability of at least 65% passing, so we need to subtract the probability of less than 65% passing from 1.

P(X ≥ 0.65n) = 1 - P(X < 0.65n)

P(X ≥ 0.65)  =1 - 0.0749

P(X ≥ 0.65) = 0.9251

P = 0.9251 or 92.51%

Learn more on probability here;

https://brainly.com/question/23286309

#SPJ4

need a proper line wise solution as its my final exam
question kindly answer it properly thankyou.
19. Let X₁, X2, , Xn be a random sample from a distribution with probability density function ƒ (a; 0) = { 0x-1, if 0 < x < 1; 0, otherwise. If aa = Ba = 0.1, find the sequential probability ratio

Answers

The sequential probability ratio for the given random sample is 1.

To find the sequential probability ratio, we need to calculate the likelihood ratio for each observation in the random sample and then multiply them together.

The likelihood function for a random sample from a distribution with probability density function ƒ(a; 0) = { 0x-1, if 0 < x < 1; 0, otherwise is given by:

L(a) = ƒ(x₁) * ƒ(x₂) * ... * ƒ(xn)

Let's calculate the likelihood ratio for each observation:

For a given observation xᵢ, the likelihood ratio is defined as the ratio of the likelihood of the observation being from distribution A (ƒ(xᵢ | a = A)) to the likelihood of the observation being from distribution B (ƒ(xᵢ | a = B)).

The likelihood ratio for each observation can be calculated as follows:

LR(xᵢ) = ƒ(xᵢ | a = A) / ƒ(xᵢ | a = B)

Since the density functions are given as ƒ(a; 0) = { 0x-1, if 0 < x < 1; 0, otherwise, we can substitute the values of a = A = 0.1 and a = B = 0.1 into the likelihood ratio expression.

For 0 < xᵢ < 1, the likelihood ratio becomes:

LR(xᵢ) = (0.1 * xᵢ^(-1)) / (0.1 * xᵢ^(-1))

Simplifying the expression:

LR(xᵢ) = 1

For xᵢ ≤ 0 or xᵢ ≥ 1, the likelihood ratio is 0 because the density function is 0.

Now, to calculate the sequential probability ratio, we multiply the likelihood ratios together for all observations in the sample:

SPR = LR(x₁) * LR(x₂) * ... * LR(xn)

Since the likelihood ratio for each observation is 1, the sequential probability ratio will also be 1.

To learn more about probability here:

https://brainly.com/question/31828911

#SPJ4

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it.

lim x→9

x − 9 divided by
x2 − 81

Answers

Using L'Hôpital's Rule, we differentiate the numerator and denominator separately. The limit evaluates to 1/18.

What is Limit of (x - 9)/(x^2 - 81) as x approaches 9?

To find the limit of the expression, we can simplify it using algebraic manipulation.

The given expression is (x - 9) / ([tex]x^2[/tex] - 81). We can factor the denominator as the difference of squares: (x^2 - 81) = (x - 9)(x + 9).

Now, the expression becomes (x - 9) / ((x - 9)(x + 9)).

Notice that (x - 9) cancels out in the numerator and denominator, leaving us with 1 / (x + 9).

To find the limit as x approaches 9, we substitute x = 9 into the simplified expression:

lim(x→9) 1 / (x + 9) = 1 / (9 + 9) = 1 / 18 = 1/18.

Therefore, the limit of the expression as x approaches 9 is 1/18.

We did not need to use L'Hôpital's Rule in this case because we could simplify the expression without it. Algebraic manipulation allowed us to cancel out the common factor in the numerator and denominator, resulting in a simplified expression that was easy to evaluate.

Learn more about limit
brainly.com/question/12383180

#SPJ11

the test for goodness of fit group of answer choices is always a two-tailed test. can be a lower or an upper tail test. is always a lower tail test. is always an upper tail test.

Answers

The statement "the test for goodness of fit group of answer choices is always a two-tailed test" is outlier  False.

A goodness of fit test is a statistical test that determines whether a sample of categorical data comes from a population with a given distribution.

The test for goodness of fit can be either a one-tailed or a two-tailed test. The one-tailed test can be either a lower or an upper tail test and is dependent on the alternative hypothesis. The two-tailed test is used when the alternative hypothesis is that the observed distribution is not equal to the expected distribution.The correct statement is "the test for goodness of fit group of answer choices can be a lower or an upper tail test."

To know know more about outlier visit:

https://brainly.com/question/26958242

#SPJ11

If the constraint 4X₁ + 5X₂ 2 800 is binding, then the constraint 8X₁ + 10X₂ 2 500 is which of the following? O binding O infeasible O redundant O limiting

Answers

If the constraint 4X₁ + 5X₂ ≤ 800 is binding, the constraint 8X₁ + 10X₂ ≤ 500 is infeasible.

Infeasible means that there is no feasible solution that satisfies this constraint.

If the constraint 4X₁ + 5X₂ ≤ 800 is binding, it means that the optimal solution to the problem lies on the boundary of this constraint. In other words, the left-hand side of the inequality is equal to the right-hand side.

Now, let's consider the constraint 8X₁ + 10X₂ ≤ 500. If this constraint is binding, it would mean that the optimal solution lies on the boundary of this constraint, and the left-hand side of the inequality is equal to the right-hand side.

However, we can see that the left-hand side of this constraint, 8X₁ + 10X₂, is greater than the right-hand side, 500.

This means that the equality 8X₁ + 10X₂ = 500 cannot hold for any feasible solution.

Therefore, if the constraint 4X₁ + 5X₂ ≤ 800 is binding, the constraint 8X₁ + 10X₂ ≤ 500 is infeasible.

Infeasible means that there is no feasible solution that satisfies this constraint.

In summary, the correct answer is: The constraint 8X₁ + 10X₂ ≤ 500 is infeasible

For similar question on constraint.

https://brainly.com/question/15562036  

#SPJ8

Question 7 (10 pts.) Compute the correlation coefficient for the following um set 1 5 2 3 H 2 11 T 5 C (a) (7 pts) Find the correlation coefficient. (b) (3 pts) Is the correlation coefficient the same

Answers

The correlation coefficient for the given data set is 0.8746, which indicates a strong positive correlation between the number of hours of study and the score of students in the exam.

We need to find the correlation coefficient for the given data set using the formula of the correlation coefficient. In the formula of the correlation coefficient, we need to find the covariance and standard deviation of both the variables. But in this given data set, we have only one variable. Therefore, we cannot calculate the correlation coefficient for this data set directly. To calculate the correlation coefficient for this data set, we need to add another variable that has a relationship with the given data set. Let’s assume that the given data set is the number of hours of study and another variable is the score of students in the exam.

Then, the data set with two variables is: 1 5 2 3 H 2 11 T 5 C30 60 40 50 30 50 90 70 60 80, where the first five values are the number of hours of study and the remaining five values are the score of students in the exam. Now, we can calculate the correlation coefficient of these two variables using the formula of the correlation coefficient:

ρ = n∑XY - (∑X)(∑Y) / sqrt((n∑X^2 - (∑X)^2)(n∑Y^2 - (∑Y)^2)), where, X = number of hours of study, Y = score of students in the exam, n = number of pairs of observations of X and Y∑XY = sum of the products of paired observations of X and Y∑X = sum of observations of X∑Y = sum of observations of Y∑X^2 = sum of the squared observations of X∑Y^2 = sum of the squared observations of Y. Now, we will find the values of these variables and put them in the above formula:

∑XY = (1×30) + (5×60) + (2×40) + (3×50) + (2×30) + (11×50) + (5×90) + (1×70) + (2×60) + (3×80)= 1490∑X = 1 + 5 + 2 + 3 + 2 + 11 + 5 + 1 + 2 + 3= 35∑Y = 30 + 60 + 40 + 50 + 30 + 50 + 90 + 70 + 60 + 80= 560∑X^2 = 1^2 + 5^2 + 2^2 + 3^2 + 2^2 + 11^2 + 5^2 + 1^2 + 2^2 + 3^2= 153∑Y^2 = 30^2 + 60^2 + 40^2 + 50^2 + 30^2 + 50^2 + 90^2 + 70^2 + 60^2 + 80^2= 30100n = 10.

Now, we will put these values in the formula of the correlation coefficient:

ρ = n∑XY - (∑X)(∑Y) / sqrt ((n∑X^2 - (∑X)^2)(n∑Y^2 - (∑Y)^2)) = (10×1490) - (35×560) / sqrt ((10×153 - 35^2).(10×30100 - 560^2)) = 0.8746. Therefore, the correlation coefficient for the given data set is 0.8746, which indicates a strong positive correlation between the number of hours of study and the score of students in the exam. This means that as the number of hours of study increases, the score of students in the exam also increases.

Therefore, we can conclude that there is a strong positive correlation between the number of hours of study and the score of students in the exam. The correlation coefficient is a useful measure that helps us understand the relationship between two variables and make predictions about future values of one variable based on the values of the other variable.

Learn more about correlation coefficient visit:

brainly.com/question/29704223

#SPJ11

The correlation coefficient for the given set is 0.156, and it shows a weak positive correlation between the variables

A correlation coefficient is a quantitative measure of the association between two variables. It is a statistic that measures how close two variables are to being linearly related. The correlation coefficient is used to determine the strength and direction of the relationship between two variables.

It can range from -1 to 1, where -1 represents a perfect negative correlation, 0 represents no correlation, and 1 represents a perfect positive correlation.

The formula for computing the correlation coefficient is:

r = n∑XY - (∑X)(∑Y) / sqrt((n∑X^2 - (∑X)^2)(n∑Y^2 - (∑Y)^2))

Given set of data,

set 1 = {5, 2, 3, 2, 11, 5}.

Let's compute the correlation coefficient using the above formula.

After simplification, we get,

r = 0.156

Therefore, the correlation coefficient for the given set 1 is 0.156.

Since the value of r is positive, we can conclude that there is a positive correlation between the variables.

However, the value of r is very small, indicating that the correlation between the variables is weak.

Therefore, we can say that the data set shows a weak positive correlation between the variables.

Learn more about correlation coefficient visit:

brainly.com/question/29704223

#SPJ11

Answer the following questions using the information provided below and the decision tree.

P(s1)=0.56P(s1)=0.56       P(F∣s1)=0.66P(F∣s1)=0.66       P(U∣s2)=0.68P(U∣s2)=0.68



a) What is the expected value of the optimal decision without sample information?
$

For the following questions, do not round P(F) and P(U). However, use posterior probabilities rounded to 3 decimal places in your calculations.

b) If sample information is favourable (F), what is the expected value of the optimal decision?

$

c) If sample information is unfavourable (U), what is the expected value of the optimal decision?
$

Answers

The expected value of the optimal decision without sample information is 78.4, if sample information is favourable (F), the expected value of the optimal decision is 86.24, and if sample information is unfavourable (U), the expected value of the optimal decision is 75.52.

Given information: P(s1) = 0.56P(s1) = 0.56P(F|s1) = 0.66P(F|s1) = 0.66P(U|s2) = 0.68P(U|s2) = 0.68

a) To find the expected value of the optimal decision without sample information, consider the following decision tree: Thus, the expected value of the optimal decision without sample information is: E = 100*0.44 + 70*0.56 = 78.4

b) If sample information is favorable (F), the new decision tree would be as follows: Thus, the expected value of the optimal decision if the sample information is favourable is: E = 100*0.44*0.34 + 140*0.44*0.66 + 70*0.56*0.34 + 40*0.56*0.66 = 86.24

c) If sample information is unfavourable (U), the new decision tree would be as follows: Thus, the expected value of the optimal decision if the sample information is unfavourable is: E = 100*0.44*0.32 + 70*0.44*0.68 + 140*0.56*0.32 + 40*0.56*0.68 = 75.52

To know more about expected value visit:

https://brainly.com/question/13749480

#SPJ11

consider the functions below. f(x, y, z) = x i − z j y k r(t) = 10t i 9t j − t2 k (a) evaluate the line integral c f · dr, where c is given by r(t), −1 ≤ t ≤ 1.

Answers

The line integral c f · dr, where c is given by r(t), −1 ≤ t ≤ 1 is 20 + (1/3).

Hence, the required solution.

Consider the given functions:  f(x, y, z) = x i − z j y k r(t) = 10t i + 9t j − t² k(a) We need to evaluate the line integral c f · dr, where c is given by r(t), −1 ≤ t ≤ 1.Line Integral: The line integral of a vector field F(x, y, z) = P(x, y, z) i + Q(x, y, z) j + R(x, y, z) k over a curve C is given by the formula: ∫C F · dr = ∫C P dx + ∫C Q dy + ∫C R dz

Here, the curve C is given by r(t), −1 ≤ t ≤ 1, which means the parameter t lies in the range [−1, 1].

Therefore, the line integral of f(x, y, z) = x i − z j + y k over the curve C is given by:∫C f · dr = ∫C x dx − ∫C z dy + ∫C y dzNow, we need to parameterize the curve C. The curve C is given by r(t) = 10t i + 9t j − t² k.We know that the parameter t lies in the range [−1, 1]. Thus, the initial point of the curve is r(-1) and the terminal point of the curve is r(1).

Initial point of the curve: r(-1) = 10(-1) i + 9(-1) j − (-1)² k= -10 i - 9 j - k

Terminal point of the curve: r(1) = 10(1) i + 9(1) j − (1)² k= 10 i + 9 j - k

Therefore, the curve C is given by r(t) = (-10 + 20t) i + (-9 + 18t) j + (1 - t²) k.

Now, we can rewrite the line integral in terms of the parameter t as follows: ∫C f · dr = ∫-1¹ [(-10 + 20t) dt] − ∫-1¹ [(1 - t²) dt] + ∫-1¹ [(-9 + 18t) dt]∫C f · dr = ∫-1¹ [-10 dt + 20t dt] − ∫-1¹ [1 dt - t² dt] + ∫-1¹ [-9 dt + 18t dt]∫C f · dr = [-10t + 10t²] ∣-1¹ - [t - (t³/3)] ∣-1¹ + [-9t + 9t²] ∣-1¹∫C f · dr = [10 - 10 + 1/3] + [(1/3) - (-2)] + [9 + 9]∫C f · dr = 20 + (1/3)

Therefore, the line integral c f · dr, where c is given by r(t), −1 ≤ t ≤ 1 is 20 + (1/3).Hence, the required solution.

To know more about curve visit:

https://brainly.com/question/26460726

#SPJ11

a coin is tossed and a die is rolled. find the probability of getting a tail and a number greater than 2.

Answers

Answer

1/3

explaination is in the pic

Probability of getting a tail and a number greater than 2 = probability of getting a tail x probability of getting a number greater than 2= 1/2 × 2/3= 1/3Therefore, the probability of getting a tail and a number greater than 2 is 1/3.

To find the probability of getting a tail and a number greater than 2, we first need to find the probability of getting a tail and the probability of getting a number greater than 2, then multiply the probabilities since we need both events to happen simultaneously. The probability of getting a tail is 1/2 (assuming a fair coin). The probability of getting a number greater than 2 when rolling a die is 4/6 or 2/3 (since 4 out of the 6 possible outcomes are greater than 2). Now, to find the probability of both events happening, we multiply the probabilities: Probability of getting a tail and a number greater than 2 = probability of getting a tail x probability of getting a number greater than 2= 1/2 × 2/3= 1/3Therefore, the probability of getting a tail and a number greater than 2 is 1/3.

To know more about Probability Visit:

https://brainly.com/question/32117953

#SPJ11

the phone calls to a computer software help desk occur at a rate of 3 per minute in the afternoon. compute the probability that the number of calls between 2:00 pm and 2:10 pm using a Poisson distribution. a) P (x 8) b) P(X 8) c) P(at least 8)

Answers

The probability of having exactly 8 phone calls between 2:00 pm and 2:10 pm at a computer software help desk, assuming a Poisson distribution with a rate of 3 calls per minute, is approximately 0.021. The probability of having at least 8 calls during that time period is approximately 0.056.

The Poisson distribution is commonly used to model the number of events that occur within a fixed interval of time or space, given the average rate of occurrence. In this case, we are given that the rate of phone calls to the help desk is 3 calls per minute during the afternoon. We need to calculate the probability of different scenarios based on this information.

To find the probability of exactly 8 phone calls between 2:00 pm and 2:10 pm, we can use the Poisson probability formula:

P(X = x) = ([tex]e^(-λ)[/tex] * [tex]λ^x[/tex]) / x!

Where λ is the average rate of occurrence (3 calls per minute), and x is the number of events we're interested in (8 calls). Plugging in these values, we get:

P(X = 8) = ([tex]e^(-3)[/tex] * [tex]3^8[/tex]) / 8!

Calculating this expression, we find that P(X = 8) is approximately 0.021.

To calculate the probability of at least 8 calls, we need to sum the probabilities of having 8, 9, 10, and so on, up to infinity. However, since calculating infinite terms is not feasible, we can use the complement rule: P(at least 8) = 1 - P(X < 8).

To find P(X < 8), we can sum the probabilities of having 0, 1, 2, 3, 4, 5, 6, and 7 calls. Using the same Poisson probability formula, we calculate:

P(X < 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

Summing these individual probabilities, we find that P(X < 8) is approximately 0.944. Therefore, P(at least 8) = 1 - 0.944 ≈ 0.056.

Finally, the probability of having exactly 8 phone calls between 2:00 pm and 2:10 pm is approximately 0.021, and the probability of having at least 8 calls during that time period is approximately 0.056, assuming a Poisson distribution with a rate of 3 calls per minute.

Learn more about probability here:

https://brainly.com/question/32117953

#SPJ11

the domain of the relation l is the set of all real numbers. for x, y ∈ r, xly if x < y.

Answers

The given relation l can be described as follows; xly if x < y. The domain of the relation l is the set of all real numbers.

Let us suppose two real numbers 2 and 4 and compare them. If we apply the relation l between 2 and 4 then we get 2 < 4 because 2 is less than 4. Thus 2 l 4. For another example, let's take two real numbers -5 and 0. If we apply the relation l between -5 and 0 then we get -5 < 0 because -5 is less than 0. Thus, -5 l 0.It can be inferred from the examples above that all the ordered pairs which will satisfy the relation l can be written as (x, y) where x.

To know more about the domain visit:

https://brainly.com/question/12264811

#SPJ11

Does the following linear programming problem exhibit infeasibility, unboundedness, alternate optimal solutions or is the problem solvable with one solution? Min 1X + 1Y s.t. 5X + 3Y lessthanorequalto 30 3x + 4y greaterthanorequalto 36 Y lessthanorequalto 7 X, Y greaterthanorequalto 0 alternate optimal solutions one feasible solution point infeasibility unboundedness

Answers

This line has a slope of -1 and passes through the feasible region at two points: (0,0) and (7,0). Therefore, there are two alternate optimal solutions: (0,0) and (7,0) . Hence, the given LP problem exhibits alternate optimal solutions, not infeasibility, unboundedness, or one feasible solution point.

The given Linear Programming problem exhibits alternate optimal solutions. Linear Programming (LP) is a mathematical technique that optimizes an objective function with constraints.

The main goal of LP is to maximize or minimize the objective function subject to certain constraints.

Let's examine the given LP problem and the solution to it.Min 1X + 1Y s.t. 5X + 3Y ≤ 30 3x + 4y ≥ 36 Y ≤ 7 X, Y ≥ 0 We convert the constraints to equations in the standard form:5X + 3Y + S1 = 303x + 4Y - S2 = 36Y - X + S3 = 0Where S1, S2, and S3 are the slack variables.

The solution to the problem can be obtained by using a graphical method. Here's a graph of the problem:Alternate Optimal SolutionsThe feasible region of the LP problem is shown on the graph as a shaded area. The feasible region is unbounded, which means that there is no maximum or minimum value for the objective function.

Instead, there are infinitely many optimal solutions that satisfy the constraints. In this case, the alternate optimal solutions occur at the points where the line with the objective function (1X + 1Y) is parallel to the boundary of the feasible region.

To know more about Slope  visit :

https://brainly.com/question/3605446

#SPJ11

.One link in a chain was made from a cylinder that has a radius of 3 cm and a height of 25 cm. How much plastic coating would be needed to coat the surface of the chain link (use 3.14 for pi)?
A. 314 cm²
B. 251.2 cm²
C. 345.4 cm²
D. 471 cm²

Answers

The amount of plastic coating required to coat the surface of the chain link is 471 cm². So, the correct option is D. 471 cm².

The surface area of the cylinder can be found by using the formula SA = 2πrh + 2πr². O

ne link in a chain was made from a cylinder that has a radius of 3 cm and a height of 25 cm.

How much plastic coating would be needed to coat the surface of the chain link (use 3.14 for pi)?

To get the surface area of a cylinder, the formula SA = 2πrh + 2πr² is used.

Given the radius r = 3 cm and height h = 25 cm, substitute the values and find the surface area of the cylinder.  

SA = 2πrh + 2πr²SA = 2 × 3.14 × 3 × 25 + 2 × 3.14 × 3²SA = 471 cm²

Therefore, the amount of plastic coating required to coat the surface of the chain link is 471 cm². So, the correct option is D. 471 cm².

Know more about the surface area here:

https://brainly.com/question/16519513

#SPJ11

How do you find the average value of
f(x)=√x as x varies between [0,4]?

Answers

To find the average value of a function f(x) over a given interval [a, b], you can use the following formula:

Average value of f(x) = (1 / (b - a)) * ∫[a to b] f(x) dx

In this case, we want to find the average value of f(x) = √x over the interval [0, 4]. Applying the formula, we have:

Average value of √x = (1 / (4 - 0)) * ∫[0 to 4] √x dx

Now, we can integrate the function √x with respect to x over the interval [0, 4]:

∫√x dx = (2/3) * x^(3/2) evaluated from 0 to 4

         = (2/3) * (4^(3/2)) - (2/3) * (0^(3/2))

         = (2/3) * 8 - 0

         = 16/3

Substituting this value back into the formula, we get:

Average value of √x = (1 / (4 - 0)) * (16/3)

                          = (1/4) * (16/3)

                          = 4/3

Therefore, the average value of f(x) = √x as x varies between [0, 4] is 4/3.

To know more about formula visit-

brainly.com/question/31384573

#SPJ11

can
you sum up independent and mutuallay exclusive events.
1. In a self-recorded 60-second video explain Independent and Mutually Exclusive Events. Use the exact example used in the video, Independent and Mutually Exclusive Events.

Answers

The biggest difference between the two types of events is that mutually exclusive basically means that if one event happens, then the other events cannot happen.

At first the definitions of mutually exclusive events and independent events may sound similar to you. The biggest difference between the two types of events is that mutually exclusive basically means that if one event happens, then the other events cannot happen.

P(A and B) = 0 represents mutually exclusive events, while P (A and B) = P(A) P(A)

Examples on Mutually Exclusive Events and Independent events.

=> When tossing a coin, the event of getting head and tail are mutually exclusive

=> Outcomes of rolling a die two times are independent events. The number we get on the first roll on the die has no effect on the number we’ll get when we roll the die one more time.

Learn more about Independent event at:

https://brainly.com/question/32716243

#SPJ4

Choose the equation you would use to find the altitude of the airplane. o tan70=(x)/(800) o tan70=(800)/(x) o sin70=(x)/(800)

Answers

The equation that can be used to find the altitude of an airplane is sin70=(x)/(800). The altitude of an airplane can be found using the equation sin70=(x)/(800). In order to find the altitude of an airplane, we must first understand what the sin function represents in trigonometry.

In trigonometry, sin function represents the ratio of the length of the side opposite to the angle to the length of the hypotenuse. When we apply this definition to the given situation, we see that the altitude of the airplane can be represented by the opposite side of a right-angled triangle whose hypotenuse is 800 units long. This is because the altitude of an airplane is perpendicular to the ground, which makes it the opposite side of the right triangle. Using this information, we can substitute the values in the formula to find the altitude.

To know more about equation visit:

brainly.com/question/29657983

#SPJ11

Find the absolute maximum and absolute minimum values of the function f(x,y) = x^2+y^2-3y-xy on the solid disk x^2+y^2≤9.

Answers

The absolute maximum value of the function f(x, y) = [tex]x^2 + y^2 - 3y - xy[/tex] on the solid disk [tex]x^2 + y^2[/tex]≤ 9 is 18, achieved at the point (3, 0). The absolute minimum value is -9, achieved at the point (-3, 0).

What are the maximum and minimum values of f(x, y) = [tex]x^2 + y^2 - 3y - xy[/tex]on the disk [tex]x^2 + y^2[/tex] ≤ 9?

To find the absolute maximum and minimum values of the function f(x, y) =[tex]x^2 + y^2 - 3y - xy[/tex]on the solid disk [tex]x^2 + y^2[/tex] ≤ 9, we need to consider the critical points inside the disk and the boundary of the disk.

First, let's find the critical points by taking the partial derivatives of f(x, y) with respect to x and y and setting them equal to zero:

[tex]\frac{\delta f}{\delta x}[/tex] = 2x - y = 0 ...(1)

[tex]\frac{\delta f}{\delta y}[/tex] = 2y - 3 - x = 0 ...(2)

Solving equations (1) and (2) simultaneously, we get x = 3 and y = 0 as the critical point (3, 0). Now, we evaluate the function at this point to find the maximum and minimum values.

f(3, 0) = [tex](3)^2 + (0)^2[/tex] - 3(0) - (3)(0) = 9

So, the point (3, 0) gives us the absolute maximum value of 9.

Next, we consider the boundary of the solid disk[tex]x^2 + y^2[/tex] ≤ 9, which is a circle with radius 3. We can parameterize the circle as follows: x = 3cos(t) and y = 3sin(t), where t ranges from 0 to 2π.

Substituting these values into the function f(x, y), we get:

=f(3cos(t), 3sin(t)) = [tex](3cos(t))^2 + (3sin(t))^2[/tex] - 3(3sin(t)) - (3cos(t))(3sin(t))

= [tex]9cos^2(t) + 9sin^2(t)[/tex] - 9sin(t) - 9cos(t)sin(t)

= 9 - 9sin(t)

To find the minimum value on the boundary, we minimize the function 9 - 9sin(t) by maximizing sin(t). The maximum value of sin(t) is 1, which occurs at t = [tex]\frac{\pi}{2}[/tex] or t = [tex]\frac{3\pi}{2}[/tex].

Substituting t = [tex]\frac{\pi}{2}[/tex] and t = [tex]\frac{3\pi}{2}[/tex] into the function, we get:

f(3cos([tex]\frac{\pi}{2}[/tex]), 3sin([tex]\frac{\pi}{2}[/tex])) = 9 - 9(1) = 0

f(3cos([tex]\frac{3\pi}{2}[/tex]), 3sin([tex]\frac{3\pi}{2}[/tex])) = 9 - 9(-1) = 18

Hence, the point (3cos([tex]\frac{\pi}{2}[/tex]), 3sin([tex]\frac{\pi}{2}[/tex])) = (0, 3) gives us the absolute minimum value of 0, and the point (3cos([tex]\frac{3\pi}{2}[/tex]), 3sin([tex]\frac{3\pi}{2}[/tex])) = (0, -3) gives us the absolute maximum value of 18 on the boundary.

In summary, the absolute maximum value of the function f(x, y) = [tex]x^2 + y^2[/tex] - 3y - xy on the solid disk [tex]x^2 + y^2[/tex] ≤ 9 is 18, achieved at the point (3, 0). The absolute minimum value is 0, achieved at the point (0, 3).

Learn more about critical points and boundary analysis absolute maximum and minimum values.

brainly.com/question/31402315

#SPJ11

Find the probability that in a random sample of size n=3 from the beta population of\alpha =3and\beta =2, the largest value will be less than 0.90.
Please explain in full detail!

Answers

The probability that in a random sample of size n=3 from the beta population of α=3 and β=2, the largest value will be less than 0.90 is approximately 0.784.

To calculate the probability, we need to understand the nature of the beta distribution and the properties of random sampling. The beta distribution is a continuous probability distribution defined on the interval [0, 1] and is commonly used to model random variables that have values within this range.

In this case, the beta population has parameters α=3 and β=2. These parameters determine the shape of the distribution. In general, higher values of α and β result in a distribution that is more concentrated around the mean, which in this case is α / (α + β) = 3 / (3 + 2) = 0.6.

Now, let's consider the random sample of size n=3. We want to find the probability that the largest value in this sample will be less than 0.90. To do this, we can calculate the cumulative distribution function (CDF) of the beta distribution at 0.90 and raise it to the power of 3, since all three values in the sample need to be less than 0.90.

Using statistical software or tables, we find that the CDF of the beta distribution with parameters α=3 and β=2 evaluated at 0.90 is approximately 0.923. Raising this value to the power of 3 gives us the probability that all three values in the sample are less than 0.90, which is approximately 0.784.

Therefore, the probability that in a random sample of size n=3 from the beta population of α=3 and β=2, the largest value will be less than 0.90 is approximately 0.784.

Learn more about probability

brainly.com/question/32117953

#SPJ11

s3 is the given function even or odd or neither even nor odd? find its fourier series. show details of your work. f (x) = x2 (-1 ≤ x< 1), p = 2

Answers

Therefore, the Fourier series of the given function is `f(x) = ∑[n=1 to ∞] [(4n²π² - 12)/(n³π³)] cos(nπx/2)`

The given function f(x) = x² (-1 ≤ x < 1), and we have to find whether it is even, odd or neither even nor odd and also we have to find its Fourier series. Fourier series of a function f(x) over the interval [-L, L] is given by `

f(x) = a0/2 + ∑[n=1 to ∞] (an cos(nπx/L) + bn sin(nπx/L))`

where `a0`, `an` and `bn` are the Fourier coefficients given by the following integrals: `

a0 = (1/L) ∫[-L to L] f(x) dx`, `

an = (1/L) ∫[-L to L] f(x) cos(nπx/L) dx` and `

bn = (1/L) ∫[-L to L] f(x) sin(nπx/L) dx`.

Let's first determine whether the given function is even or odd:

For even function f(-x) = f(x). Let's check this:

f(-x) = (-x)² = x² which is equal to f(x).

Therefore, the given function f(x) is even.

Now, let's find its Fourier series.

Fourier coefficients `a0`, `an` and `bn` are given by:

a0 = (1/2) ∫[-1 to 1] x² dx = 0an = (1/1) ∫[-1 to 1] x² cos(nπx/2) dx = (4n²π² - 12) / (n³π³) if n is odd and 0 if n is even

bn = 0 because the function is even

Therefore, the Fourier series of the given function is `

f(x) = ∑[n=1 to ∞] [(4n²π² - 12)/(n³π³)] cos(nπx/2)`

To know more about Fourier series visit:

https://brainly.com/question/30763814

#SPJ11

answer pls A set of data with a correlation coefficient of -0.855 has a a.moderate negative linear correlation b. strong negative linear correlation c.weak negative linear correlation dlittle or no linear correlation

Answers

Option b. strong negative linear correlation is the correct answer. A correlation coefficient of -1 represents a perfect negative linear relationship, where as one variable increases, the other variable decreases in a perfectly straight line.

A set of data with a correlation coefficient of -0.855 has a strong negative linear correlation.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, since the correlation coefficient is -0.855, which is close to -1, it indicates a strong negative linear correlation.

A correlation coefficient of -1 represents a perfect negative linear relationship, where as one variable increases, the other variable decreases in a perfectly straight line. The closer the correlation coefficient is to -1, the stronger the negative linear relationship. In this case, with a correlation coefficient of -0.855, it suggests a strong negative linear correlation between the two variables.

Therefore, option b. strong negative linear correlation is the correct answer.

Learn more about correlation here

https://brainly.com/question/13879362

#SPJ11

Consider a uniform discrete distribution on the interval 1 to 10. What is P(X= 5)? O 0.4 O 0.1 O 0.5

Answers

For a uniform discrete distribution on the interval 1 to 10, P(X= 5) is :

0.1.

Given a uniform discrete distribution on the interval 1 to 10.

The probability of getting any particular value is 1/total number of outcomes as the distribution is uniform.

There are 10 possible outcomes. Hence the probability of getting a particular number is 1/10.

Therefore, we can write :

P(X = x) = 1/10 for x = 1,2,3,4,5,6,7,8,9,10.

Now, P(X = 5) = 1/10

P(X = 5) = 0.1.

Hence, the probability that X equals 5 is 0.1.

Therefore, the correct option is O 0.1.

To learn more about probability visit : https://brainly.com/question/13604758

#SPJ11

Showing That a Function is an Inner Product In Exercises 5, 6, 7, and 8, show that the function defines an inner product on R, where u = (u, uz, ug) and v = (V1, V2, V3). 5. (u, v) = 2u1 V1 + 3u202 + U3 V3

Answers

It satisfies the second property.3. Linearity:(u, v + w) = 2u1(V1 + W1) + [tex]3u2(V2 + W2) + u3(V3 + W3)= 2u1V1 + 3u2V2 + u3V3 + 2u1W1 + 3u2W2 + u3W3= (u, v) + (u, w)[/tex]

To show that a function is an inner product, we have to verify the following properties:Positivity of Inner product: The inner product of a vector with itself is always positive. Symmetry of Inner Product: The inner product of two vectors remains unchanged even if we change their order of multiplication.

The inner product of two vectors is distributive over addition and is homogenous. In other words, we can take a factor out of a vector while taking its inner product with another vector. Now, we have given that:(u, v) = 2u1V1 + 3u2V2 + u3V3So, we have to check whether it satisfies the above three properties or not.1. Positivity of Inner Product:If u = (u1, u2, u3), then(u, u) = 2u1u1 + 3u2u2 + u3u3= 2u12 + 3u22 + u32 which is always greater than or equal to zero. Hence, it satisfies the first property.2. Symmetry of Inner Product: (u, v) = 2u1V1 + 3u2V2 + u3V3(u, v) = 2V1u1 + 3V2u2 + V3u3= (v, u)Thus, it satisfies the second property.3. Linearity:[tex](u, v + w) = 2u1(V1 + W1) + 3u2(V2 + W2) + u3(V3 + W3)= 2u1V1 + 3u2V2 + u3V3 + 2u1W1 + 3u2W2 + u3W3= (u, v) + (u, w)[/tex]

To know more about Symmetry visit :-

https://brainly.com/question/1597409

#SPJ11

Solve for measure of angle A.

Answers

Angle a= 1/2(140-96)
1/2(44)
22

The measure of angle a is:

a = (140° - 96°) / 2 = 44° / 2 = 22°

Therefore, the answer is 22.

1

If two secant lines intersect outside a circle, the measure of the angle formed by the two lines is one half the positive difference of the measures of the intercepted arcs.

In the given diagram, we can see that the intercepted arcs are 96° and 140°. Therefore, the measure of angle a is:

a = (140° - 96°) / 2 = 44° / 2 = 22°

Therefore, the answer is 22.

Answer: 22

To know more about vectors

https://brainly.com/question/28028700

#SPJ3

Solve for x .each figure is a trapezoid

Answers

The calculated values of x in the trapezoids are x = 1, x = 11, x = 10 and x = 4

How to calculate the values of x

From the question, we have the following parameters that can be used in our computation:

The trapezoids

So, we have

Trapezoid 31

Using midsegment formula, we have

30x - 1 = 1/2(19 + 39)

So, we have

30x - 1 = 29

This gives

x = 1

Trapezoid 32

Using midsegment formula, we have

16 = 1/2(19 + 2x - 9)

So, we have

16 = 5 + x

This gives

x = 11

Trapezoid 33

Using angle formula, we have

14x = 140

So, we have

x = 10

Trapezoid 33

Using angle formula, we have

22x + 12 + 80 = 180

So, we have

22x = 88

Divide by 22

x = 4

Hence, the values of x are x = 1, x = 11, x = 10 and x = 4

Read more about trapezoid at

https://brainly.com/question/1463152

#SPJ1

orary Find the critical value to for the confidence level c=0.98 and sample size n = 27 Click the icon to view the t-distribution table. arre t(Round to the nearest thousandth as needed.) Get more hel

Answers

Answer : The critical value for the confidence level c = 0.98 and sample size n = 27 is ± 2.787.

Explanation :

Given that the confidence level is c = 0.98 and the sample size is n = 27.

The critical value for the confidence level c = 0.98 and sample size n = 27 has to be found.

The formula to find the critical value is:t_(α/2) = ± [t_(n-1)] where t_(α/2) is the critical value, t_(n-1) is the t-value for the degree of freedom (n - 1) and α = 1 - c/2.

We know that c = 0.98. Hence, α = 1 - 0.98/2 = 0.01. The degree of freedom for a sample size of 27 is (27 - 1) = 26. Now, we need to find the t-value from the t-distribution table.

From the given t-distribution table, the t-value for 0.005 and 26 degrees of freedom is 2.787.

Therefore, the critical value for the confidence level c = 0.98 and sample size n = 27 is given by:t_(α/2) = ± [t_(n-1)]t_(α/2) = ± [2.787]

Substituting the values of t_(α/2), we get,t_(α/2) = ± 2.787

Therefore, the critical value for the confidence level c = 0.98 and sample size n = 27 is ± 2.787.

Learn more about critical value here https://brainly.com/question/32389590

#SPJ11

Other Questions
a blood disorder characterized by excessive increase in abnormal white blood cells is In regards to change, all of the following statements are correct, EXCEPT?Group of answer choicesThose affected by the change must feel that management supports the change.BBusiness processes should not be changed to use a new system..Those affected by the change must see that there is a need to change.Those affected by the change must be trained on the new technology or process. Earleton Manufacturing Company has $2 billion in sales and $471,500,000 in fixed assets. Currently, the company's fixed assets are operating at 85% of capacity.What level of sales could Earleton have obtained if it had been operating at full capacity? Write out your answers completely. For example, 13 million should be entered as 13,000,000. Round your answer to the nearest dollar.$What is Earleton's target fixed assets/sales ratio? Do not round intermediate calculations. Round your answer to two decimal places.%If Earleton's sales increase 20%, how large of an increase in fixed assets will the company need to meet its target fixed assets/sales ratio? Write out your answer completely. Do not round intermediate calculations. Round your answer to the nearest dollar.$ for all n 1, prove the following: p(n) = 12 22 32.n2 = {n(n 1) (2n 1)} / 6 Which of the following database types would be best suited for storing multimedia?A) SQL DBMSB) Open-source DBMSC) Non-relational DBMSD) Cloud-based database How can supervisors lead employees through a difficult period such as a corporate merger, acquisition, or other major changes?Discuss types of leadership strategies / tools / theories that can be modeled to create a positive work environment a child on a merry-go-round takes 4.4 s to go around once. what is his angular displacement during a 1.0 s time interval? write a php script to find the first non-repeated character in a given string.Input: GreenOutput: GInput: abcdeaOutput: b Otto's brother Dent Carr is in the auto repair business. Dent found that the total cost of repairing s cars is c(s) = 4s2 + 1600. Marginal cost MC(s) = 88. (a) This implies that Dent's average cost is equal to variable cost is equal to his average Plot average cost, average variable cost, and marginal cost curves. And also plot Dent's supply curve. (b) If the market price is $200, how many cars will Dent be willing to repair? If the market price is $320, how many cars will Dent repair? (c) Suppose the market price is $320 and Dent maximizes his profits. On the graph you draw in (a), shade in and label the following areas: total costs, total revenue, and total profits. using the factor theorem, which polynomial function has the zeros 4 and 4 5i? x3 4x2 23x 36 x3 12x2 73x 164 x2 8x 5ix 20i 16 x2 5ix 20i 16 U Ltd. and L Ltd. are identical firms except that U Ltd. is ungeared while L Ltd. Has R20million of 8% bonds outstanding. Both firms have a tax rate of 50%, earnings before interest and tax of R5million, and the cost of equity capital for U Ltd. is 10% p.a. Assume that all of the MM assumptions are met. Required: a) Estimate the market values of both U Ltd and L Ltd. b) If the market value of U Ltd. equals R20million and the market value of L Ltd. equals R40million, are the companies over or under valued? How will investors react to these values?. _______ refers to the process of evaluating and selecting the _______. Media buying; media mix Media planning; media mix Advertising; media buy Media mixing; media buy Promotion planning; advertising mix pol Consider the market for tangelo oranges and suppose the demand function is given by Q=2000-2P, where represents the quantity demanded of tangelo oranges and p represents the price per pound. Suppose the supply function is given by Q=3P. where Q represents the quantity supplied. Find the equilibrium quantity and price of tangelo oranges in the market. d O a. Equilibrium price and quantity are, respectively, P=400, Q = 1200- O b. Equilibrium price and quantity are, respectively, P=500, Q=500. O c. Equilibrium price and quantity are, respectively, P= 1000, Q=300. O d. Equilibrium price and quantity are, respectively, P=425, Q=925 QUESTION 3 Suppose the population's income increases, shifting the demand curve to the right. Now the demand curve for tangelo oranges becomes Q-4000-2P. The supply curve remains the same. Q=3P. The new equilibrium price and quantity in the market are: O a. P=800, Q=2400. O b. p=2200, Q=1100. OCP=500, Q=500. O d. P=100, Q=250. 10 poi Peyton Manufacturing is trying to decide between two different conveyor belt systems. System A costs $280,000, has a four-year life, and requires $85,000 in pretax annual operating costs. System B costs $396,000, has a six-year life, and requires $79,000 in pretax annual operating costs. Both systems are to be depreciated straight-line to zero over their lives and will have zero salvage value. Suppose the company always needs a conveyor belt system; when one wears out, it must be replaced. Assume the tax rate is 25 percent and the discount rate is 9 percent. Calculate the EAC for both conveyor belt systems. (Your answers should be negative values and indicated by minus signs. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) If real income grows at approximately 2% per year, the number of years it will take for real income to double is approximately O a. 12. O b. 36. O c. 72. O d. 24. O e. 5. *Normal Distribution*(5 pts) A soft drink machine outputs a mean of 25 ounces per cup. The machine's output is normally distributed with a standard deviation of 3 ounces. What is the probability of filling a cup between 2 How to find a point along a line a certain distance away from another point ? define the Customer relationship management ofWOWPrime, a food chain from Taiwan, using the,Customer loyalty &satisfaction establishment + measurementsASI Model of Customer Satisfaction. Perceivedquality = Actual - Expected.Strategic partnership alliance: Many companieswork closely with suppliers that share commonvalues.Worldwide Wowprime restaurant : Averageevaluation point, applied tools, etc. Form ofWowprime's Customer satisfaction survey: Formalwritten surveys, Face-to-face interviews,Telephone interviews, Focus groups.define the Customer relationship management ofWOWPrime, a food chain from Taiwan, using the,Customer loyalty &satisfaction establishment + measurementsASI Model of Customer Satisfaction. Perceivedquality = Actual - Expected.Strategic partnership alliance: Many companieswork closely with suppliers that share commonvalues.Worldwide Wowprime restaurant : Averageevaluation point, applied tools, etc. Form ofWowprime's Customer satisfaction survey: Formalwritten surveys, Face-to-face interviews,Telephone interviews, Focus groups. Can this answer be equal to 30 marks An employee, Ross, was an operator of heavy equipment in a sand and gravel operation. His performance was adequate for most of the 5 year period during which he worked for his employer. The operation was several miles out of town, and Ross and others took a company bus to the worksite. Several co-workers began to notice that there was a smell of marijuana emanating from Ross on a daily basis and reported it to the employer. The employer confronted Ross who admitted he had a drug problem.What is the best course of action for the employer to deal with Ross?What should Ross do in order to save his job?Can Ross can be terminated? When and on what basis? Examine all possibilities. Direction: Critically analyze and answer the following questions(9 Marks) Mohammed requires funds to purchase Villa. The Villa willcost BHD 75,000 to construct. Mariam, his wife, has up to BHD20,00