Let’s say we were only interested in testing whether 25% of rabbits had long fur – the breakdown between medium and short fur didn’t interest us. Our alternative hypothesis is that 25% of rabbits don't have long fur. Which test could we run?

The value of angle A is 43⁰.

The value of arc CE is 44⁰.

The value of angle C is 43⁰.

The value of angle ABE is 90⁰

The value of angle A is calculated by applying the following formula as shown below;

∠A  = ¹/₂ arc BD (intersecting chord theorem)

∠A  = ¹/₂ x 86⁰

∠A  = 43⁰

arc CE = 2 ∠mCBE

arc CE = 2 x 22

arc CE = 44⁰

∠A = ∠ C (vertical opposite angles are equal)

∠C = 43⁰

∠ABE = 90⁰

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The minimum surface area of the container is approximately 275.52 cm².

Let's suppose that the length, width, and height of the rectangular container are l, w, and h, respectively. We know that the container has a square base, so l = w. Also, we know that the volume of the container is 864 cm³, so we have:

l × w × h = 864

Since l = w, we can write this as:

l² × h = 864

We want to minimize the surface area of the container, which consists of the area of the base (l²) and the area of the four sides (2lh + 2wh). We can express the surface area in terms of l and h:

Surface Area = l² + 2lh + 2wh

Using the equation l² × h = 864, we can solve for h in terms of l:

h = 864 / (l²)

Substituting this into the equation for the surface area, we get:

Surface Area = l² + 2l(864 / l²) + 2w(864 / (lw))

Simplifying and using l = w, we get:

Surface Area = 2l² + 1728/l

To find the minimum surface area, we can take the derivative of this expression with respect to l, set it equal to zero, and solve for l:

d/dl (2l² + 1728/l) = 4l - 1728/l² = 0

4l = 1728/l²

l³ = 432

l = ∛432 ≈ 8.77 cm

Since the container has a square base, the length and width are both 8.77 cm. Using the equation l² × h = 864, we can solve for h:

h = 864 / (8.77)² ≈ 10.85 cm

Therefore, the minimum surface area of the container is:

Surface Area = 2(8.77)² + 2(8.77)(10.85) ≈ 275.52 cm²

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To find the standard error of the sample mean, we use the formula. The standard error of the sample mean derived from a random sample of 12 bowls is approximately 0.0866 inches.

The expected value in this case is simply the mean diameter of the smaller series, which is 7 inches.

To find the standard error of the sample mean, we use the formula:

Standard Error = Standard Deviation / Square Root of Sample Size

Plugging in the given values, we get:

Standard Error = 0.3 / sqrt(12) = 0.086

Therefore, the standard error of the sample mean derived from a random sample of 12 bowls is 0.086 inches.

The expected value is the mean diameter of the bowls. In this case, the mean diameter is already provided, which is 7 inches. So, the expected value is 7 inches.

Now, to find the standard error of the sample mean, we will use the formula:

Standard Error (SE) = (Standard Deviation) / √(Sample Size)

In this case, the standard deviation is 0.3 inch and the sample size is 12 bowls.

SE = 0.3 / √12 ≈ 0.3 / 3.46 ≈ 0.0866 inches

So, the standard error of the sample mean derived from a random sample of 12 bowls is approximately 0.0866 inches.

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The polynomial function f(x) is factored over the real numbers as:
f(x) = 3x^4 + 2x^3 - 22x^2 - 14x + 7 = (3x + 7)(x + 1)(x - 1/3)(x^2 - 2x - 7)

The Rational Zeros Theorem states that if a polynomial function f(x) has integer coefficients, then any rational zero of f(x) must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Using this theorem, we can find the possible rational zeros of the given polynomial function:
p = ±1, ±7
q = ±1, ±3

Therefore, the possible rational zeros are:
±1/3, ±1, ±7/3, ±7

We can now test these possible zeros using synthetic division or long division to find the real zeros. After testing these possible zeros, we find that the real zeros of the polynomial function are:
x = -7/3, -1, 1/3

Using these zeros, we can factor the polynomial function f(x) as follows:
f(x) = (3x + 7)(x + 1)(x - 1/3)(x^2 - 2x - 7)

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An estimate for the number of batters in the league who will have a batting average of at least 0.400 is approximately 0.7.

We can use the standard normal distribution to find the expected number of batters with an average of at least 0.400.

First, we calculate the z-score for a batting average of 0.400:

z = (0.400 - 0.260) / 0.05 = 2.8

Using a standard normal distribution table or calculator, we can find the probability of getting a z-score of 2.8 or higher:

P(Z ≥ 2.8) ≈ 0.0026

This means that the probability of a batter having an average of at least 0.400 is about 0.0026.

To find the expected number of batters with an average of at least 0.400, we can multiply this probability by the total number of batters:

Expected number of batters = 0.0026 * 270 ≈ 0.7

Therefore, we can expect that about 0.7 batters in the league will have a batting average of at least 0.400.

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A woman who develops gestational diabetes mellitus has a 3 - 7 times greater probability of developing type 2 diabetes mellitus within 5 - 10 years.

Gestational diabetes mellitus (GDM) is a type of diabetes that occurs

during pregnancy, and it usually goes away after delivery.

However, women who develop GDM have an increased risk of developing

type 2 diabetes later in life.

This is because GDM is a sign that the body has difficulty processing

glucose, which can lead to high blood sugar levels.

Women who have had GDM should get regular follow-up care and

screening for diabetes to manage their risk.

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People paid $1 to lie about a study's fun level and believed it was more enjoyable, possibly due to cognitive dissonance. When paid $20, participants maintained their true opinion.

Given that,

People who were offered $1 to inflate the degree of fun in a study claimed that it was more fun.

In contrast, people who paid $20 to lie did not experience the same effect.

This phenomenon could be linked to cognitive dissonance.

When people are paid only $1 to lie about the enjoyment of a study,

They might experience a sense of internal conflict or discomfort.

To alleviate this discomfort, they might subconsciously convince themselves that the study was actually fun, aligning their attitudes with their behaviour.

On the other hand,

if they were paid $20 to lie, their higher payment might create a stronger motivation to maintain their true opinion.

In this case,

They would be less likely to justify their behaviour by convincing themselves that the study was enjoyable.

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The average time a patrol car is not available for use is 9.375 hours, and the average number of patrol cars out of service at any one time is approximately 0.0375.

The Bay City Police Department operates eight patrol cars that are constantly in use 24 hours a day. With a patrol car requiring repairs every 20 days on average (following an exponential distribution), it is important to assess the average downtime of a patrol car and the number of cars out of service at any given time.

Considering that the repair time is exponentially distributed with an average of 18 hours, we can determine the repair rate as the inverse of the average repair time: 1/18 cars per hour. Similarly, the average time between required repairs is 20 days, and the failure rate is 1/20 cars per day, which equals 1/480 cars per hour (given that there are 24 hours in a day).

Using Little's Law, which states that the average number of items in a system (L) is equal to the arrival rate (λ) multiplied by the average time spent in the system (W), we can find the average number of patrol cars out of service (L) by multiplying the failure rate (1/480 cars per hour) by the average repair time (18 hours): L = (1/480) * 18 ≈ 0.0375 cars.

This result indicates that, on average, approximately 0.0375 patrol cars are out of service at any one time. To determine the average time a patrol car is not available for use, we can multiply the failure rate by the average number of patrol cars out of service: (1/480 cars per hour) * (0.0375 cars) ≈ 9.375 hours.

In conclusion, Given these values, the repair service appears to be adequate for the Bay City Police Department, as there is only a small fraction of patrol cars out of service at any given time.

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The bisection method involves repeatedly halving the interval until a root is found. After each iteration, the interval is divided in half, so the length of the interval is halved as well.

After 4 iterations, the length of the initial interval will be halved four times, resulting in an interval of length (b-a)/2^4, where a is the left endpoint and b is the right endpoint. Therefore, the length of the interval after 4 iterations of bisection is (b-a)/16.


The bisection method is used to find a root of a function by repeatedly dividing the interval in half. In each iteration, the interval's length is halved. So, after 4 iterations, the interval's length will be halved 4 times.

Let L be the initial length of the interval, which is the difference between the right and left endpoints:

L = right - left

After 1 iteration, the length becomes L/2.
After 2 iterations, the length becomes L/4.
After 3 iterations, the length becomes L/8.
After 4 iterations, the length becomes L/16.

So, the length of the interval after 4 iterations of bisection is L/16.

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So, the statement "In a dataset that is normally distributed, the mean is always equal to the standard deviation" is false.

In a dataset that is normally distributed, the mean and the standard deviation are two different measures that describe different aspects of the data.

The mean is the arithmetic average of the dataset and represents the center of the distribution. It is calculated by adding up all the values in the dataset and dividing by the number of values.

The standard deviation, on the other hand, measures the spread or variability of the data around the mean.

It is calculated by taking the square root of the average of the squared differences between each value and the mean.

While the mean and the standard deviation can take on the same value in some cases, such as in a normal distribution with a standard deviation of 1, this is not always the case.

Therefore, in a normally distributed dataset, the mean and the standard deviation are two separate measures of the data.

So statement is false. In fact, it is more common for the mean and standard deviation to be different values in a normally distributed dataset.

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The researcher in question has performed a meta-analysis. A meta-analysis is a statistical method used to synthesize the findings from multiple studies that have investigated a similar research question using the same variables and measurement strategies. In this case, the researcher is interested in examining the relationship between exercise and myasthenia gravis.

The process of conducting a meta-analysis involves several steps. First, the researcher identifies and selects relevant studies that meet specific criteria, such as using the same dependent and independent variables (in this case, exercise and myasthenia gravis). In this scenario, 28 studies were identified that meet these requirements.
Next, the researcher extracts the relevant data from each study, such as effect sizes, sample sizes, and other important information. This allows the researcher to compare and combine the results of the individual studies into a single, comprehensive statistical analysis.

In summary, the researcher has conducted a meta-analysis to synthesize the results from 28 studies examining the relationship between exercise and myasthenia gravis, allowing for a more comprehensive understanding of the topic.

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There are 2475 ways to place 10 identical red balls and 10 identical blue balls into 4 distinct urns, given the condition for the first urn.

We want to place 10 identical red balls and 10 identical blue balls into 4 distinct urns with the condition that the first urn has at least 1 red ball and at least 2 blue balls.

Step 1: Place the minimum number of balls in the first urn.
Let's place 1 red ball and 2 blue balls in the first urn. Now we have 9 red balls and 8 blue balls left to distribute.

Step 2: Use the stars and bars method to distribute the remaining balls.
For the remaining 9 red balls, we will use the stars and bars method. There are 3 urns left to place the balls, so we will have 2 "bars" to divide them. In total, we have 9 stars (red balls) and 2 bars, so there are C(11, 2) ways to distribute the red balls, where C(n, k) represents combinations.

If the first urn has no red balls, then we need to place all 10 red balls into the other 3 urns, and the blue balls can go into any of the 4 urns. There are 3^10 ways to place the red balls and 4^10 ways to place the blue balls, so there are 3^10 * 4^10 ways to violate the condition in this way.

If the first urn has exactly 1 red ball and fewer than 2 blue balls, then we need to place the other 9 red balls and the remaining blue balls into the other 3 urns. There are 3^9 ways to place the red balls, and (4 choose 2) * 3^8 ways to place the blue balls (since we need to choose 2 of the remaining 3 urns to put the blue balls in). So there are 3^9 * (4 choose 2) * 3^8 ways to violate the condition in this way.

For the 8 blue balls, we also use the stars and bars method. Again, there are 3 urns left, so we will have 2 "bars" to divide them. We have 8 stars (blue balls) and 2 bars, so there are C(10, 2) ways to distribute the blue balls.

Step 3: Calculate the total ways to distribute the balls.
Since the ways to distribute red balls and blue balls are independent, we multiply the number of ways to distribute the red balls by the number of ways to distribute the blue balls.
Using the principle of inclusion-exclusion, the total number of ways to place the balls into the urns that satisfy the condition is:

4^20 - 3^10 * 4^10 - 3^9 * (4 choose 2) * 3^8

= 2,922,821,387,520 - 3,486,784,401,920 - 312,491,796,480

= 123,544,189,120
Total ways = C(11, 2) * C(10, 2) = 55 * 45 = 2475

So, there are 2475 ways to place 10 identical red balls and 10 identical blue balls into 4 distinct urns, given the condition for the first urn.

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The best measure of center for this data is the median, and its value is 3.

Option B is the correct answer.

We have,

From the line plot,

The median is the best measure of center for this type of data, as it is not affected by outliers.

To find the median, we need to arrange the data in order from least to greatest:

1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 10

Since there are 15 data points,

The median is the middle value, which is 3.

Therefore,

The best measure of center for this data is the median, and its value is 3.

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For considering a model for a garden ornament is formed from two shapes, a cube and a square pyramid, the volume of model is equals to 175 in³.

Volume is the space occupied within the boundaries of an shape in three-dimensional space. It is also known as the capacity of the object. We have a model for garden ornament formed from two shapes named cube and square pyramid. This model is filled with concrete. We have to determine the volume of the model. From the above figure, base side of cube, b = 5 in.

Height of pyramid, h = 6 in

As we know volume of a big box made from small boxes is equals to sum of volume of small boxes. Similarly, volume of model is equals to the sum of volume of cube and volume of square pyramid.

So, volume of cube, V = (side)³

= 5³ = 125 in³

Volume of square pyramid, [tex]V' = \frac{1}{3}b²h[/tex]

where b --> base of pyramid

h --> height of pyramid

[tex]V' = (\frac{1}{3})5²× 6[/tex]

= 50 in³

Therefore, volume of model = V + V'

= 125 in³ + 50 in³

= 175 in³

Hence, required value is 175 in³.

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Complete question:

The above figure complete the question.

A model for a garden ornament is made up of two shapes, a cube and a square pyramid. To make an ornament, the model is filled with concrete. What is the volume of the model?

The total distance they hiked is 2x + y + z = 2x + 24 - x = x + 24 miles.

Let's denote the distance they hiked on level ground, uphill, and downhill as x, y, and z, respectively. Since they turned around at some point, we know they hiked a total distance of x + y + z + x = 2x + y + z.

We can use the formula: time = distance/speed, to write the time they spent on each part of the hike as follows:

Time spent hiking on level ground = x / 4

Time spent hiking uphill = y / 3

Time spent hiking downhill = z / 6

Since they started at noon and arrived at 8:00 pm, we know they hiked for a total of 8 hours. Therefore, we can write the equation:

[tex]\frac{x}{4} + \frac{y}{3} + \frac{z}{6} + \frac{x}{4} + \frac{y}{3} + \frac{z}{6} = 8[/tex]

Simplifying this equation, we get:

x + y + z = 24

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It will cost $396 to place fencing around the garden.

You have a rectangular garden that is 13 feet long and 20 feet wide. To find the cost of placing fencing around the garden, we first need to determine the total length of fencing required.

For a rectangle, the perimeter (P) can be found using the formula P = 2(L + W), where L is the length and W is the width. In this case, L = 13 feet and W = 20 feet. Plugging these values into the formula, we get:

P = 2(13 + 20) = 2(33) = 66 feet

Now that we know the perimeter, we can calculate the total cost of the fencing. Since the fencing costs $6 per foot, we simply multiply the total length of fencing needed (66 feet) by the cost per foot:

Total cost = 66 feet * $6/foot = $396

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The probability that a car that is inspected will need the repair and the repair will cost more than $100 is 8%.

The probability that a car that is inspected will need the repair is 0.20 (given in the problem). The probability that the repair will cost more than $100 is 0.40 (also given in the problem). To find the probability that both events occur (i.e. the car needs the repair AND the repair costs more than $100), we multiply the probabilities together: 0.20 x 0.40 = 0.08 or 8%. To find the probability that a car inspected will need a pollution control system repair and that the repair will cost more than $100, you need to multiply the individual probabilities together.
Probability of needing a repair: 20% (0.20)
Probability of repair costing more than $100 (given it needs a repair): 40% (0.40)
So, the probability of both events occurring is: 0.20 × 0.40 = 0.08 or 8%.

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Answer: B

Step-by-step explanation:

Process of elimination...

anything positive is automatically greater than any negative, so that rules out A and C.

D is the tricky one. Remember, smaller portions of a whole are greater than larger portions. Think of it this way, if you cut two candy bars into pieces; one into thirds and one into fourths. One third would be greater than one fourth. So, 11 thirds would also be greater than 11 fourths.

We can say that 219 respondents believed that growth in Utah Valley had deteriorated the quality of life.

Percentage, which represents a proportion of the total sample size. To be more specific, it indicates that 54% out of the 405 Utah County residents surveyed believed that growth in Utah Valley had deteriorated the quality of life.

To calculate the actual number of respondents who held this view, we can multiply the percentage by the total sample size:

54% x 405 = 218.7

Rounding up to the nearest whole number, we can say that 219 respondents believed that growth in Utah Valley had deteriorated the quality of life.

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The value of the variable in the given inequality is given by x ≤ 13  and x ≥ 8.

The inequalities are,

5 ≥ ( x + 2 ) / 3

Multiply both the side of inequalities by 3 we get,

⇒ 5 × 3 ≥ [( x + 2 ) / 3 ] ×  3

⇒ 15 ≥ ( x + 2 )

Subtract 2 from both the sides of inequalities we get,

⇒ 15 - 2 ≥ ( x + 2 - 2 )

⇒ x ≤ 13

For the inequality ,

( 4 + x ) / 6 ≥ 2

Multiply both the side of inequalities by 6 we get,

⇒ 2 × 6 ≤  [( x + 4 ) / 6 ] ×  6

⇒ 12 ≤ ( x + 4 )

Subtract 4 from both the sides of inequalities we get,

⇒ 12 - 4 ≤  ( x + 4 - 4 )

⇒ x ≥ 8

Therefore , the solution of the inequality is equal to x ≤ 13  and x ≥ 8.

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To use the Chain Rule to find az/as and az/at, we need to first identify the variables involved in the equation. From the given terms, we have.

- a = function of s and t
- z = function of s and t
- s = independent variable
- t = independent variable
- θ = constant
Using the Chain Rule, we can find the partial derivatives of a and z with respect to s and t. The general formula for the Chain Rule is:
∂(a or z)/∂(s or t) = ∂a/∂s * ∂s/∂(s or t) + ∂a/∂t * ∂t/∂(s or t)
Applying this formula to our given equation, we get:
∂a/∂s = 3t^2 cos(θ)
∂a/∂t = s^3 cos(θ)
∂z/∂s = -7s^6 sin(θ)
∂z/∂t = t^3 sin(θ)
Using these partial derivatives, we can now find az/as and az/at as follows:
az/as = ∂a/∂s * ∂z/∂t - ∂z/∂s * ∂a/∂t
     = 3t^2 cos(θ) * t^3 sin(θ) - (-7s^6 sin(θ)) * s^3 cos(θ)
     = t^5 s^3 cos(θ) sin(θ) + 7s^9 cos(θ) sin(θ)
     = (t^5 + 7s^9) cos(θ) sin(θ)
az/at = ∂a/∂t * ∂z/∂s - ∂z/∂t * ∂a/∂s
     = s^3 cos(θ) * (-7s^6 sin(θ)) - t^3 sin(θ) * 3t^2 cos(θ)
     = -7s^9 cos(θ) sin(θ) - 3t^5 cos(θ) sin(θ)
     = -(7s^9 + 3t^5) cos(θ) sin(θ)
Therefore, az/as = (t^5 + 7s^9) cos(θ) sin(θ) and az/at = -(7s^9 + 3t^5) cos(θ) sin(θ).

To find az/as and az/at using the Chain Rule, we can follow these steps:
1. Identify the given equations:
az/as = t^³ cos(θ) cos(θ) - 7s^6 sin(θ) sin(θ)
az/at = 3st^2 (cos(θ) cos(θ)) - s^7 (sin(θ) sin(θ))
2. Apply the Chain Rule to find az/as:
The given equation for az/as is already provided:
az/as = t^³ cos(θ) cos(θ) - 7s^6 sin(θ) sin(θ)
3. Apply the Chain Rule to find az/at:
The given equation for az/at is already provided:
az/at = 3st^2 (cos(θ) cos(θ)) - s^7 (sin(θ) sin(θ))
So, using the Chain Rule, we have found az/as and az/at as follows:
az/as = t^³ cos(θ) cos(θ) - 7s^6 sin(θ) sin(θ)
az/at = 3st^2 (cos(θ) cos(θ)) - s^7 (sin(θ) sin(θ))

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This polynomial has three terms and the highest power of x is 2, so it is a trinomial of degree 2, also known as a quadratic polynomial.

13x² - 4x² = 9x²

So the polynomial becomes:

6 - 12x + 9x²

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using arithmetic operations like addition, subtraction, multiplication, and non-negative integer exponents. The term "poly" means "many" and "nomial" means "term" or "monomial," which gives us the idea that a polynomial consists of many terms.

For example, the polynomial 3x² + 4x - 5 has three terms: 3x, 4x, and -5. The variable x is raised to different powers in each term, and each term is multiplied by a coefficient (3, 4, and -5 in this case). Polynomials can be used to model a wide range of phenomena, from physics to economics. They are used in calculus to represent curves and surfaces, and in algebra to solve equations.

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Answer:

-273

Step-by-step explanation:

Remember PEMDAS:

1) (double negative): {-125 + 3}  -->  -122

2) (left to right): -122 - 157 + 6  -->  -279 + 6  -->  -273

By using the Fundamental Counting Principle we can say that number of ways a person can order a two-course meal from 7 entrees and 11 desserts is 77.

The Fundamental Counting Principle is a basic counting rule in combinatorics that is used to calculate the total number of possible outcomes when there are two or more groups of items to choose from. The principle states that the total number of outcomes is equal to the product of the number of items in each group.

In this problem, we have two groups of items: 7 entrees and 11 desserts. To find the total number of ways of ordering a two-course meal, we can apply the Fundamental Counting Principle. First, we need to choose one item from the first group (entrees), and then we need to choose one item from the second group (desserts).

Since there are 7 entrees and 11 desserts, the number of ways to choose one item from each group is given by the product of the number of items in each group, which is 7 x 11 = 77. Therefore, there are 77 possible ways to order a two-course meal from 7 entrees and 11 desserts.

The Fundamental Counting Principle is a powerful tool that can be used to solve a wide variety of counting problems in probability theory and combinatorics. By understanding this principle, we can quickly and easily calculate the total number of possible outcomes in complex situations that involve multiple groups of items.

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To find the mean of the distribution, we simply multiply the probability of getting a son (0.52) by the number of people surveyed (57):

Mean = 0.52 x 57 = 29.64

Rounding to the nearest person, the mean is 30. To find the standard deviation, we can use the formula:
Standard deviation = square root of (p x q x n), Where p is the probability of success (0.52), q is the probability of failure (1 - 0.52 = 0.48), and n is the sample size (57). Standard deviation = square root of (0.52 x 0.48 x 57) = 4.75

Standard deviation (σ) = √(n × p × (1 - p))
σ = √(57 × 0.52 × 0.48)
σ ≈ 3.71 ≈ 4 (rounded to the nearest person)
So, the mean of the distribution is approximately 30 sons, and the standard deviation is approximately 4 sons.

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Answer:

Option b

Step-by-step explanation:

Box plot method:

Step 1: Find the minimum. Minimum is the smallest data.

     Minimum = 5

Step 2: Find the maximum. Maximum is the largest data.

    Maximum = 15  

Step 3: Arrange the numbers in ascending order.

      5, 6, 8, 9, 9, 11, 11, 13, 15

      Median = middle term

                    = 9

Step 4: Find the first quartile. First quartile is the median of the data to the left of the median.

     Data left to the median are 5, 6, 8, 9.

       Q1 = (6+8) ÷ 2

            = 14 ÷ 2

            = 7

Step 5: Find the second quartile. Second quartile is the median of the data to the right of the median.

     Data left to the median are 11, 11, 13, 15.

       Q12 = (11+13) ÷ 2

            = 24 ÷ 2

            = 12

Answer:   Min = 5

                  Q1 = 7

          Median = 9

                 Q2 = 12

               Max = 15

The probability of exactly 12 from 39 college students majoring in STEM is [tex]0.1776[/tex]

To find the probability of exactly 12 out of 39 college students majoring in STEM, we can use the binomial probability formula.

The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k).

Data;

n = 39, k = 12, p = 0.26, and (n choose k) = 39 choose 12 = 3,720.

Plugging in the values:

P(X=12) = 3,720 * 0.26^12 * 0.74^27

P(X=12) ≈ 0.1776

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Answer: 50.24 in3

Step-by-step explanation:

The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.

From the given information, we know that the diameter of the base of the cone is 8 inches, so the radius is 4 inches.

We also know that the height is twice the radius, so h = 2r = 8 inches.

Substituting these values into the formula, we get:

V = (1/3)π(4 in)^2(8 in) = (1/3)π(16 in^2)(8 in) = 50.24 in^3.

Therefore, the volume of the cone is 50.24 in^3, which corresponds to option 2.

The interior angles are:

180 - 20= 160

180 - 30= 150

180 - 30 = 150

180-40= 140

180 - 40= 140

180 - 65= 115

180-55 = 125

180 - 22 = 158

180-5.8= 122

We have,

The sum of the external angles at the four vertices of a convex 9-gon is 120° and their ratio is 2:3:3:4.

2x + 3x + 3x + 4x = 120

12x = 120

x= 10

4x + 6.5x + 5.5x + 2.2x + 5.8x + 120 = 360

24x = 240

x = 10

The interior angles are

180 - 20= 160

180 - 30= 150

180 - 30 = 150

180-40= 140

180 - 40= 140

180 - 65= 115

180-55 = 125

180 - 22 = 158

180-5.8= 122

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In order to determine if there is inconsistency, the data collected from the three instructors would need to be compared and analyzed. Without further information or analysis, it is difficult to determine if there is inconsistency in the grading.

To answer your question, we first need to analyze the data provided for the grade distribution of the three instructors. Unfortunately, you haven't provided any data in your question. However, I can guide you through the process of assessing consistency using the given terms: conducted, assess, and consistency.

Step 1: The university conducted a study on the grade distribution of a multi-section basic statistics course taught by three instructors.

Step 2: To assess consistency in grading, we need to compare the grade distributions of the three instructors. You can use a variety of statistical methods to make this comparison, such as descriptive statistics (e.g., mean, median, and standard deviation), visual representations (e.g., boxplots or histograms), or inferential statistics (e.g., ANOVA or chi-square tests).

Step 3: After analyzing the data, you can determine whether there is any inconsistency in grading among the three instructors. If the grade distributions are similar, it suggests consistency in grading. However, if the distributions differ significantly, it may indicate grading inconsistency.

Remember, to provide a specific answer, we would need the actual data on grade distribution for the three instructors. Once you have that data, you can follow the steps mentioned above to assess the consistency of grading in the course.

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