In ΔDEF, d = 5.2 inches, e = 6.8 inches and ∠F=166°. Find the length of f, to the nearest 10th of an inch.

The number of calories that Taylor would have to burn at her next workout to have the same average as Macy is given as follows:

312.4 calories.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Hence the mean amount for each person is given as follow:

Hence the number of calories needed in the sixth workout for Taylor is obtained considering a mean of 420.4 as follows:

420.4 = (442 x 5 + n)/6

2210 + n = 2522.4

n = 2522.4 - 2210

n = 312.4 calories.

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Answer:

$0.52

Step-by-step explanation:

1. Find the cost of 1 pencil by dividing the cost of 7 pencils by 7 pencils:

1.82 / 7 = 0.26

This means 1 pencil cost $0.26.

2. To find the cost of 2 pencils multiply the cost of 1 pencil by 2:

0.26 x 2 = 0.52

Hence, 2 pencils cost $0.52 of 7 pencils cost $1.82.

The probability that the rat presses the red button exactly 2 times is 1/9, which corresponds to option C in the multiple-choice list.

To calculate the probability of the rat pressing the red button exactly 2 times, we need to consider the sample space of possible outcomes. Since there are 3 buttons and the rat presses them twice, there are 3 x 3 = 9 possible outcomes.
Now, let's identify the favorable outcomes: The only outcome that satisfies the condition of pressing the red button exactly 2 times is when the rat presses the red button first and then presses the red button again (RR).
There is only 1 favorable outcome, so the probability of pressing the red button exactly 2 times is:
P(RR) = Number of favorable outcomes / Total number of possible outcomes
P(RR) = 1/9

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Answer:

C: m∠5 + m∠6 =180°

D: m∠2 + m∠3 = m∠6

E: m∠2 + m∠3 + m∠5 = 180°

Answer: 17 is a prime number.

Explanation:

17 is a prime number because it is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, 17 can only be divided evenly by 1 and 17. It is not possible to find any other whole number that can divide into 17 without a remainder. This property is what makes 17 a prime number.

Answer:

17

Step-by-step explanation:

17 is the only # in the set that is only divisible by 1 and itself, make it prime.

On the other hand,

10 is divisible by:

1, 10

2, 5.

12 is divisible by:

1, 12

2, 6

3, 4

So only 17 is prime.

The dimensions of the actual painting are 32 inches by 40 inches

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

Scale = 4:1.

The dimensions of the scaled painting are 8 inches by 10 inches.

So, we have

Actual = 4 * 8 inches by 4 * 10 inches

Evaluate

Actual = 32 inches by 40 inches

Hence, the dimension is 32 inches by 40 inches

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It takes 15,699.5 grams of CaC2 to thoroughly react with 490 moles of water.

The balanced chemical equation for the reaction of calcium carbide (CaC₂) with water (H₂O) is:

CaC₂ + 2H₂O → Ca(OH)₂ + C₂H₂

From the equation, we can see that 1 mole of CaC₂ reacts with 2 moles of H₂O. Therefore, to find the number of moles of CaC₂ needed to react completely with 490 moles of H₂O, we divide 490 by 2:

Number of moles of CaC₂ = 490 moles of H₂O / 2 = 245 moles of CaC₂

Now, we need to use the molar mass of CaC₂ to convert the number of moles to grams:

Molar mass of CaC2 = 64.10 g/mol

Mass of CaC₂ = Number of moles of CaC₂ x Molar mass of CaC₂

= 245 moles x 64.10 g/mol

= 15,699.5 g

Therefore, 15,699.5 grams of CaC₂ are needed to react completely with 490 moles of H₂O.

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Given that the hits to a web site occur at a rate of 10 per minute between 7:00 P.M. and 10:00 P.M., we can say that the web site experiences a Poisson process. The value of land for this Poisson process is 260.

The random variable X represents the number of hits to the web site between 7:56 P.M. and 8:22 P.M.

To find the values of λ, we need to use the formula for the Poisson distribution:

P(X = k) = (λ^k * e^-λ) / k!

where λ is the average number of hits per unit time.

Since we are interested in the hits between 7:56 P.M. and 8:22 P.M., which is a duration of 26 minutes, we need to adjust the rate of hits accordingly. Therefore, λ for this duration would be:

λ = 10 hits/min * 26 min = 260 hits

So, the values of λ for this Poisson process would be λ = 260.

To determine the values of λ (lambda) for this Poisson process, we need to first calculate the time interval between 7:56 P.M. and 8:22 P.M. and then find the expected number of hits to the website during that time.

Step 1: Calculate the time interval
The time interval between 7:56 P.M. and 8:22 P.M. is 26 minutes.

Step 2: Determine the expected number of hits
The website receives hits at a rate of 10 per minute. To find the expected number of hits during the 26-minute interval, multiply the rate by the length of the interval:
10 hits/minute * 26 minutes = 260 hits

Step 3: State the value of λ for the Poisson process
The random variable X represents the number of hits to the website during this interval. Since the expected number of hits is 260, the value of λ for this Poisson process is 260.

Your answer: The value of λ for this Poisson process is 260.

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In the original derivation of logistic regression from Naive Bayes assumptions, we assumed that the variance σ^2 of a class-conditional probability distribution is independent of class index k and feature index j. Now, by generalizing and allowing σ^2_jk to depend on both indices, the class-conditional probability distribution p(x|y=k) is now affected by this change.

This new assumption affects the logistic regression formula p(y|X) because it no longer relies on the original independence assumption. Consequently, the logistic regression model will need to account for the new variances σ^2_jk, which depend on both class index k and feature index j.

The new form of logistic regression will likely be different from the original formula, as it must now accommodate the modified variances in class-conditional probability distributions. Unfortunately, without more information, it is not possible to provide the exact new form of logistic regression here. However, it's important to note that this new form should consider the dependency of σ^2_jk on both indices j and k.

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To solve this problem, we need to use the formula for permutations, which is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects we are choosing. In this case, we are choosing 5 digits from a set of 6 digits (since we can't repeat any digit), so we have:

6P5 = 6! / (6 - 5)! = 6 x 5 x 4 x 3 x 2 = 720

Therefore, there are 720 5-digit numbers that can be formed using only the digits 3, 8, 1, 2, 5, and 7, where no digit is used more than once.
To form a 5-digit number using the digits 3, 8, 1, 2, 5, and 7 without repetition, follow these steps:

1. Choose a digit for the first position: You have 6 options (3, 8, 1, 2, 5, or 7).
2. Choose a digit for the second position: You now have 5 remaining options (since you cannot repeat the digit chosen in step 1).
3. Choose a digit for the third position: You have 4 remaining options (excluding the digits chosen in steps 1 and 2).
4. Choose a digit for the fourth position: You have 3 remaining options (excluding the digits chosen in steps 1, 2, and 3).
5. Choose a digit for the fifth position: You have 2 remaining options (excluding the digits chosen in steps 1, 2, 3, and 4).

Now, multiply the number of options for each position: 6 × 5 × 4 × 3 × 2 = 720

So, there are 720 different 5-digit numbers that can be formed using the digits 3, 8, 1, 2, 5, and 7 without repetition.

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Your answer: b. The larger the p-value, the more confident we are that we should reject the null hypothesis that the population coefficient is equal to 0.

Option b is true regarding p-values associated with the estimated coefficients in a linear regression model. The p-value represents the probability of observing a test statistic as extreme or more extreme than the one observed, assuming that the null hypothesis is true.

Therefore, the larger the p-value, the more likely it is that the estimated coefficient is not significantly different from 0 and we fail to reject the null hypothesis. A p-value of less than 0.05 is commonly used to indicate statistical significance. The R-square value, which measures the proportion of variance in the dependent variable explained by the independent variable(s), is not directly related to the p-value.

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Answer:

39.25 mm

Step-by-step explanation:

Based on the given scenario, an X-Bar/S chart would be the most appropriate type of control chart to use for monitoring the nonconformance rate per day. This is because the X-Bar/S chart is designed to monitor the process mean and variability over time, which is important for detecting any shifts or trends in the nonconformance rate.

The automated data collection system will record data for 25,000 parts per day, which provides enough data points to construct an X-Bar/S chart with sufficient sample size. By analyzing the chart, quality control personnel can quickly identify any deviations from the expected nonconformance rate and take corrective action as necessary to maintain the stability and quality of the manufacturing process.

A U chart would be used for this scenario. The automated data collection system records data for a large number of parts (25,000) daily. The nonconformance rate is given in NCPPM (nonconforming parts per million), which represents a count of nonconforming parts in a sample. U charts are appropriate for monitoring the average number of nonconformities per unit in a process, making it the most suitable choice among P, U, and X-Bar/S Charts for this case.

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To determine which data set will follow the simple linear regression (SLR) model, we need to look for a relationship between the independent variable (xi) and the response variable (yi).

The SLR model assumes that there is a linear relationship between the two variables, meaning that as the value of xi increases or decreases, the value of yi also increases or decreases in a straight line.
Therefore, the data set that shows a clear linear relationship between xi and yi is most likely to follow the SLR model. We can use a scatter plot to visualize the relationship between the two variables and determine if it is linear.
If the scatter plot shows a roughly straight line relationship between xi and yi, then the data set is likely to follow the SLR model. On the other hand, if the scatter plot shows a curved or non-linear relationship between xi and yi, then the data set is not likely to follow the SLR model.
So, in summary, the data set that shows a clear linear relationship between xi and yi is the one that is most likely to follow the simple linear regression (SLR) model.

Simple linear regression (SLR), it is important to note that SLR is a method used to model the relationship between a response variable (yi) and an independent variable (observation xi). In this model, the response variable yi is a linear function of the independent variable xi.
Since you have not provided specific data sets to choose from, I am unable to directly indicate which data set will follow this model. However, to identify a data set that would likely follow the simple linear regression model, look for one that exhibits a linear relationship between the independent variable (xi) and the response variable (yi). In such a data set, you would observe a pattern where, as xi increases or decreases, yi would also consistently increase or decrease in a relatively straight line.
To summarize, to determine if a data set follows the simple linear regression model, check if it exhibits a linear relationship between the independent variable (observation xi) and the response variable (yi).

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It will take approximately 6.96 years for the fish population to reach 2700. The initial fish population (P0) is 400, and after the first year, the population triples, making it 1200. The carrying capacity (K) is 5400. We can use these values to find the constant k.

a. To determine the constant k, we can use the initial conditions given in the problem. In the first year, the number of fish tripled, which means the population increased by a factor of 3. Therefore, we can set P(1) = 3(400) = 1200. We also know that the carrying capacity is 5400, so we can set K = r(1-Pmax/P0) where r is the intrinsic growth rate and P0 is the initial population. Substituting in the values we get K = 0.372.

Now we can solve the logistic equation:

dP/dt = kP(1-P/5400)

Separating variables and integrating, we get:

ln|P/ (5400-P)| = 0.372t + C

where C is the constant of integration. To find C, we can use the initial condition that P(0) = 400:

ln|400/5000| = C

C = -4.605

Substituting C back into the equation, we get:

ln|P/ (5400-P)| = 0.372t - 4.605

Taking the exponential of both sides:

|P/ (5400-P)| = e^(0.372t-4.605)

Multiplying both sides by the denominator and simplifying:

P = 5400e^(0.372t-4.605) / (1 + e^(0.372t-4.605))

b. We want to find the time t when the population reaches 2700. So we can set P = 2700 and solve for t:

2700 = 5400e^(0.372t-4.605) / (1 + e^(0.372t-4.605))

Multiplying both sides by the denominator and simplifying:

2700 + 2700e^(0.372t-4.605) = 5400e^(0.372t-4.605)

Dividing both sides by 2700 and simplifying:

1 + e^(0.372t-4.605) = 2

Taking the natural logarithm of both sides:

0.372t - 4.605 = ln(1)

0.372t = 4.605

t = 12.4 years

Therefore, it will take approximately 12.4 years for the population to reach 2700.

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If at the beginning of the year, a company estimates total overhead costs of $1,309,620. The amount of overhead should be applied to a job that uses 30 machine hours that year is: 13,140.

Overhead rate per machine hour = Total estimated overhead costs / Estimated number of machine hour

Overhead rate per machine hour = $1,309,620 / 2,990

Overhead rate per machine hour  = $438 per machine hour

Overhead applied to job = Overhead rate per machine hour x Number of machine hours used

Overhead applied to job = $438 x 30

Overhead applied to job = $13,140

Therefore, the amount of overhead is $13,140.

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The length and the width of the bar are 11.06 feet and 5.83 feet respectively

Let the width of the chocolate bar be x

From the question, the length of the chocolate bar is 0.6 feet shorter than twice its width. Therefore, the length (l) can be expressed as:

l = 2x - 0.6

The base area of the chocolate bar is given as 63.80 square feet. We can use this information to write an equation for the area of the chocolate bar in terms of its length and width:

area = length * width

63.80 = (2x - 0.6) * x

Expanding the right-hand side, we get:

63.80 = 2x² - 0.6x

Subtracting 63.80 from both sides, we get:

2x² - 0.6x - 63.80 = 0

Dividing both sides by 2, we get:

x² - 0.3x - 31.90 = 0

We can now solve this quadratic equation using the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 1, b = -0.3, and c = -31.90

Substituting in the values, we get:

x = (-(-0.3) ± sqrt((-0.3)^2 - 4(1)(-31.90))) / 2(1)

x = (0.3 ± sqrt(0.09 + 127.60)) / 2

x = (0.3 ± 11.36) / 2

We can now solve for the two possible values of x:

x = (0.3 + 11.36) / 2 = 5.83 or x = (0.3 - 11.36) / 2 = -5.53

Since the width of the chocolate bar cannot be negative, therefore, the width of the chocolate bar is 5.83 feet.

We can now use the equation for the length of the chocolate bar to find its length:

l = 2x - 0.6

l = 2(5.83) - 0.6

l = 11.06

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Answer:

Magnitude: 23.4 kph

Direction: 50.2° below horizontal.

Step-by-step explanation:

15² + 18² = s²

s² = 549

s = 23.4

Θ = tan^-1 18/15

Θ = 50.2°

The velocity vector is the sum of the two vectors which is a vector that starts at the boat and goes until the lower tip of the vertical arrow.

Its magnitude is 23.4 kph, and its direction is 50.2° below horizontal.

Answer:  boats vector is 23.45 kph, 50.2° south of east

Step-by-step explanation:

A  vector has both direction and magnitude.

The vector for the boat is the shortest route from the boat to that end point which is a diagonal.

In order to find magnitude you use pythagorean

c²=a²+b²

m=15²+18²

m=√549

magnitude=23.45 kph

direction you would use tan∅

tan∅=opp/adj=18/15

∅= [tex]tan^{-1} \frac{18}{15}[/tex]

∅=50.2

So the boats vector is 23.45 kph, 50.2° south of east

At the 0.05 significance level, for a p-value of 0.0005, you should find in favor of the alternative hypothesis and reject the null hypothesis, i.e., Option B is the correct answer.

The significance level, also known as alpha, is the threshold used to determine whether to reject or fail to reject the null hypothesis. In this case, the significance level is 0.05, which means that there is a 5% chance of rejecting the null hypothesis when it is true.

The p-value, on the other hand, is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. A small p-value indicates strong evidence against the null hypothesis, while a large p-value suggests weak evidence against it.

In this scenario, the p-value of 0.0005 is smaller than the significance level of 0.05, indicating strong evidence against the null hypothesis. As such, you should find in favor of the alternative hypothesis and reject the null hypothesis. This means that there is significant evidence to support the alternative hypothesis and suggest that the observed results are not due to chance.

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To find the distance from y to the plane in R3 spanned by u, we first need to find the projection of y onto u.

We can do this using the formula: proj_u(y) = ((y ⋅ u) / ||u||^2) * u
where ⋅ represents the dot product, and ||u|| is the length of u. Plugging in the values given,

we get: proj_u(y) = ((3(-8) - 2(5) - 4(-5)) / (1^2 + 2^2 + 2^2)) * <1, 2, 2>
          = (-44 / 9) * <1, 2, 2>
          = <-44/9, -88/9, -88/9>

Next, we can find the distance from y to the plane by subtracting the projection from y, and taking the length of the resulting vector.

That is: distance from y to plane = ||y - proj_u(y)||
                        = ||<0, 3, -4> - <-44/9, -88/9, -88/9>||
                        = ||<44/9, 35/9, -4/9>||
                        = sqrt((44/9)^2 + (35/9)^2 + (-4/9)^2)
                        = sqrt(2029/81)

Therefore, the distance from y to the plane in R3 spanned by u is sqrt(2029/81), or approximately 4.208 units.

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The length of arc AB using the measure circle are 5) 6.28 feet and 6) 18.84 feet.

To find the length of arc AB with a measure of 80°, use the formula:

length of arc AB = (measure of arc AB / 360°) x circumference of circle

The diameter of the circle is given as 9 feet, so the radius is 4.5 feet. The circumference of the circle is:

circumference = 2 x π x radius

circumference = 2 x 3.14 x 4.5

circumference = 28.26 feet

Using the formula:

length of arc AB = (80° / 360°) x 28.26

length of arc AB = 0.2222 x 28.26

length of arc AB = 6.28 feet

Rounding to the nearest hundredth:

length of arc AB ≈ 6.28 feet

To find the length of arc AB with a measure of 240°, use the same formula as above:

length of arc AB = (measure of arc AB / 360°) x circumference of circle

Using the same values for the diameter and radius of the circle:

length of arc AB = (240° / 360°) x 28.26

length of arc AB = 0.6667 x 28.26

length of arc AB = 18.84 feet

Rounding to the nearest hundredth:

length of arc AB ≈ 18.84 feet

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When the eigenvalues of a matrix are equal, it means that the matrix has repeated eigenvalues. This can occur for matrices of any size, but is most commonly encountered for 2x2 or 3x3 matrices.

When a matrix has repeated eigenvalues, it can exhibit some special behaviors that are not observed for matrices with distinct eigenvalues. In particular, the matrix may not be diagonalizable, meaning that it cannot be transformed into a diagonal matrix using a change of basis. Instead, it may have only one eigenvector associated with the repeated eigenvalue, or it may have a full set of linearly independent generalized eigenvectors.

In the case of a 2x2 matrix A with repeated eigenvalues λ, the matrix may be expressed in Jordan canonical form as:

A = P * J * P^-1

where J is a matrix with λ on the diagonal and 1 on the super-diagonal, and P is the matrix whose columns are the eigenvectors and generalized eigenvectors of A. In this case, the solutions of the system x' = Ax may have a non-trivial component along the generalized eigenvector, which can lead to more complicated behavior than for matrices with distinct eigenvalues.

Overall, the presence of repeated eigenvalues in a matrix can indicate that the matrix has some special structure or symmetry, and may require additional techniques beyond diagonalization to fully understand its behavior.

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1. There are 3 decision nodes in the tree.
2. The best course of action for the hospital is option B - seek approval first, and proceed with Plan B if approved, and Plan A if denied.
3. The answer is E) B & C only. The decision tree shows conditional probabilities, but TreePlan is not maximizing the EMV. The probability of approval for Plan B does not depend on when approval is sought.
4. The EMV for choosing Plan B from the start is -137.5.

1. Decision nodes are points in a decision tree where a decision must be made. To determine the number of decision nodes in the tree, count the number of places where a choice must be made between different options.

2. To determine the best course of action, you would analyze the decision tree by considering the expected monetary value (EMV) of each path. Choose the path with the highest EMV.

3. Examine your decision tree and determine which conclusions apply. Some things to consider are:
  A) Conditional probabilities: Are there probabilities given based on the outcomes of previous decisions?
  B) "Rolling back" the decision tree: Is the tree being analyzed by working backward from the final outcomes to determine the best course of action?
  C) Probability of approval: Does the chance of getting approval for Plan B change based on when approval is sought?

4. To find the EMV for choosing Plan B from the start, calculate the probability-weighted average of the possible monetary outcomes for that path. Multiply the probability of each outcome by its monetary value, then sum those products.

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The final volume of the wooden post after the hole has been drilled is 778.41 cm³.

The volume of a right rectangular prism is given by the formula V = l × w × h, where l, w, and h represent the length, width, and height of the prism, respectively. In this case, the wooden post has dimensions of 5 cm by 9 cm by 24 cm, so its original volume is:

V1 = 5 cm × 9 cm × 24 cm = 1080 cm³

Now, we need to find the volume of the cylindrical hole. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the cylinder and h is its height. In this case, the hole has a radius of 2 cm and goes through the entire length of the wooden post, so its volume is:

V2 = π × 2 cm² × 24 cm ≈ 301.59 cm³

To find the final volume of the wooden post, we need to subtract the volume of the hole from the original volume:

Vfinal = V1 - V2 = 1080 cm³ - 301.59 cm³ = 778.41 cm³

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Answer:

A rectangle's perimeter and its area have

the same numerical value. The length of the

rectangle is 6 centimeters.

Write an equation that can be used to find x, the

width of the rectangle in centimete

Step-by-step explanation:

Answer :

According to the question it's given that,

A rectangle's perimeter and its area have the same numerical value. The length of the rectangle is 6 centimeters.

Required Formulas,

[tex]:\implies[/tex] perimeter of rectangle is 2(l+ b)

[tex]:\implies[/tex] Area of rectangle = l × b

Also, Length of rectangle is 6 cm.

Perimeter of rectangle

[tex]:\implies[/tex] 2(6 + x)

[tex]:\implies[/tex] 12 + 2x

Area of rectangle

[tex]:\implies[/tex] l × b

[tex]:\implies[/tex] 6 × x

[tex]:\implies[/tex] 6x

Now, A rectangle's perimeter and its area have the same numerical value.

Perimeter of rectangle = Area of rectangle

[tex]:\implies[/tex] 12 + 2x = 6x (required equation)

Therefore this is the required equation to find the width of the rectangle.

To find the top 10% salaries of workers at the company, we need to use the standard normal distribution table. First, we need to find the z-score that corresponds to the top 10% of the distribution, which is 1.28 (found using the table).

Next, we can use the formula:

z = (x - mean) / (standard deviation / sqrt(sample size))

We know the mean is $60,000, the standard deviation is $9,000, and the sample size is 36. We can solve for x:

1.28 = (x - 60,000) / (9,000 / sqrt(36))

1.28 = (x - 60,000) / 1,500

1.28 * 1,500 = x - 60,000

1,920 + 60,000 = x

x = $61,920

Therefore, the top 10% salaries of workers at the company is $61,920 or more.
To find the top 10% salary for workers at this company, we need to first determine the z-score that corresponds to the 90th percentile. This is because 100% - 10% = 90%.

Step 1: Look up the z-score for the 90th percentile in a standard normal distribution table. You will find a z-score of approximately 1.28.

Step 2: Use the z-score formula to find the salary corresponding to this z-score:
X = μ + Z * σ / √n
where X is the salary, μ is the mean, Z is the z-score, σ is the standard deviation, and n is the sample size.

Step 3: Plug in the given values:
X = $60,000 + 1.28 * $9,000 / √36

Step 4: Simplify the equation:
X = $60,000 + 1.28 * $9,000 / 6

Step 5: Calculate the result:
X = $60,000 + $1,920 = $61,920

The top 10% of salaries for workers at this company is $61,920 or more, rounded to the nearest dollar.

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The coordinate of point w is (3.75, 0.25).

Option D is the correct answer.

We have,

From the graph, we can see that,

The coordinate on the x-coordinate at point w is 3.75.

The coordinate on the y-coordinate at point w is 0.25.

Thus,

The coordinate of point w is (3.75, 0.25).

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The coupon give Shanice 75 percent off the original price of the pair of jeans.

At a clothing store, a pair of jeans costs $40. Using a coupon, Shanice is

able to pay $10 less than the original price. Therefore, the percentage off  the original price the coupon represents can be calculated as follows:

Therefore,

Price Shanice bought the jeans = 40 - 10 = 30 dollars

Hence,

let

x = percentage off the original price

Therefore,

x / 100 × 40 = 30

40x / 100 = 30

cross multiply

3000 = 40x

divide both sides by 40

x = 3000 / 40

x = 75%

Therefore,  the coupon gives Shanice 75% off of the original price.

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The probability of rejecting a good shipment of 100 items with 2% defective rate is 0.0913.

For part a, we can use the binomial distribution formula to calculate the probability of getting no defectives in a sample of 5 items, given that 20% of the 50 items are defective:

P(accepting a poor shipment) = P(sample of 5 contains no defectives)
= C(5,0) * (0.2)^0 * (0.8)^5
= 0.3277

So the probability of accepting a poor shipment of 50 items with 20% defective rate is 0.3277.

For part b, we can again use the binomial distribution formula to calculate the probability of getting at least one defective in a sample of 5 items, given that only 2% of the 100 items are defective:

P(rejecting a good shipment) = P(sample of 5 contains at least one defective)
= 1 - P(sample of 5 contains no defectives)
= 1 - C(5,0) * (0.02)^0 * (0.98)^5
= 0.0913

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The sides of the quadrilateral are

FG = 11

GH = 22

HJ = 33

FJ = 44

When the quadrilateral are similar according to the ratio 7 : 11 and the similar sides are:

FG : AB

GH : BC

HJ : CD

FJ : AD

Since FJ : AD the ratio is 11 : 7, therefore where FJ = 11 then AD = 7 = x

FG : AB

AB = 2x = 2 * 7 = 14

For FG

11 ⇔ 7

FG ⇔ 14

cross multiplying

7 * FG = 14 * 11

FG = 22

For GH

11 ⇔ 7

GH ⇔ BC = 3 * 7 = 21

cross multiplying

7 * GH = 21 * 11

GH = 33

For HJ

11 ⇔ 7

HJ ⇔ CD = 4 * 7 = 28

cross multiplying

7 * GH = 28 * 11

GH = 44

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