The number of hours it will take the airplane to fly the given distance would be = 4.5 hours
How to calculate the number of hours that can be used for the distance?To calculate the number of hours that can be used for the distance, the following needs to be done. That is;
The number of hours it take to complete 3600 miles = 3 hours
Therefore the number of hours it will take to complete 5400miles = X hours.
That is;
3600 miles = 3 hours
5400 miles = X hours
make X the subject of formula;
X = 5400×3/3600
= 16,200/3600
= 4.5 hours.
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Mavis wants to move each counter to an adjacent square (horizontally or vertically, but not diagonally), so that as originally, each square contains exactly one counter. In how many ways can she do this
Thus, there are over 2 trillion ways for Mavis to move each counter to an adjacent square without having any of them end up in the same square.
There are several ways Mavis can move each counter to an adjacent square, but the question is how many ways can she do this without having two counters end up in the same square.
First, let's consider the top row of the board. There are 7 counters, and each counter has two adjacent squares that it can move to.
However, the counter on each end only has one adjacent square to move to. So, the total number of ways to move the counters in the top row without any of them ending up in the same square is:
2 x 2 x 2 x 2 x 2 x 2 x 1 = 64
Now, let's consider the second row. There are also 7 counters in this row, but the two end counters now have two adjacent squares to move to.
However, there is a new constraint: each counter in the second row must move to a square that is not occupied by a counter in the top row.
This means that the first and last counters in the second row each have three possible squares to move to, while the other five counters each have two possible squares to move to.
So, the total number of ways to move the counters in the second row without any of them ending up in the same square is:
3 x 2 x 2 x 2 x 2 x 2 x 3 = 288
We can continue this process for each row, taking into account the constraints of not having any counters end up in the same square and not moving to squares already occupied in the previous row.
In the end, the total number of ways Mavis can move the counters to adjacent squares is the product of the number of ways for each row:
64 x 288 x 288 x 288 x 288 x 288 x 64 = 2,051,717,760,000
So, there are over 2 trillion ways for Mavis to move each counter to an adjacent square without having any of them end up in the same square.
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The FDA regulates that fresh Albacore tuna fish contains at most 0.82 ppm of mercury. A scientist at the FDA believes the mean amount of mercury in tuna fish for a new company exceeds the ppm of mercury. A test statistic was found to be 2.576 and a critical value was found to be 1.645, what is the correct decision and summary
the test statistic is 2.576 and the critical value is 1.645.
Since the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the mean amount of mercury in tuna fish for the new company exceeds 0.82 ppm.
To make a decision in this scenario, we need to use a hypothesis test. Let's set up the null and alternative hypotheses:
Null hypothesis (H0):
The mean amount of mercury in the tuna fish produced by the new company is less than or equal to 0.82 ppm.
Alternative hypothesis (Ha):
The mean amount of mercury in the tuna fish produced by the new company is greater than 0.82 ppm.
The test statistic is 2.576 and the critical value is 1.645.
Since the test statistic is greater than the critical value and is in the rejection region of the null hypothesis, we reject the null hypothesis.
we cannot say for certain whether this difference is statistically significant without knowing the sample size, the standard deviation of the sample, and the level of significance.
Reject the null hypothesis at the chosen significance level (which we don't have in this case), which suggests that the mean amount of mercury in the tuna fish produced by the new company is likely to be greater than 0.82 ppm.
This means that we have evidence to suggest that the mean amount of mercury in the tuna fish produced by the new company exceeds 0.82 ppm, as suspected by the scientist at the FDA.
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Two sample t tests are designed to learn if there is support for a relationship between variables when:
Two sample t-tests are designed to learn if there is support for a relationship between variables when there are two independent groups and we want to compare their means.
Specifically, the two sample t-test is used to determine whether the means of two groups are significantly different from each other. The test is based on the assumption that the populations from which the samples are drawn are normally distributed, and that the variances of the two populations are equal.
If these assumptions are met, we can use the two sample t-test to test the null hypothesis that the means of the two groups are equal. The test produces a t-statistic and a p-value, which can be used to determine whether the null hypothesis should be rejected or not.
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A scale model of the front view of Tony’s house is shown.
What is the minimum amount of paint needed for two coats?
A. 594 square centimeters
B. 297 square centimeters
C. 216 square centimeters
D. 81 square centimeters
The minimum amount of paint needed for two coats will be 297 square centimeters.
The shape is a combination of the rectangle and the triangle. Then the area of the shape is calculated as,
A = 1/2 x 18 x 9 + 18 x 12
A = 81 + 216
A = 297 square centimeters
Hence, the minimum amount of paint needed for two coats will be 297 square centimeters.
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PLEASE ANSWER ASPA DONT BE A SCAM
A sprinkler set in the middle of a lawn sprays in a circular pattern. The area of the lawn that gets sprayed by the sprinkler can be described by the equation (x+6)2+(y−9)2=196.
What is the greatest distance, in feet, that a person could be from the sprinkler and get sprayed by it?
14 ft
15 ft
13 ft
16 ft
The greatest distance a person could be from the sprinkler and still get sprayed by it is 28 feet, which is equal to the diameter of the circle described by the equation (x+6)²+(y−9)²=196.
In this problem, we are given an equation that describes the area covered by a sprinkler set in the middle of a lawn. Specifically, the equation (x+6)²+(y−9)²=196 represents a circle with center (-6,9).
Radius
= √196
= 14
The greatest distance that a person could be from the sprinkler and still get sprayed by it is equal to the diameter of the circle.
The diameter is simply twice the radius, which is 2 × 14 = 28 feet.
To understand why the diameter is the maximum distance a person could be from the sprinkler and still get sprayed, we can visualize the circle as the area covered by the sprinkler's spray. Any point inside the circle would be sprayed by the sprinkler, while any point outside of the circle would not. Since the diameter is the longest distance between two points on the circle, any point beyond the diameter would be outside the area covered by the sprinkler's spray.
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Find f(x) if f(2) = 1 and the tangent line at x has slope (x − 1)ex2 − 2x.
f(x)= _____________
If f(2) = 1 and the tangent line at x has slope (x − 1)ex2 − 2x. f(x) = ((x^2 - 2x + 1)/2)e^(x^2 - 2x).
To find f(x), we'll first integrate the given slope function to obtain the original function. The slope of the tangent line is given as (x - 1)e^(x^2 - 2x).
Let F'(x) = (x - 1)e^(x^2 - 2x). To find f(x), we need to integrate F'(x) with respect to x:
∫(x - 1)e^(x^2 - 2x) dx
Now, we can use substitution. Let u = x^2 - 2x, then du = (2x - 2) dx. Therefore, the integral becomes:
∫((u + 1)/2)e^u du
Now, we can integrate by parts. Let v = e^u, then dv = e^u du. Let w = (u + 1)/2, then dw = 1/2 du. Using integration by parts formula:
∫w dv = wv - ∫v dw
∫(u + 1)/2 * e^u du = ((u + 1)/2)e^u - ∫(1/2)e^u du
Now integrate the remaining part:
∫(1/2)e^u du = (1/2)e^u + C
Substituting back:
f(x) = ((x^2 - 2x + 1)/2)e^(x^2 - 2x) + C
Now, use the given condition f(2) = 1:
1 = ((2^2 - 2*2 + 1)/2)e^(2^2 - 2*2) + C
1 = (1)e^0 + C
C = 0
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a.They need to elect a slate of officers including a president, vice president, recording secretary, corresponding secretary, treasurer, historian, and statistician. If each of the members can be elected to any of the positions and each member may only hold one position, how many different slates of officers can be elected
Therefore, The number of different slates of officers that can be elected is 5,040. This is calculated using the permutation formula with 7 positions to fill and 7 members who can be elected to each position.
To find the number of different slates of officers that can be elected, we need to use the permutation formula. The formula for permutations is n!/(n-r)!, where n is the total number of items and r is the number of items selected. In this case, we have 7 positions to fill and 7 members who can be elected to each position. Therefore, the number of different slates of officers that can be elected is 7!/(7-7)! = 7! = 5,040.
There are seven positions that need to be filled including president, vice president, recording secretary, corresponding secretary, treasurer, historian, and statistician. Each member can be elected to any position and can only hold one position. To find the number of different slates of officers that can be elected, we use the permutation formula. We have 7 positions to fill and 7 members who can be elected to each position, so the number of different slates of officers that can be elected is 7!/(7-7)! = 7! = 5,040.
Therefore, The number of different slates of officers that can be elected is 5,040. This is calculated using the permutation formula with 7 positions to fill and 7 members who can be elected to each position.
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You number each subject in the population. Then place numbered cards in a bowl, mix them thoroughly, and select as many cards as needed. This is an example of which sampling method? ç”案选项组 Random Sampling Stratified Sampling Cluster Sampling Systematic Sampling
The described sampling method is an example of random sampling.
The sampling method described in the question is known as simple random sampling, which is a common method of selecting a representative sample from a population.
In this method, each member of the population is assigned a unique number, and a certain number of individuals are selected randomly from the population.
Simple random sampling is a type of probability sampling, which means that each member of the population has an equal chance of being selected for the sample.
This is important because it ensures that the sample is representative of the population as a whole, and reduces the risk of sampling bias.
The process of simple random sampling is straightforward and easy to implement, making it a popular choice for researchers. However, it can be time-consuming and may not be practical for very large populations. In such cases, other sampling methods such as stratified sampling or cluster sampling may be more appropriate.
Overall, simple random sampling is a reliable and effective method of selecting a representative sample from a population, and is widely used in research studies and surveys.
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The parameter ______ represents the proportion of successes in a population and the statistic ______ represents the proportion of successes in a sample.
The statistic p-hat and the parameter p indicate the proportion of successes in a sample and the population, respectively.
Two typical metrics are the population mean and standard deviation. Greek letters, such as (mu) for the mean and (sigma) for the standard deviation, are frequently used in statistics to denote population parameters.
P′ is equal to x / n, where x is the total number of successes and n is the sample size. As a point estimate for the genuine population percentage, the variable p′ represents the sample proportion. P is a parameter that describes a population-related percentage number. For instance, according to the 2010 United States Census, 83.7% of Americans were not classified as Hispanic or Latino.
[tex]p=xn_p = x_n[/tex]
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George spent 80% of his savings to buy a camera. The camera cost $580. How much did he have in savings before he bought the camera?
Answer:
George had $725 in savings
Step-by-step explanation:
Let's assume that George had x dollars in savings before he bought the camera.
According to the problem, George spent 80% of his savings to buy the camera, which means he had 20% of his savings left after the purchase. We can write this as:
0.20x = amount of savings left after buying the camera
We also know that the camera cost $580. We can set up an equation to relate the cost of the camera to the amount of savings that George had before buying the camera:
0.80x = $580
Solving for x, we get:
x = $580 / 0.80
x = $725
Therefore, George had $725 in savings before he bought the camera.
The volume of a rectangular box is 343 ft3. If the width is 4 times longer than the height, and the length is 16 times longer than the height, find the dimensions of the box.
The dimensions of the rectangular box are height = 7 ft, width = 28 ft, and length = 112 ft.
Let the height of the box be h. Then, the width is 4h, and the length is 16h. We know that the volume of the box is 343 ft³, so we can set up the equation: V = l*w*h = (16h)(4h)(h) = 64h³
64h³ = 343
h³ = 343/64 = 27/4
h = (27/4)^(1/3) = 3/2
So the height of the box is 3/2 ft. Using this value, we can find the width and length:
Width = 4h = 4(3/2) = 6 ft
Length = 16h = 16(3/2) = 24 ft
Therefore, the dimensions of the rectangular box are height = 7 ft, width = 28 ft, and length = 112 ft.
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Suppose you calculated a paired-samples t test, with 30 pairs of scores. Mean mean difference is 6 and the standard error is 2.1. What is the .95 confidence interval
This means that we can be 95% confident that the true population means difference lies between 1.7075 and 10.2925.
Confidence interval = Mean difference ± (t-value × standard error)
Substituting the given values into the formula, we get:
Confidence interval = 6 ± (2.045 × 2.1)
Confidence interval = 6 ± 4.2925
A confidence interval is a statistical concept used to estimate the range of values in which a population parameter is likely to fall. It is calculated using sample data and is used to provide an estimate of the true population parameter.
The confidence interval is a range of values that is constructed around a point estimate, such as the sample mean or proportion. This range is based on the level of confidence chosen by the researcher, typically 90%, 95%, or 99%. For example, a 95% confidence interval means that if we were to repeat the sampling process many times, we would expect the true population parameter to fall within the range of values calculated for 95% of those samples.
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an ols estimator meets all three small sample properties under certain conditions plus consistency.
Yes, it is true that an OLS (ordinary least squares) estimator meets all three small sample properties (unbiasedness, efficiency, and minimum variance) under certain conditions, in addition to being consistent.
These conditions include the assumption that the error term has a zero mean and constant variance, and that the errors are independent and identically distributed (IID). When these assumptions hold, the OLS estimator is considered to be BLUE (Best Linear Unbiased Estimator) and is a reliable tool for estimating the unknown parameters in a linear regression model. However, it is important to note that these assumptions may not always hold in practice, and alternative estimation methods may need to be considered.
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A school system has 16 bus drivers that must cover 12 bus routes. Each driver can cover at most one route. The driver's bids for the various routes are listed in the file P05_45.xlsx. Each bid indicates the amount the driver will charge the school system to drive that route. How should the drivers be assigned to the routes to minimize the school system's cost
Since each driver can cover at most one route, we will continuous this process until all 12 routes have been assigned to a driver. This will ensure that the school system pays the least amount possible for the 12 bus routes.
To minimize the school system's cost while assigning drivers to the bus routes, follow these steps:
1. Open the file P05_45.xlsx and arrange the data in a clear format, such as a table with drivers listed vertically and routes listed horizontally. Each cell should contain the amount a driver charges for a specific route.
2. Identify the lowest bid for each route. You can do this by going through each column (representing a route) and finding the minimum amount.
3. Assign the driver with the lowest bid to the corresponding route. Make sure to keep track of which drivers have already been assigned to avoid assigning them to multiple routes.
4. Continue this process for all 12 routes. Remember, each of the 16 drivers can only be assigned to one route.
5. Once all drivers have been assigned to the routes, add up the amounts for each assigned driver to find the total cost for the school system.
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To verify that all sales that have been shipped to customers have been recorded, a test of transactions should be completed on a representative sample drawn from:
To verify that all sales that have been shipped to customers have been recorded, a test of transactions should be completed on a representative sample drawn from the sales records or shipping records.
The sample should be chosen randomly and be large enough to provide a reasonable level of confidence in the accuracy of the recorded transactions. This test will help ensure that all sales have been properly recorded in the accounting system and that there are no unrecorded sales. It is important to perform this test on a regular basis to maintain the integrity of the financial records.
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what is
15+28+12+20=
Answer: 75
Step-by-step explanation:
To find the sum of these numbers, we simply add them together:
15 + 28 + 12 + 20 = 75
Therefore, the sum of 15, 28, 12, and 20 is 75.
Evaluate the solution at the specified value of the independent variable. When t = 0, N = 150, and when t = 1, N = 300. What is the value of N when t = 4?
The value of N when t=4 is: N = 300 + 450 = 750.
To evaluate the solution at the specified value of the independent variable, we need to find the relationship between N and t. Given the information, we have two points: (0, 150) and (1, 300).
Step 1: Calculate the slope (m) between the two points.
m = (N2 - N1) / (t2 - t1) = (300 - 150) / (1 - 0) = 150
Step 2: Use one of the points (e.g., (0, 150)) and the slope to find the equation N = mt + b.
150 = 150 * 0 + b
b = 150
Step 3: Write the equation with the slope and intercept.
N = 150t + 150
Step 4: Evaluate the value of N when the specified value of the independent variable t = 4.
N = 150 * 4 + 150
N = 600 + 150
N = 750
The value of N when t = 4 is 750.
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What is the probability that in a randomly selected composition of n has a second part and it is equal to 1
The probability of selecting a composition of n with a second part equal to 1 is equal to (n-1)/4.
Let us consider a composition of n as an ordered sequence of positive integers where the sum of the integers is n.
The number of compositions of n is equal to 2ⁿ⁻¹,
Since there are n-1 spaces between the numbers where we can choose to either include or exclude a separator.
To calculate the probability that a randomly selected composition of n has a second part equal to 1,
Consider the second part of the composition.
It can be any positive integer from 1 to n-1, inclusive.
For the second part to be equal to 1,
Choose 1 as the second number in the composition and distribute the remaining n-2 among the remaining slots.
There are n-1 slots left since the second slot is already occupied by the number 1.
The remaining n-2 can be distributed in 2ⁿ⁻³ ways, since there are n-3 spaces left to distribute the remaining numbers.
Therefore, the probability of selecting a composition of n with a second part equal to 1 is,
P = (n-1) × 2ⁿ⁻³ / 2ⁿ⁻¹
= ( n - 1 ) × 2ⁿ⁻³⁻ⁿ⁺¹
= ( n - 1 ) × 2⁻²
= (n-1) / 4
Therefore, the probability is equal to (n-1)/4.
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True or false: If a relationship exists between a response variable Y and a predictor variable X it is appropriate to say that X causes variation in Y.
If a relationship exists between a response variable Y and a predictor variable X, it is appropriate to say that X causes variation in Y is True.
There could be other factors or variables that influence the relationship between X and Y. It is important to distinguish between correlation and causation.
To establish causation, a researcher needs to conduct a controlled experiment, where all other factors are held constant except for the predictor variable X.
This will allow the researcher to isolate the effect of X on Y and determine whether it is indeed causing variation in Y.
In conclusion, while a relationship between X and Y may suggest causation, it is not appropriate to make that assumption without conducting a controlled experiment or considering other factors that may be influencing the relationship.
True. If a relationship exists between a response variable Y and a predictor variable X, it is appropriate to say that X causes variation in Y.
In statistics, response variables, also known as dependent variables, are the outcomes we are interested in explaining or predicting.
Predictor variables, also called independent variables, are the factors that might influence these outcomes.
When analyzing data, we often use regression models to determine the strength and direction of the relationship between the response variable Y and the predictor variable X.
A positive relationship between X and Y means that as X increases, Y also increases, while a negative relationship implies that as X increases, Y decreases.
A strong relationship between the variables indicates that the predictor variable X accounts for a significant portion of the variation in the response variable Y.
However,
It's crucial to note that a correlation between X and Y does not guarantee causality.
Confounding variables, which are factors not included in the analysis but may influence the response variable, could be causing the observed relationship.
Further analysis,
Such as experiments or controlling for potential confounding variables, might be needed to establish causation.
In summary,
When a relationship exists between a response variable Y and a predictor variable X, it is appropriate to say that X causes variation in Y, but it's important to consider that correlation does not necessarily mean causation.
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In recent years, the United States has experienced a sharp increase in obesity rates (in particular amongst teenagers), which is considered to increase the probability of chronic diseases like diabetes. Even if the dependency ratio is constant, what would be the effect of such a trend on the size of the government debt
The increase in obesity rates in the United States, particularly among teenagers, can have a significant impact on the size of the government debt, even if the dependency ratio remains constant.
Obesity is linked to an increased risk of chronic diseases such as type 2 diabetes, heart disease, and certain cancers. These chronic diseases require costly medical treatments and care, which can put a strain on the government's finances. In turn, the government may need to spend more on healthcare programs, such as Medicaid and Medicare, to cover the costs of treating these chronic diseases.
Additionally, obesity can lead to a reduction in economic productivity and an increase in disability rates, which can result in lower tax revenues and higher disability payments. This reduction in economic productivity can also have a negative impact on economic growth, further exacerbating the debt problem.
Therefore, the increase in obesity rates in the United States can lead to increased government spending on healthcare and disability programs, lower tax revenues, and slower economic growth. All of these factors can contribute to an increase in the size of the government debt.
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In the original Milgram experiment, only men participated. In another version of the experiment, there were only women participants. How did women's obedience in the experiment compare to men's
In the original Milgram experiment, only men participated, and the study aimed to investigate their obedience to authority figures. Later, a version of the experiment was conducted with only women participants to compare their obedience levels to men's.
In the replication of the Milgram experiment with only women participants, the level of obedience was found to be similar to that of the original experiment with only men. In fact, the results showed that women were just as likely as men to obey authority figures and administer the maximum level of electric shocks to the supposed "learner" in the experiment. This suggests that obedience to authority is not gender-specific and that both men and women can be equally susceptible to obeying orders, even when they conflict with their own moral beliefs.
To answer your question, women's obedience in the Milgram experiment was found to be similar to men's obedience. Both genders displayed high levels of obedience to the authority figure, even when instructed to administer painful electric shocks to the "learner." This result suggests that obedience to authority is not solely dependent on gender but is rather a widespread human tendency.
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On a toll road, there are 7 lanes for drivers to pay their toll. Customer arrival times are random, with an exponential distribution. Service times are random, with an exponential distribution. What is the proper description for this queueing system.
Queueing system can be analyzed using queueing theory to determine performance measures such as the average queue length, average waiting time, and utilization of the service channels.
The queueing system you have described can be modeled as an M/M/7 queue, where:
M represents that inter-arrival times and service times are exponentially distributed.
M represents that the arrival process is memoryless, meaning that the probability of a customer arriving at any given time does not depend on the previous arrival times or the state of the system.
7 represents the number of service channels, or lanes, available for customers to pay their toll.
The notation for this system is M/M/7, which indicates that it has an infinite queue capacity and that there is no limit to the number of customers that can be waiting in the queue.
In this queueing system, customers arrive randomly and independently, and they join the queue if all lanes are busy. They are served on a first-come, first-served basis, with the service times also being exponentially distributed.
This queueing system can be analyzed using queueing theory to determine performance measures such as the average queue length, average waiting time, and utilization of the service channels.
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Suppose that I have a sample of 25 women and they spend an average of $100 a week dining out, with a standard deviation of $20. The standard error of the mean for this sample is $4. Create a 95% confidence interval for the mean and wrap words around your results.
We can say with 95% confidence that the true mean amount that women in the population spend dining out per week lies within the range of $91.74 to $108.26.
Based on the given information, we can calculate a 95% confidence interval for the mean amount that women in the population spend dining out per week. With a sample size of 25 and a standard error of $4, we can use the formula:
95% CI = sample mean +/- (critical value x standard error)
To find the critical value, we need to look up the t-distribution with degrees of freedom (df) = n-1 = 24 and a significance level of alpha = 0.05/2 = 0.025 (since we are interested in a two-tailed test). From a t-table or calculator, we find that the critical t-value is approximately 2.064.
Plugging in the values, we get:
95% CI = $100 +/- (2.064 x $4)
95% CI = $100 +/- $8.26
95% CI = ($91.74, $108.26)
Therefore, we can say with 95% confidence that the true mean amount that women in the population spend dining out per week lies within the range of $91.74 to $108.26. This means that if we were to repeatedly take random samples of 25 women and calculate their mean amount spent dining out, about 95% of the intervals we construct using this method would contain the true population mean.
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Suppose your TA is applying to graduate schools. His chances to be admitted to each school are 5% and are the same for any school. How many different schools does he need to apply to if he wants his chance to be admitted to at least one school to be above 90%, 95%
We get x = 59. Therefore, your TA should apply to 59 schools to have a greater than 95% chance of being admitted to at least one school.
To calculate the number of different schools your TA needs to apply to in order to have a certain chance of being admitted to at least one school, we can use the formula:
n = log(1 - p) / log(1 - q)
Where n is the number of schools, p is the desired probability of being admitted to at least one school (i.e. 0.9 or 0.95), and q is the probability of not being admitted to any one school (i.e. 0.95).
Using this formula with p = 0.9 and q = 0.95, we get:
n = log(1 - 0.9) / log(1 - 0.05)
n ≈ 14
So your TA would need to apply to at least 14 different schools to have a chance of being admitted to at least one school above 90%.
Using the same formula with p = 0.95 and q = 0.95, we get:
n = log(1 - 0.95) / log(1 - 0.05)
n ≈ 29
So your TA would need to apply to at least 29 different schools to have a chance of being admitted to at least one school above 95%.
To determine the number of schools your TA needs to apply to in order to have at least a 90% and 95% chance of being admitted to at least one school, we'll use the concept of complementary probability.
Step 1: Calculate the probability of NOT being admitted to any school
The probability of not being admitted to a single school is 95% (100% - 5%).
Step 2: Use complementary probability to find the required probability
Let x be the number of schools your TA needs to apply to. The probability of not being admitted to any of the x schools is (0.95)^x.
Step 3: Find the number of schools for a 90% chance
We want the probability of being admitted to at least one school to be above 90%. Therefore, we want the complementary probability to be less than 10% (100% - 90%):
(0.95)^x < 0.10
Solving for x, we get x = 45. Therefore, your TA should apply to 45 schools to have a greater than 90% chance of being admitted to at least one school.
Step 4: Find the number of schools for a 95% chance
Similarly, for a 95% chance, we want the complementary probability to be less than 5% (100% - 95%):
(0.95)^x < 0.05
Solving for x, we get x = 59. Therefore, your TA should apply to 59 schools to have a greater than 95% chance of being admitted to at least one school.
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IF triangle ABC is isosceles, angle B is the vertex angle, AB = 20x - 2, BC = 12x + 30, and AC = 25x, find x and the length of each side of the triangle.
Answer:
x=-2.5(ERROR)
Step-by-step explanation:
An isosceles triangle is a triangle with two sides of equal length, called legs. The third side of the triangle is called the base. The vertex angle is the angle between the legs 1.
Since triangle ABC is an isosceles triangle with vertex angle B, we know that AB = AC.
Therefore, we can set up an equation:
20x - 2 = 25x
Solving for x:
20x - 25x = 2
-5x = 2
x = -2/5
Since x cannot be negative, there must be an error in the problem statement.
I hope this helps!
Could someone help and show me the workings for these two question?
The mean of the given data is 194.25 and the standard deviation from the given data is 18475.6875.
(a) Given that, the size of rocks at both 5 m and 25 m from the base of the cliff.
Using given mean and standard deviation formulae, we get
Here, mean=3885/20
= 194.25
Standard deviation=369513.75/20
= 18475.6875
Therefore, the mean of the given data is 194.25 and the standard deviation from the given data is 18475.6875.
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Suppose you have a job as a political poll person, approximately 130 million people voted in the last presidential election. How many people do you have to sample to be 95% certain you can identify a difference of 1%
The people do you have to sample size to be 95% certain you can identify a difference of 1% is 9604.
A minimum sample size is the number of participants required to provide findings that accurately reflect the community under investigation while yet maintaining the intended confidence interval (margin of error) and confidence level.
The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.
As we are given here a margin of error of 0.01. Also from standard normal tables, we have here:
P(-1.96 < Z < 1.96) = 0.95
Therefore 1.96 is the z critical value that is to be used here.
As we are not given a prior proportion value here, we take p = 0.5, to get a conservative value of the sample size.
The margin of error now is computed as:
MOE = x*P(1 - p)
n = 22 P(1-7 .)2 x 0.25 = 9604 MOE2
Therefore 9604 is the required minimum sample size here.
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Answer Immeditely Please
The length of segment AD is given as follows:
AD = 4.
What is the geometric mean theorem?The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.
Hence, in this problem, we have that the altitude of BD = 2 is the geometric mean of DC = 1 and AD, hence:
AD x 1 = 2²
AD = 4 units.
Which is the length of segment AD.
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im being nice
what is 4x2
be my friend pls
Answer: 8
Step-by-step explanation: you multiply 4 times 2 and get 8 basic math
In a manufacturing process, a random sample of 9 bolts has a mean length of 3 inches with a variance of .09. What is the 90 percent confidence interval for the true mean length of the bolt? Assume that X, the length of a bolt, is distributed normally.