the box in the center of a boxplot marks: group of answer choices the range covered by the middle half of the data. the full range covered by the data. the range covered by the middle three-quarters of the data. the span of one standard deviation on each side of the mean.

The value of C is given as follows:

b. [tex]c = \sqrt{31}[/tex]

The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds true:

c^2 = a^2 + b^2 - 2ab cos(C)

The parameters for this problem are given as follows:

a = 5, b = 6 and C = 60º.

Hence the length C is obtained as follows:

c² = 5² + 6² - 2 x 5 x 6 x cosine of 60 degrees

c² = 31.

[tex]c = \sqrt{31}[/tex]

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For the conversion of polar coordinates into cartesian coordinates means (r, θ) changed into (x,y), the Cartesian equation for the polar equation r = 9 sin(θ), is equals to x² + y² - 9y = 0.

In the polar coordinate system has different characteristics. To convert polar coordinates to Cartesian or rectangular coordinates, solve for the x and y coordinates separately.

We have a polar equation, r = 9 sin(θ). We have to convert this polar equation into cartesian equation. To convert from polar coordinates (r, θ) to cartesian coordinates ( x, y ). So, we use the following equations, x = rcos(θ)

y = r sin(θ)

Now, x² + y² = r² sin²(θ) + r²cos(θ)

= r²( sin²(θ) + cos²(θ))

= r²

Here, we have r = 9 sin(θ)

=>[tex] r = 9 \frac{ 9y}{r}[/tex]

=> r² = 9y

So, we can write as, x² + y² = 9y

=> x² + y² - 9y = 0

Hence, required equation is x² + y² - 9y = 0.

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From the phenotypic variance (p) of the genetically variable and genetically identical plants, the value of the broad-sense heritability (H) of seed number for the roadside population of bluebonnets is equals to the 0.6.

We have, population of graduation studying students in bluebonnets along a roadside. Sample size of plants = 100

variance for plants = 25

=> standard deviations = 5

We have to determine the broad-sense heritability (H) of seed number for the roadside. Broad-sense heritability [tex]H2 = \frac{V_G }{ V_P} [/tex] ---(1)

The phenotypic variation [tex]V_P = V_G + V_E [/tex], here [tex] V_P = 25[/tex]

[tex]25 = V_G + V_E[/tex] ------(II)

In the identical population, [tex] V_G = 0[/tex] and here [tex] V_P = 10[/tex]

=> [tex]10 = 0 + V_E [/tex]

=> [tex]V_E= 10[/tex]

By substituting [tex]V_E[/tex] value in equation (II), we will determine [tex]25 = V_G + 10 [/tex]

=> [tex]V_G = 15[/tex]

Substitute the values of [tex]V_G and V_E [/tex] of the roadside population in equation (1), [tex]H²=\frac{15}{25}=0.6[/tex].

The key to the answer is assumption should be the genetic variance of the genetically identical plants is the same as the genetically variable population. In the event that we don't make this supposition, at that point our concern turns out to be very entangled in light of the fact that then we should likewise realize the genetic variance effect of the plant in its environment as well.

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The F statistic for this data set is 1.93, with a p-value of 0.098. This means that we cannot reject the null hypothesis that there is no difference between the means of the cities at a significance level of 0.05.

Therefore, we cannot conclude that there is a significant difference in hotel costs per night between the five cities.

To find the value of the test statistic to test for a difference between cities, we need to perform a statistical test such as a one-way ANOVA (analysis of variance) test. This test compares the variation between the means of multiple groups to the variation within each group. The test statistic for a one-way ANOVA is F.

To calculate the F statistic, we need to first find the sum of squares within groups (SSW) and the sum of squares between groups (SSB). SSW measures the variation within each group and SSB measures the variation between groups.

SSW = ∑(xi – xj)² / df_within

where xi is the value of each observation, xj is the mean of each group, and df_within is the degrees of freedom within groups, which is equal to the total number of observations minus the number of groups.

SSB = ∑(xj – xbar)² / df_between

where xbar is the grand mean of all the observations, and df_between is the degrees of freedom between groups, which is equal to the number of groups minus one.

Once we have calculated SSW and SSB, we can calculate the F statistic as:

F = SSB / df_between / (SSW / df_within)

If the F statistic is greater than the critical value from the F distribution table, we can reject the null hypothesis that there is no difference between the means of the groups.

In this case, we have five cities: New York, Los Angeles, Atlanta, Houston, and Phoenix. We can use Excel or another statistical software to calculate the ANOVA test.

The F statistic of 1.93 and the associated p-value of 0.098 indicate that we cannot reject the null hypothesis at a significance level of 0.05. This suggests that there is no significant difference in hotel costs per night among the five cities: New York, Los Angeles, Atlanta, Houston, and Phoenix. The analysis was performed using a one-way ANOVA test, comparing the variation between the means of the cities to the variation within each city.

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a.  Outliers are observed values far from the main group of data.

In a histogram they are separated from the others by space.

Outliers must be looked at twice, once with and once without the outliers. C.

b. The median is more resistant, which indicates that it usually changes less than the mean when comparing data with and without outliers. A.

Outliers are data points that are significantly different from the other values in a data set.

These observations can be identified by looking at a histogram, where they are separated from the main group of data by a significant space.

Outliers can be mistakes or they may represent real but unusual values.

It is important to look at outliers in closer context to determine how to treat them.

Sometimes they may be included in the analysis, but other times they may be removed or corrected.
To determine which measure of center, mean or median, is more resistant to outliers, we need to understand what "resistant to outliers" means.

Resistance to outliers refers to how much a measure of center is affected by the presence of outliers.

A measure that is more resistant to outliers will change less when outliers are present.
The median is more resistant to outliers than the mean.

This means that the median usually changes less than the mean when comparing data with and without outliers.

The reason for this is that the median is calculated by taking the middle value of the data set, which is less affected by extreme values than the mean, which takes into account all values in the data set.
Outliers should be examined carefully in the context of the data set to determine how to treat them.

The median is more resistant to outliers than the mean, which makes it a better measure of center when outliers are present.

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To construct a confidence interval for the standard deviation, we can use the chi-square distribution. The formula for the confidence interval is: ( n - 1 )S^2 / χ^2(α/2, n-1) ≤ σ^2 ≤ ( n - 1 )S^2 / χ^2(1-α/2, n-1),

where n is the sample size, S is the sample standard deviation, α is the level of significance (1-0.99 = 0.01), and χ^2 is the chi-square distribution with (n-1) degrees of freedom.

1. Identify the sample size (n), sample standard deviation (s), and the confidence level (99%).

n = 20
s = 1.76 mm
confidence level = 99%

Calculate the lower and upper bounds for the confidence interval of the population standard deviation (σ) using the sample standard deviation (s) and Chi-square values.

Lower bound: √((n-1) * s² / χ²_upper) = √(19 * 1.76² / 38.582) ≈ 1.25 mm
Upper bound: √((n-1) * s² / χ²_lower) = √(19 * 1.76² / 6.844) ≈ 2.57 mm
Interpret the confidence interval.

The 99% confidence interval for the standard deviation of the length of straws is (1.25 mm, 2.57 mm). This means that we are 99% confident that the true standard deviation of the straw lengths lies within this interval. The straw manufacturing company can use this information to assess the accuracy of their cutting machine.

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The measures of the angles in the triangle are 30 degrees, 60 degrees, and 90 degrees.

In this case, we are given that the angles of the triangle are in the ratio of 1:2:3. This means that the three angles can be expressed as x, 2x, and 3x, where x is some constant factor.

To find the value of x, we need to use the fact that the sum of the angles in a triangle is 180 degrees. So, we can write an equation:

x + 2x + 3x = 180

Simplifying the equation, we get:

6x = 180

Dividing both sides by 6, we get:

x = 30

Now that we know the value of x, we can use that to find the measure of each angle in the triangle.

The first angle is x, which we know is 30 degrees.

The second angle is 2x, which is 2 times 30, or 60 degrees.

The third angle is 3x, which is 3 times 30, or 90 degrees.

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Complete Question:

The angles of a triangle are in the ratio of 1:2:3. Find the measure of each angle of the triangle

Answer:

Step-by-step explanation:

First, we need to figure out how many 1/4 teaspoons are in 1 teaspoon:

1 teaspoon = 4 (1/4) teaspoons

So for 1 teaspoon of seasoning, we need:

1 teaspoon seasoning * 1 1/2 cups water per 1/4 teaspoon seasoning

= 4 (1/4) teaspoons seasoning * 1 1/2 cups water per 1/4 teaspoon seasoning

= 6 cups of water

Therefore, if a large batch of soup is made using 1 teaspoon of seasoning, we would need 6 cups of water.

According to the National Survey on Drug Use and Health, approximately 18.53% of U.S. adults (ages 18 and older) experienced some form of mental illness in 2016.

Approximately 18.53% of U.S. adults suffered from mental illness in 2016. This percentage represents the prevalence of mental health disorders among the adult population, which is important to understand in order to address and provide support for those affected.

This includes a range of conditions such as anxiety disorders, depression, bipolar disorder, and schizophrenia. It's important to note that mental illness can vary in severity and can impact individuals differently, and seeking professional help can greatly improve one's quality of life.

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To find the capuchin monkey's weight with the same standardized weight as the lowland gorilla, we need to first calculate the z-score of the gorilla's weight.

The z-score represents how many standard deviations a data point is away from the mean.

For the gorilla with a weight of 345 pounds, the z-score can be calculated as follows: Z-score = (Weight - Mean) / Standard Deviation
Z-score = (345 - 275) / 40 = 70 / 40 = 1.75.

So a gorilla weighing 345 pounds has a standardized weight of 1.75 standard deviations above the mean. Now we need to find out how much a capuchin monkey would have to weigh to have the same standardized weight.

We can use the same formula and solve for x: z = (x - mean) / standard deviation .

1.75 = (x - 6) / 1.1
1.925 = x - 6
x = 7.925

So a capuchin monkey would have to weigh approximately 7.925 pounds to have the same standardized weight as a gorilla weighing 345 pounds. It's important to note that standardized weights are not the same as actual weights.

They are simply a way to compare values from different distributions on a common scale.

Now that we have the z-score, we can use it to find the capuchin monkey's weight with the same standardized weight: Weight = Mean + (Z-score × Standard Deviation), Weight = 6 + (1.75 × 1.1) = 6 + 1.925 = 7.925.

Therefore, a capuchin monkey would have to weigh approximately 7.93 pounds to have the same standardized weight as the lowland gorilla.

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False, For this situation, the professor should not use a t test with related samples.

The scenario described in the question involves two independent samples (upper and lower classmen) and not related samples. A t-test for related samples is used when the same group of participants is measured twice, resulting in paired or dependent samples.

Since the variances of the two independent samples are equal, the appropriate test in this scenario is a two-sample t-test for equal variances. However, the sample size of 10 for each group is relatively small, and the normality assumption of the t-test may not hold. Therefore, the professor should first check the normality assumption of the data using a normal probability plot or a Shapiro-Wilk test. If the assumption is not met, nonparametric tests such as the Wilcoxon rank-sum test can be used as an alternative.

In summary, the correct statistical test for this scenario is a two-sample t-test for equal variances or a nonparametric alternative if the normality assumption is not met. The t-test for related samples is not appropriate in this case.

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Based on the given information, we know that one bicycle trail in a new housing development is 3 miles long and the other trail is the same length as the first trail.

Therefore, the length of the second trail is also 3 miles.

Hence, the answer is: 3 miles

It seems like there's a missing piece of information in your question about the length of the second trail.

However, I will try my best to help you with the given information.
Two bicycle trails are developed in the housing development.

The first trail is 3 miles long, and we need to find the length of the second trail.

Unfortunately, there is no information provided about the second trail's length.

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The Masters golf tournament belongs to a large scale event category, given the corresponding variations in its impacts such as attracting thousands of visitors and generating significant economic activity in the host city.

The Masters Golf Tournament belongs to a large-scale event category. Large-scale events typically have significant impacts, including attracting international attention, generating substantial economic benefits, and requiring considerable planning and resources.

In the case of the Masters Golf Tournament, it is an annual event held at Augusta National Golf Club in Georgia, USA, and it attracts professional golfers from around the world, as well as a global audience, creating corresponding variations in economic, social, and environmental impacts.

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The x-coordinate that makes this relation not a function.

A relation is not a function if one of the inputs (x-coordinates) is mapped into two or more different outputs.

Here we have the relation:

(4, 8), (-3, 6), (-3, 7), (1, 6)

If you look at the inputs, you can see that:

x = -3

Is mapped into two different outputs, so that is the x-coordinate that makes this not a function.

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The observed score on y for Carl is 7.

In regression analysis, the predicted values of the dependent variable (in this case, happiness) are calculated based on the values of the independent variable(s) (in this case, average amount of sleep) using a regression equation. If Carl's predicted happiness score based on the regression equation is 6, but his actual reported happiness score is 7, then his observed score on y is 7.

The difference between his predicted and observed score can be used to evaluate the accuracy of the regression equation in predicting happiness based on sleep, and to identify any outliers or other factors that may be influencing the relationship between the two variables.

Overall, the observed score on y for Carl is 7.

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The angle of depression the plane should descend is 1.43 degrees.

A plane is flying at an altitude of 25,000 ft when it start it descent to the airport. The plane is a horizontal distance of 1000,000 ft from the airport.

Therefore, let's find the angle of depression.

Hence, this situation forms a right angle triangle.

Therefore,

tan ∅ = opposite / adjacent

where

Hence,

tan ∅ = 25000 / 1000000

∅ = tan⁻¹ 25 / 1000

∅ =  tan⁻¹  0.025

∅ = 1.43209618416

∅ = 1.43 degrees

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Answer:

$16

Step-by-step explanation:

25% off of 100% = 75%

0.75x=12, where x is the original cost

x=16

Step-by-step explanation:

The top right one most closely approximates the data.

Answer:I'm gonna have to go with top right

Step-by-step explanation:

A linear line is a straight line, the image you gave wasn't to clear but it looks like the right one.

If "3 marks" are awarded for each "correct-answer" and "-1 marks" for each "incorrect-answer", then the total score of Varun in quiz is 47.

Out of the 25 questions in the quiz, Varun attempted all of them, which means he has answered 25 questions in total.

Out of the 25 questions, Varun answered only 18 correctly, which means he answered 7 questions incorrectly.

Therefore, the total score for his correct answers would be : 18 × 3;

⇒ 54 marks,

The total score for his incorrect answers would be : 7 × (-1) = -7;

Varun did not leave any question "un-attempted", so he did not gain or lose any marks for those questions.

Varun's total score in the quiz would be : (Score for correct answers) + (Score for incorrect answers)

⇒ Total Score = 54 + (-7) = 47 marks,

Therefore, Varun's total score in quiz is 47 marks.

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The given question is incomplete, the complete question is

In a Mathematics quiz, the total number of questions are 25. According to the marking scheme, 3 marks are given for every correct answer and -1 marks for every incorrect answer, and 0 for questions not attempted.

Varun attempts all questions but only 18 of his answers are correct. What is his total score in the quiz?

The regular cost per month for a Switch Gears Activity Box subscription is $12.

To find the regular cost per month, Derek needs to subtract the discount he received from the total cost and divide the result by the number of months in his subscription. Let x be the regular cost per month. Then, the equation can be written as follows:

8x - 15 = 81

In this equation, 8x represents the total cost of the 8-month subscription at the regular price. Subtracting $15 from this total cost gives the amount Derek actually paid. Therefore, 8x - 15 = $81.

To find the regular cost per month, Derek needs to isolate x on one side of the equation. He can do this by adding 15 to both sides of the equation, then dividing both sides by 8. The resulting equation is:

8x = 96

x = 12

Derek can now use this information to budget for future subscriptions or compare it to other subscription services.

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The explicit formula for this sequence 6, 12, 24, 48, 96, .. is equal to aₙ = 6 * 2ⁿ⁻¹.

The sequence shown above is a geometric sequence because each term is obtained by multiplying the previous term by 2. To find the explicit formula for this sequence, we can use the formula:

aₙ = a₁ * rⁿ⁻¹

where:

aₙ = the nth term of the sequence

a₁ = the first term of the sequence

r = the common ratio between terms

n = the position of the term in the sequence

In this case, a₁ = 6 and r = 2, so the formula becomes:

aₙ = 6 * 2ⁿ⁻¹

Using this formula, we can find any term in the sequence by plugging in the value of n. For example, to find the 7th term, we would plug in n = 7:

a₇ = 6 * 2⁷⁻¹ = 6 * 2⁶ = 384

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The best description of the shape and center of the dotplot is that distribution of math classes is unimodal symmetric with a center around 4 classes. The Option C is correct.

A dot plot shows the frequency of each value in a dataset. To identify if the distribution of classes is unimodal symmetric, we will check if the dots are roughly evenly distributed around a central line which is the 4 classes.

This indicates the distribution is symmetric. We have a single peak in the data. If there is only one prominent cluster of dots, then, the distribution is unimodal. So, the distribution of classes is unimodal symmetric on the dot plot.

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Answer:

c

Step-by-step explanation:

took the test

Operating Income $21,950

Yes. The franchisees still earn target profit.

Requirement 1.

Contribution margin per unit $4.55

X Average sales volume units 7,000

Contribution margin $31,850

Less: Fixed expenses $7,800

Operating Income $24,050

Requirement 2.

Contribution margin per unit $4.05 ($6.50 - $2.45)

X Average sales volume units 7,500

Contribution margin $30,375

Less: Fixed expenses $8,425

Operating Income $21,950

Yes. The franchisees still earn the target profit.

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A binomial distribution is characterized by two outcomes (success or failure) and a fixed number of trials with the same probability of success on each trial.

In this case, X represents the number of times you roll the dice before achieving a Yahtzee.

However, X is not a binomial distribution because it doesn't have a fixed number of trials. You continue rolling until you get a Yahtzee, which could take an unpredictable number of attempts. Instead, X follows a geometric distribution, which describes the number of trials needed for the first success in a sequence of Bernoulli trials.

Yes, X is binomial because it has the following properties:

1. There are a fixed number of trials (rolling the dice repeatedly)
2. Each trial is independent of the others (the outcome of one roll does not affect the outcome of the next)
3. There are only two possible outcomes for each trial (either a Yahtzee is rolled or it isn't)
4. The probability of success (rolling a Yahtzee) is constant for each trial (1/6 to the 5th power, or about 0.00077)

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Each part will be approximately 8.04 inches long.

We can express this as:

Length of each part = Total length of ribbon / Number of parts

In this case, the total length of the ribbon is 4 feet, and we want to divide it into six equal parts. So, we can substitute these values into the above formula:

Length of each part = 4 feet / 6 parts

To solve this division problem, we can either use a calculator or do long division:

4 / 6 = 0.6666666667

So, each part will be approximately 0.67 feet long. Alternatively, we can convert this to inches, which is a more common unit of measurement for small lengths:

0.67 feet x 12 inches/foot = 8.04 inches

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We can conclude that $(\frac{-2}{p})=1$ if and only if $p\equiv \pm 1\pmod{8}$, and $(\frac{-2}{p})=-1$ if and only if $p\equiv \pm 3\pmod{8}$.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities. It is a way of expressing a number as a quotient of two integers, where the top number is called the numerator, and the bottom number is called the denominator.

By the multiplicative property of the Legendre symbol, we know that $(\frac{-2}{p}) = (\frac{-1}{p}) (\frac{2}{p})$.

We have $(\frac{-1}{p})=(-1)^{\frac{p-1}{2}}$. Therefore, $(\frac{-1}{p})=1$ if $p\equiv 1\pmod{4}$, and $(\frac{-1}{p})=-1$ if $p\equiv 3\pmod{4}$.

To evaluate $(\frac{2}{p})$, we use the quadratic reciprocity law. We have $(\frac{2}{p})=(-1)^{\frac{p^2-1}{8}}(\frac{p}{2})$, where $(\frac{p}{2})$ is the Legendre symbol.

We have $(\frac{p}{2})=1$ if $p\equiv \pm 1\pmod{8}$ and $(\frac{p}{2})=-1$ if $p\equiv \pm 3\pmod{8}$.

Therefore, $(\frac{2}{p})=(-1)^{\frac{p^2-1}{8}}(\frac{p}{2})$ is equal to $1$ if $p\equiv \pm 1\pmod{8}$ and $-1$ if $p\equiv \pm 3\pmod{8}$.

Putting it all together, we have $(\frac{-2}{p}) = (\frac{-1}{p}) (\frac{2}{p}) = 1$ if $p\equiv 1\pmod{4}$ and $p\equiv \pm 1\pmod{8}$, and $(\frac{-2}{p}) = (\frac{-1}{p}) (\frac{2}{p}) = -1$ if $p\equiv 3\pmod{4}$ and $p\equiv \pm 3\pmod{8}$.

Therefore, we can conclude that $(\frac{-2}{p})=1$ if and only if $p\equiv \pm 1\pmod{8}$, and $(\frac{-2}{p})=-1$ if and only if $p\equiv \pm 3\pmod{8}$.

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Logarithms are a useful tool in determining the acidity or basicity of a solution. pH is a measure of the concentration of hydrogen ions in a solution and is calculated using the formula pH = -log[H+].

A solution with a pH of 7 is considered neutral, while a pH below 7 indicates acidity and a pH above 7 indicates basicity.

Using logarithms, we can determine the pH of 7 solutions ranging from strong acid to neutral to strong base. To do this, we need to measure the concentration of hydrogen ions in each solution and then use the formula above to calculate the pH.

For example, if we have a solution with a hydrogen ion concentration of 0.001 M, we can calculate the pH as follows:

pH = -log(0.001) = 3

This solution would be considered a strong acid, as it has a pH below 7. Similarly, a solution with a hydrogen ion concentration of 10^-7 M (which is the same as a concentration of 1x10^-7 M) would have a pH of 7 and would be considered neutral.

Finally, a solution with a hydrogen ion concentration of 10^-11 M would have a pH of 11 and would be considered a strong base.

In summary, using logarithms, we can determine the acidity or basicity of a solution by calculating its pH. A pH of 7 is considered neutral, while a pH below 7 indicates acidity and a pH above 7 indicates basicity.

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The hypergeometric probabilities for the given values of n and x are:

(a) P(X = 2) = 0.5143

(b) P(X = 3) = 0.1429

(c) P(X = 0) = 0.3571

(d) P(X = 3) = 0.0714

The hypergeometric probability mass function is given by:

P(X = x) = (rCx)(N-rCn-x) / (NCn)

where N is the total number of items in the population, r is the number of "successes" in the population, n is the sample size, and x is the number of "successes" in the sample.

(a) For n = 4 and x = 2:

P(X = 2) = (4C2)(8-4C4-2) / (8C4)

= (6)(6) / (70)

= 0.5143

(b) For n = 6 and x = 3:

P(X = 3) = (4C3)(8-4C6-3) / (8C6)

= (4)(1) / (28)

= 0.1429

(c) For n = 3 and x = 0:

P(X = 0) = (4C0)(8-4C3-0) / (8C3)

= (1)(20) / (56)

= 0.3571

(d) For n = 3 and x = 3:

P(X = 3) = (4C3)(8-4C3-3) / (8C3)

= (4)(1) / (56)

= 0.0714

Therefore, the hypergeometric probabilities for the given values of n and x are:

(a) P(X = 2) = 0.5143

(b) P(X = 3) = 0.1429

(c) P(X = 0) = 0.3571

(d) P(X = 3) = 0.0714

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The final cost of filling up the tank with 750 liters of oil at a price of 81.5p per liter with a 7.5% discount is 56,540.62p.

The price of oil is 81.5p per litre. If we want to calculate the cost of filling up the tank, we need to know how many liters of oil we need to add.

To do this, we need to subtract the current amount of oil in the tank (450 liters) from the maximum capacity of the tank (1200 liters):

1200 - 450 = 750 liters

So we need to add 750 liters of oil to fill up the tank.

Next, we need to calculate the cost of adding 750 liters of oil at the price of 81.5p per liter:

750 x 81.5 = 61,125p

To calculate the discount, we first need to find 7.5% of the total cost. We can do this by multiplying the total cost by 7.5% expressed as a decimal:

61,125 x 0.075 = 4,584.38p

So the discount is 4,584.38p.

To find the final cost after the discount, we need to subtract the discount from the total cost:

61,125 - 4,584.38 = 56,540.62p

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