Assuming that X and Y are bivariate normal random variables with zero mean, variances og and oy, and a parameter of -1, this means that the correlation between X and Y is -1.
A bivariate normal distribution is a probability distribution of two variables that are normally distributed, and the joint distribution of these two variables is also normally distributed. This means that the distribution of X and Y can be fully described by their means, variances, and correlation coefficient.
In this case, since the correlation coefficient is -1, this indicates that X and Y are perfectly negatively correlated. This means that as one variable increases, the other variable decreases by an equivalent amount.
It is worth noting that the joint distribution of X and Y can be expressed using their means, variances, and correlation coefficient through a multivariate normal distribution. This is a generalization of the bivariate normal distribution to more than two variables.
Assume that X and Y are bivariate normal random variables, both having zero mean, variances σx and σy, and correlation coefficient -1.
Since X and Y are bivariate normal random variables, their joint distribution is described by the bivariate normal distribution. Given that both variables have zero mean, their means are μx = 0 and μy = 0.
The variances for X and Y are denoted as σx and σy respectively, which describe the spread or dispersion of the variables around their mean values.
The correlation coefficient between X and Y is given as -1. This indicates a perfect negative linear relationship between the two variables, meaning that as X increases, Y decreases and vice versa. In other words, the variables are completely negatively related to each other.
In summary, you are assuming that X and Y are bivariate normal random variables with zero mean, variances σx and σy, and a perfect negative linear relationship indicated by a correlation coefficient of -1.
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When a marketing manager surveys a few of the customers for the purpose of drawing a conclusion about the entire list of customers, she is applying:
a.) inferential statistics b.) descriptive statistics c.) numerical measures d.) quantitative models
When a marketing manager surveys a few of the customers for the purpose of drawing a conclusion about the entire list of customers, she is applying inferential statistics.
Hence option a is the correct answer.
Inferential statistics is referred to that field of statistics which uses analytical tools to draw conclusions about a population by examining (or, surveying) random samples (taken from the population).
Inferential statistics generalizes the observations derived from the sample as the observations from the population.
Here the marketing manager surveys a few of the customers who work as representation of the population of customers to draw conclusions, that is the observation is generalized for the entire list of customers though it is based on replies from a few customers.
Thus, the marketing manager is applying inferential statistics.
Hence option a is the correct answer.
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5. (16 marks) It is given that the moment generating function of a negative binomial random variable is mx(t)= (1 - p)^r /(1 - pe^t)^r where p and r are the parameters. Find the expected value and variance using the moment generating function.
To find the expected value and variance of a negative binomial random variable with moment generating function mx(t) = (1 - p)^r / (1 - pe^t)^r, we need to use the following formulas:
The nth moment of a random variable is given by mx^(n)(0), the nth derivative of the moment generating function evaluated at t = 0.
The expected value of a random variable is given by mx^(1)(0).
The variance of a random variable is given by mx^(2)(0) - [mx^(1)(0)]^2.
Using these formulas, we can find the expected value and variance of the negative binomial random variable.
First, let's find the first two derivatives of the moment generating function:
mx'(t) = r(1-p)^rpe^t / (1-pe^t)^(r+1)
mx''(t) = r(1-p)^rpe^t(r+1-pe^t) / (1-pe^t)^(r+2)
Now we can evaluate the moment generating function and its derivatives at t = 0 to find the expected value and variance:
mx(0) = (1 - p)^r / (1 - p)^r = 1
mx'(0) = r(1-p)^r p / (1-p)^(r+1)
mx''(0) = r(r+1)(1-p)^r p / (1-p)^(r+2) + r(1-p)^r p / (1-p)^(r+1)
Using the formulas for the expected value and variance, we have:
E[X] = mx'(0) = r(1-p) / p
Var[X] = mx''(0) - [mx'(0)]^2 = r(1-p) / p^2
Therefore, the expected value of the negative binomial random variable is E[X] = r(1-p) / p, and the variance is Var[X] = r(1-p) / p^2, where p and r are the parameters of the distribution.
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Find the perimeter of the following polygon. Be sure to include the correct unit in your answer.
12ft
16ft
9ft
9ft
15ft
The perimeter of the polygon is 61 feet.
What is polygon?A polygon is a two-dimensional geometric shape that is defined as a closed plane figure with three or more straight sides and angles. It is a flat shape made up of line segments that are connected end to end to form a closed shape.
According to given information:The perimeter of a polygon is the total length of its sides. To find the perimeter of a polygon, we need to add up the lengths of all its sides.
In this problem, we are given the lengths of the sides of a polygon in feet: 12ft, 16ft, 9ft, 9ft, and 15ft.
To find the perimeter, we simply add up these lengths:
Perimeter = 12ft + 16ft + 9ft + 9ft + 15ft
Perimeter = 61ft
Therefore, the perimeter of the polygon is 61 feet. Note that the unit for the answer is feet, since all the lengths were given in feet.
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plssss help state test is coming up
Answer: greater than
Step-by-step explanation:
p(spinning even) = [tex]\frac{2}{5}[/tex] = 0.4
p(drawing even card) = [tex]\frac{5}{13}[/tex] = 0.384615384615
so 2/5 is greater than 5/13
r
10
O
For each radius length of a circle that is given, mark the correct area of the circle.
Use = 3.14
Radius of
Circle
5 cm
6 cm
9 cm
10 cm
Porfavorere helppp plis 15 points for it
Answer:
Below
Step-by-step explanation:
formula for area of circle: A = (pie)(r)^2
1. 5 cm radius:
A = (pie)(r)^2
A = (pie)(5)^2
A = 78.54 and 78.5 cm^2
2. 6 cm radius:
A = (pie)(r)^2
A = (pie)(6)^2
A = 113.04 cm^2
3. 9 cm radius:
A = (pie)(r)^2
A = (pie)(9)^2
A = 254.34 cm^2
10. 10 cm radius:
A = (pie)(r)^2
A = (pie)(10)^2
A = 314 cm^2
Hope this helps^^
Now that you've learned about hypothesis testing and p-values, you should also be aware that these methods can be used incorrectly. Or, even worse, maliciously. Usually it involves manipulating the data or the test in such a way to produce a desired result. There's many methods for this, and they've got some cool names like p-hacking and data dredging. In this problem, we will focus on the idea of using subsets of data to find a desired result. Nefarian just landed his first data science position as an intern at a new e-commerce company. His project was the design and test a new website layout that would lead to more purchases. To test his new layout, the company gathered four different groups of 50 customers and recorded how many of those ended up purchasing an item. This test was then repeated on multiple days. The effectiveness of Nefarian's layout is measured by the number of customers that made a purchase. This data is stored in the data frame purchases. Nefarian wants to land a permanent position at the company after his internship is over, so he really wants to impress his supervisors with his new layout. He knows that the site has an average purchase rate of 0.8 and wants to see if his layout is an improvement.
After answering the query, we may state that He may show his abilities circle as a data analyst and get the respect of his peers by doing this.
What is circle?Each point in the plane that is a certain distance from the centre (another point) forms a circle. Thus, it is a curve composed of points whose are separated from another point in the plane by a certain distance. Additionally, at every angle, it is alternately symmetric about the centre. The closed, two-dimensional plane of a circle has every pair of points equally separated from the "centre." By drawing a line through the circle, one may create a line of circular symmetry. Additionally, at every angle, it is rotationally equal about the centre.
It's vital to highlight that Nefarian's strategy is already problematic since, before starting the study, he already has a desired outcome in mind (his layout is an upgrade). This could result in confirmation bias, when he purposefully or unintentionally manipulates the evidence to support his preferred conclusion.
Furthermore, drawing conclusions that are incorrect might emerge from exploiting subsets of data to reach the intended outcome. Instead of cherry-picking certain subsets of data that just so happen to support the intended result, it is crucial to use all the information available to draw a judgement.
Nefarian should use all the available data and perform a hypothesis test using an appropriate statistical approach (such as a two-sample t-test or chi-squared test) to correctly assess the efficacy of his design. To offer a more thorough picture of the outcomes, he should additionally disclose the p-value and confidence interval.
Nefarian should concentrate on providing a comprehensive and objective study rather than attempting to manipulate the facts to suit his preferred result if he wants to make an impression on his superiors with his research. He may show his abilities as a data analyst and get the respect of his peers by doing this.
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Are the ratios 18:12 and 3:2 equivalent?
Answer:
Whenever the simplified form of two ratios are equal, then we can say that the ratios are equivalent ratios. For example, 6 : 4 and 18 : 12 are equivalent ratios, because the simplified form of 6 : 4 is 3 : 2 and the simplified form of 18 : 12 is also 3 : 2. Hope this helps FAST good luck friend of mine!!!
Step-by-step explanation:
so yes it does
Answer:
yes
Step-by-step explanation:
18/12 = 3/2
Can someone explain how to do it.
Answer:
31.4 ftStep-by-step explanation:
Arc length = θ/360 × 2πr
= 150/360 ×2π×12
= 31.4 ft
There is a 15% increase in tuition at UT for next fall. If the current tuition is $3,500 per semester, which equation could be used to find x, the new tuition for the fall? A. 0.15 • 3500 = x B. 1.15 • 3500 = xC. 0.85 • 3500 = x D. (15/100) = (x/3500)
The new tuition for the fall will be $4,025 per semester. This is exactly what we get by using equation B, since: 1.15 • 3500 = 4025
The correct equation to find the new tuition for the fall is: B. 1.15 • 3500 = x
Here's why: The problem states that there is a 15% increase in tuition, which means that the new tuition will be the current tuition plus 15% of the current tuition. Mathematically, we can represent this as:
new tuition = current tuition + 15% of current tuition
Using x to represent the new tuition, and 3500 to represent the current tuition, we can write this equation as:
x = 3500 + 0.15(3500)
Simplifying the right side, we get:
x = 3500 + 525
x = 4025
Therefore, the new tuition for the fall will be $4,025 per semester. This is exactly what we get by using equation B, since: 1.15 • 3500 = 4025
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Find the test statistic t0 for a sample with n = 10, = 7.9, s = 1.3, and ifH1:µ > 8.0. Round your answer to three decimal places.
The test statistic t0 is -0.243. This can be answered by the concept of Standard deviation.
To find the test statistic t0, you can use the following formula:
t0 = (x - µ) / (s / √n)
where x is the sample mean, µ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Plugging in the given values:
t0 = (7.9 - 8.0) / (1.3 / √10)
t0 = (-0.1) / (1.3 / 3.162)
t0 = -0.1 / 0.411
t0 = -0.243
After rounding to three decimal places, the test statistic t0 is -0.243.
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During the past week, of the 250 customers at the Dairy Queen who
ordered a Blizzard, 50 ordered strawberry. This means that of the next
five Blizzard customers, exactly one will order strawberry. A) True B)
False
B) False
The information given states that 50 out of 250 customers ordered a strawberry Blizzard, which represents a probability of 20% (50/250).
However, this does not guarantee that exactly one out of the next five customers will order a strawberry Blizzard. It only indicates the probability of a customer choosing a strawberry Blizzard based on past data.
The fact that 50 out of 250 customers ordered a strawberry Blizzard represents a probability of 20% (50/250). This probability is based on past data, and it represents the proportion of customers who have ordered a strawberry Blizzard in the past. It does not provide any information about what will happen in the future.
When we talk about the probability of an event occurring, we are making a statement about the likelihood of that event occurring based on past data and assumptions about how the future will unfold. However, the probability does not provide any guarantees about what will actually happen in the future.
Therefore, the statement "exactly one out of the next five customers will order a strawberry Blizzard" cannot be guaranteed based solely on the fact that 50 out of 250 customers have ordered a strawberry Blizzard in the past. It is important to note that probability only provides a measure of likelihood, and does not guarantee any specific outcome.
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The average weight of adult male bison in a particular federal wildlife preserve is 1450 pounds with a standard deviation of 240 pounds. Find the weight of an adult bull whose is z-score 1.5.
Answer:
Step-by-step explanation:
To find the weight of an adult bull whose z-score is 1.5, we need to use the formula:
z = (x - μ) / σ
where z is the z-score, x is the weight of the bull we want to find, μ is the population mean weight (1450 pounds), and σ is the population standard deviation (240 pounds).
We can rearrange this formula to solve for x:
x = z*σ + μ
Substituting the given values, we get:
x = 1.5 * 240 + 1450
x = 360 + 1450
x = 1810
Therefore, the weight of an adult bull whose z-score is 1.5 is 1810 pounds.
Use the t-distribution table to find the critical value(s) for the indicated alternative hypotheses, level of significance α, and sample sizes n1 and n2. Assume that the samples are independent, normal, and random. Answer parts (a) and (b).Ha : μ1 ≠ μ2 , α = 0.10 , n1 = 14 , n2 = 13(a) Find the critical value(s) assuming that the population variances are equal.____(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)(b) Find the critical value(s) assuming that the population variances are not equal.____(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.)
a) The t critical values are -1.708 and 1.708
b) The t critical values are -1.782 and 1.782
What is t-statistic ?
The t-statistic in statistics measures how far an estimated value of a parameter deviates from its hypothesised value in relation to its standard error.
T symbol in statistics mean Test statistic for t-test ( t-score )
a) At α = 0.10, df=14+13-2 = 25( two tailed)
t critical values are -1.708 and 1.708
b) At α = 0.10,
df= smaller(n1-1, n2-1)= smaller(14-1, 13-1)= smaller(13, 12) = 12
t critical values are -1.782 and 1.782
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Problem #8: Let f(x, y, z) = zyx Finckhe value of the following partial derivatives. (a) f(3,2,3) (b) fy(4,3,3) (c) fz(2,3,3)
The answers are:
(a) f(3,2,3) = 18
(b) fy(4,3,3) = 12
(c) fz(2,3,3) = 6
To find these partial derivatives, we use the formula:
∂f/∂x = yz
∂f/∂y = zx
∂f/∂z = yx
(a) To find f(3,2,3), we just plug in those values:
f(3,2,3) = (3)(2)(3) = 18
(b) To find fy(4,3,3), we plug in those values and take the partial derivative with respect to y:
fy(4,3,3) = z(4) = 12
(c) To find fz(2,3,3), we plug in those values and take the partial derivative with respect to z:
fz(2,3,3) = y(2) = 6
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Q?Identify the variable quantity as discrete or continuous.
the number of heads in 50 tossed coins?
Discrete
Continuous
The variable for an event that the number of heads in 50 tossed coins is a discrete variable. So, option(a) is right one.
A variable is a quantity whose value can be changed as a math problem. Thereare two types of variables:
Continuous variablesDiscrete variablesDiscrete variables represent counts, or the number of items in the collection. But continuous variables represent measurable quantities. Discrete variables are variables that have a measurable difference. For example, if X is equal to the number of miles (to the nearest mile) we drive to work, then X is a discrete random variable. We count the miles. Here we have an experiment of tossing a coin, We have to identify the variable used for the number of heads in 50 tossed coins. So, number of heads when flipping a coin is a discrete variable statement because once the coin is flipped, we will get head or tail result.
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To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
Equation that could be uses to find the price of one tire patch is Option A: 4x – 1.9 = 22.2.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
We can use the equation -
4x + 1.9 = 22.2
Where x is the price of one tire patch.
Multiplying both sides by 100 to get rid of the decimals -
400x + 190 = 2220
Subtracting 190 from both sides -
400x = 2030
Dividing both sides by 400 -
x ≈ 5.075
Therefore, the price of one tire patch is approximately $5.075.
The equation 4x – 1.9 = 22.2 is also valid, but it yields the same result.
The other equations are not valid.
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The number of calls to an Internet service provider during the hour between 6:00 and 7:00 p.m. is described by a Poisson distribution with mean equal to 15. Given this information, what is the expected number of calls in the first 30 minutes?
The expected number of calls in the first 30 minutes is 7.5
The Poisson distribution is frequently utilized to show the number of occasions that happen in a settled interim of time or space.
In this case, the number of calls to a Web benefit supplier during the hour between 6:00 and 7:00 p.m. is portrayed by a Poisson distribution with the mean rise to 15.
Since the Poisson distribution is memoryless, we will accept that the number of calls within the to begin with 30 minutes moreover takes after a Poisson conveyance with the mean rise to 15/2 = 7.5.
Typically since the expected number of occasions in a settled interim is relative to the length of the interim.
In this manner, the anticipated number of calls within the to begin with 30 minutes is 7.5.
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A carnival performer claims to be able to guess a persons weight within 4 pounds of their actual weight or the person wins a prize. If the person weighs 142 pounds, which equations can be used to find the minimum and maximum weights the performer can guess without the person winning a prize.
a) |x-142|=4
b) |x-4|=142
c) |x+4|=142
d) |x+142|=4
Option (1) is correct. The minimum weight an interpreter can guess without winning a prize is 138 pounds and the maximum weight is 146 pounds.
What do you mean by linear equation?
Linear equations are first-order equations. Linear equations are defined for the lines of the coordinate system. If an equation has a homogeneous variable of degree 1 (that is only one variable), it is called a linear equation in one variable. A linear equation can have more than one variable.
The correct equation would be: a) |x - 142| ≤ 4
Explanation:
The carnival performer claims to be able to guess a person's weight within 4 kilograms of their actual weight, which means that the difference between the guessed weight and the actual weight must not be more than 4 kilograms.
Let x be the weight of the carnival performer. In this case the difference between x and 142 cannot be more than 4 pounds. It can be written as:
|x - 142| ≤ 4
This inequality means that x can be any weight within 4 pounds of 142, giving the range:
142 - 4 ≤ x ≤ 142 4
138 ≤ x ≤ 146
Therefore, the minimum weight an interpreter can guess without winning a prize is 138 pounds and the maximum weight is 146 pounds.
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About 24 randomly selected people were asked how long they slept at night. The mean time was 6 hours, and the standard deviation was 1.3 hour. Calculate the 80% confidence interval of the mean time by assuming that the variable is normally distributed. Provide only the value required below. Express your answer in 3 decimal places.
The 80% confidence interval for the meantime is 5.660 to 6.340 hours.
To calculate the 80% confidence interval for the meantime, we will use the following formula:
CI = Mean ± (Z-score * (Standard deviation / √Sample size))
Here, Mean = 6 hours, Standard deviation = 1.3 hours, and Sample size = 24.
For an 80% confidence interval, the Z-score is 1.282 (from the standard normal distribution table).
Now, plug in the values:
CI = 6 ± (1.282 * (1.3 / √24))
CI = 6 ± (1.282 * (1.3 / 4.899))
CI = 6 ± (1.282 * 0.265)
CI = 6 ± 0.340
The 80% confidence interval for the meantime is 5.660 to 6.340 hours.
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Determine whether the statement is true or false.If f and g are decreasing on an interval I, then f + g is decreasing on I.
The statement is true. If f and g are decreasing on an interval I, then their sum, f + g, is also decreasing on the interval I.
Statement: If f and g are decreasing on an interval I, then f + g is decreasing on I.
Answer: True.
Explanation:
1. Since f is decreasing on interval I, this means that for any x1, x2 in I, if x1 < x2, then f(x1) > f(x2).
2. Similarly, since g is decreasing on interval I, for any x1, x2 in I, if x1 < x2, then g(x1) > g(x2).
3. Now, let's consider the function h(x) = f(x) + g(x).
4. We need to show that h is decreasing on interval I. For any x1, x2 in I with x1 < x2, we want to show that h(x1) > h(x2).
5. From steps 1 and 2, we have f(x1) > f(x2) and g(x1) > g(x2).
6. Adding these inequalities, we get f(x1) + g(x1) > f(x2) + g(x2), which means h(x1) > h(x2).
7. So, h(x) = f(x) + g(x) is decreasing on interval I.
The statement is true. If f and g are decreasing on an interval I, then their sum, f + g, is also decreasing on the interval I.
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For the scenario given, determine which of Newton's three laws is being demonstrated.
A person hit a softball with more force, and the softball accelerates faster.
The answer of the given question based on the Newton's law is , the scenario demonstrates Newton's second law of motion.
What is Newton's law?Newton's laws of motion are set of fundamental principles that describe behavior of a objects in motion. They were formulated by Sir Isaac Newton in the 17th century and are considered to be the foundation of classical mechanics. It consists of three laws of motion they are , Newton's First Law of Motion , Newton's Second Law of Motion , Newton's Third Law of Motion. These laws explain how objects move and interact with one another, and they have numerous applications in physics, engineering, and other fields.
The scenario given describes Newton's second law of motion, which states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass.
In this case, the force applied to the softball by the person's hit causes the softball to accelerate faster. The more force applied to the softball, the greater the acceleration of the softball.
Therefore, the scenario demonstrates Newton's second law of motion.
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If n is a positive integer divisible by 7, and if n < 70, what is the greatest possible value of n?
Answer:
63
Step-by-step explanation:
We can find the other multiples of a number by adding or subtracting the number.
n is less than 70 and is divisible by 7, which means we need to subtract 7 from 70.
70 - 7 = 63
The garden area is 48 000 cm². What is the area in square meters?
Answer:
4.8 squared meters
Step-by-step explanation:
divide the area value by 10,000
Find the critical value or values of based on the given information. H1: σ > 9.3 n = 18 = 0.05
The critical value for this hypothesis test is 29.71. This means that if the test statistic calculated from the sample data is greater than 29.71, we would reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the population standard deviation is greater than 9.3.
To find the critical value(s) for a one-tailed hypothesis test where the alternative hypothesis is H1: σ > 9.3, with a significance level of α = 0.05 and a sample size of n = 18, we need to use the chi-square distribution with n - 1 degrees of freedom.
The critical value can be found using a chi-square distribution table or a calculator. Specifically, we need to find the chi-square value that corresponds to a cumulative area of 1 - α = 0.95 to the right of the distribution.
The degrees of freedom is n - 1 = 18 - 1 = 17. Using a chi-square distribution table with 17 degrees of freedom and a cumulative area of 0.95 to the right, we can find the critical value to be approximately 29.71.
Therefore, the critical value for this hypothesis test is 29.71. This means that if the test statistic calculated from the sample data is greater than 29.71, we would reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the population standard deviation is greater than 9.3.
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Please help me because I am confused and my teacher did not go over this. If would be appreciated if someone responded quick! Thanks!
Answer:
Step-by-step explanation:
I don't see the question.
In a recent survey, 85% of the community favored building a police substation in their neighborhood. If 20 citizens are chosen, what is the probability that the number favoring the substation is exactly 12?
The probability of exactly 12 citizens favoring the substation out of a random pattern of 20 citizens is about 16.77%
This is a binomial probability problem, where we want to discover the chance of obtaining exactly 12 favorable responses out of 20, given that the probability of an person being in want of the substation is 0.85.
The method for the possibility of having exactly k successes in n independent Bernoulli trials, each with probability of fulfillment p, is given via the binomial distribution:
P(X = k) = (n choose k) * [tex]p^k * (1-p)^{(n-k)}[/tex]
Where (n choose k) represents the range of approaches to pick k objects from a fixed of n objects.
Using this formulation, we are able to calculate the chance of obtaining exactly 12 favorable responses out of 20 as:
P(X = 12) = (20 choose 12) * [tex](0.85)^{12} * (1-0.85)^{(20-12)}[/tex]
P(X = 12) = 0.1677 (rounded to four decimal places)
Therefore, Out of a random sample of 20 individuals, the probability of exactly 12 citizens favouring the substation is around 0.1677, or 16.77%
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2. You are interested in the effect that government directed innovation activities has on patenting. After some time spent at the National Archives, you learn about a program during the Vietnam War that gave qualifying applicants the opportunity to work at the US Government Office of Research as their service during the war as opposed to being drafted for combat. Out of the qualifying candidates, the government randomly selected who would be offered to work at the office of research
Based on the information provided, it appears that the government directed innovation activities during the Vietnam War had a unique program that gave qualifying applicants the opportunity to work at the US Government Office of Research instead of being drafted for combat. This program had a specific goal, which may have been to support innovation efforts during the war or to provide an alternative service opportunity for those who did not want to fight in combat.
Overall, this program is an interesting example of how the government can direct innovation activities through specific programs and initiatives. It also demonstrates how random selection can be used to determine who participates in these programs, which may have implications for how successful they are in achieving their goals.
In this scenario, the government implemented a program during the Vietnam War that allowed qualifying applicants to work at the US Government Office of Research as an alternative to being drafted for combat. The program's objective was to promote innovation and increase patenting by utilizing the skills and expertise of these individuals. The government randomly selected the candidates who would be offered the opportunity to work in the Office of Research, ensuring a fair selection process. This program highlights the potential impact of government-directed innovation activities on patenting and showcases how the government can actively support and encourage advancements in technology and research.
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Use properties of integrals to determine the value of I = S5 0 f(x)dx when S7 0 f(x)dx = 9, S7 5 f(x)dx = 7
we need to know the value of S₇(5) to determine the value of I.
I = S₇(0) + S₇(7) - 2S₇(5) = 9 + 7 - 2S₇(5) = 16 - 2S₇(5)
We can use the properties of integrals to determine the value of I:
I = ∫_0⁵ f(x)dx + ∫_5⁷ f(x)dx
Using the given information, we can express the two integrals on the right-hand side in terms of S₇(0) and S₇(5):
∫_0⁵ f(x)dx = S₇(0) - S₇(5)
∫_5⁷ f(x)dx = S₇(7) - S₇(5)
Substituting these expressions into the equation for I, we get:
I = (S₇(0) - S7(5)) + (S₇(7) - S₇(5))
Simplifying this expression, we get:
I = S₇(0) + S₇(7) - 2S₇(5)
Now we can use the given values of S₇(0), S₇(5), and S₇(7) to find I:
I = S₇(0) + S₇(7) - 2S₇(5) = 9 + 7 - 2S₇(5) = 16 - 2S₇(5)
Therefore, we need to know the value of S₇(5) to determine the value of I.
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Here is a point at the tip of a windmill blade. The center of teh windmill is 6 feet off the ground and the blades are 1. 5 feet long. Write an equation giving the height h of the point P after the windmill blade rotates by an angle of a. Point P is currently rotated π/4 radians from the point directly to the right of the center of the windmill
Step-by-step explanation:
The equation for the height h of point P on the windmill blade after it has rotated by an angle a can be given by:
h(a) = r - r * cos(a + α)
where:
r is the length of the windmill blade (in this case, 1.5 feet, as given in the question).a is the angle of rotation in radians.α is the angle between the reference point (directly to the right of the center of the windmill) and the initial position of the windmill blade (which is π/4 radians, as given in the question).In this case, since point P is currently rotated π/4 radians from the point directly to the right of the center of the windmill, we can substitute α with π/4 in the equation:
h(a) = 1.5 - 1.5 * cos(a + π/4)
This equation gives the height of point P on the windmill blade above the ground after it has rotated by an angle of a, with the initial position of the blade being π/4 radians from the point directly to the right of the windmill center, assuming the windmill blade is 1.5 feet long.
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The measure of the third angle is 72°.
What is the measure of angle?
An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex. Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections.
Here, we have
Given: Two angles in a triangle have measures of 35° and 73°
We have to find the measure of the third angle.
The interior angle sum of a triangle will be 180 degrees.
Since we are given two angle measures, we can set up an equation to find the unknown angle measure.
35° + 73° + x = 180°
x = 180° - 35° - 73°
x = 72°
Hence, the measure of the third angle is 72°.
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