The final measures of forecast accuracy are: CSE = -46, MAD = 18.4, MSE = 462.8, MAPE = 12.44
The forecast errors can be calculated as follows:
Period 1: 751 - 751 = 0
Period 2: 741 - 751 = -10
Period 3: 728 - 749 = -21
Period 4: 773 - 745 = 28
Period 5: 718 - 751 = -33
The cumulative sum of the forecast errors (CSE) is: 0 - 10 - 21 + 28 - 33 = -46
The mean absolute deviation (MAD) can be calculated as follows:
MAD = (abs(0) + abs(-10) + abs(-21) + abs(28) + abs(-33)) / 5
MAD = (0 + 10 + 21 + 28 + 33) / 5
MAD = 92 / 5 = 18.4
The mean squared error (MSE) can be calculated as follows:
MSE = (0^2 + (-10)^2 + ( -21)^2 + 28^2 + (-33)^2) / 5
MSE= ( 0+ 100+ 441 + 784 + 1089)/5
MSE = 2314/ 5 = 462.8
The mean absolute percent error (MAPE) can be calculated as:
MAPE = (abs(0/751) + abs(-10/741) + abs(-21/728) + abs(28/773) + abs(-33/718)) / 5 * 100
MAPE = (0 + 1.34 + 2.89 + 3.63 + 4.58) / 5 * 100
MAPE = 12.44
The final measures of forecast accuracy are:
CSE = -46
MAD = 18.4
MSE = 462.8
MAPE = 12.44
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_______The given question is incorrect, the correct question is given below:
The realized demand values A= 751, 741, 728, 773, 718
and forecast values F = 751, 751, 749, 745, 751
for periods = 1,2,3,4,5
are provided in the table below. Round only the final measure of forecast accuracy to two decimals. The cumulative sum of the forecast errors (CSE) is (Round to two decimals) The mean absolute deviation value (MAD) is (Round to two decimals) The mean squared error value (MSE) is (Round to two decimals) The mean absolute percent error value (MAPE) is (Round to two decimals.)
2. Determine a line that is parallel to the line y=-5x-5 passes through the point (1, 2). Which
of the following is an equation of this line?
Answer: y = 5x - 3
Step-by-step explanation:
The lines need the same slope
2 = 5(1) + b
2 = 5 + b
-5 -5
-3 = b
y = 5x - 3
The figure is not drawn to scale. What is the value of x, in degrees?
Answer:
48
Step-by-step explanation:
The side opposite to it has a length of 12.25. If I look below the length that is 12.25 has an angle measurement of 48 across from it.
I will give brainliest and ratings if you get this correct
Answer:
[tex]\textsf{Increasing}: \quad (- \infty, -1) \cup (1, \infty)[/tex]
[tex]\textsf{Decreasing}: \quad(-1, 1)[/tex]
[tex]\textsf{Minimum}: \quad (1, -4)[/tex]
[tex]\textsf{Maximum}: \quad (-1, 0)[/tex]
Step-by-step explanation:
[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}}\implies f'(x) > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies f'(x) < 0[/tex]
Given function:
[tex]f(x)=x^3-3x-2[/tex]
Differentiate the given function:
[tex]\implies f'(x)=3x^2-3[/tex]
To find the interval where f(x) is increasing, set the differentiated function to more than zero:
[tex]\implies 3x^2-3 > 0[/tex]
[tex]\implies 3(x^2-1) > 0[/tex]
[tex]\implies x^2-1 > 0[/tex]
[tex]\implies x^2 > 1[/tex]
[tex]\implies x < -1, \;\;\; x > 1[/tex]
So the interval on which function f(x) is increasing is:
[tex](- \infty, -1) \cup (1, \infty)[/tex]
To find the interval where f(x) is decreasing, set the differentiated function to less than zero:
[tex]\implies 3x^2-3 < 0[/tex]
[tex]\implies 3(x^2-1) < 0[/tex]
[tex]\implies x^2-1 < 0[/tex]
[tex]\implies x^2 < 1[/tex]
[tex]\implies -1 < x < 1[/tex]
So the interval on which function f(x) is decreasing is:
[tex](-1, 1)[/tex]
To find the relative extrema, set the differentiated function to zero and solve for x:
[tex]\implies 3x^2-3=0[/tex]
[tex]\implies 3(x^2-1)=0[/tex]
[tex]\implies x^2-1=0[/tex]
[tex]\implies x^2=1[/tex]
[tex]\implies x=-1,\;\;x=1[/tex]
To find the y-coordinates of the relative extrema, substitute the found values of x into the function and solve for y:
[tex]\implies f(-1)=(-1)^3-3(-1)-2=0[/tex]
[tex]\implies f(1)=(1)^3-3(1)-2=-4[/tex]
Therefore the minimum and maximum points of the function are:
[tex]\textsf{Minimum}: \quad (1, -4)[/tex]
[tex]\textsf{Maximum}: \quad (-1, 0)[/tex]
For each example, state whether the one-sample, two-independent-sample, or related-samples t test is most appropriate. If it is a related-samples t test, indicate whether the test is a repeated-measures design or a matched-pairs design. A professor tests whether students sitting in the front row score higher on an exam than students sitting in the back row. A graduate student selects a sample of 25 participants to test whether the average time students attend to a task is greater than 30 minutes. A researcher matches right-handed and left-handed siblings to test whether right-handed siblings express greater emotional intelligence than left-handed siblings. A principal at a local school wants to know how much students gain from being in an honors class. He gives students in an honors English class a test prior to the school year and again at the end of the school year to measure how much students learned during the year.
All the sample tests are stated below:
1) A two-independent-sample t test.
2) A one-sample t test.
3) A related-samples t test.
4) A related-samples t test.
What is Sample Test ?It is a subgroup of people with traits from a wider population. When population sizes are too big for the test to include all potential participants or observations, samples are utilized in statistical testing. A sample must be representative of the entire population and must not be biased toward any one trait.
A professor runs an experiment to see if front-row students perform better on an exam than back-row pupils.
This is a two-independent-sample t test, as there are two distinct groups (students in the front row and students in the back row) and the professor is interested in comparing the mean exam scores between them.
To determine whether students spend more than 30 minutes on an activity on average, a graduate student chooses a sample of 25 participants.
This is a one-sample t test, as there is only one group of participants and the graduate student is interested in comparing the mean time students attend to a task to a specific value (30 minutes).
To determine whether right-handed siblings exhibit higher emotional intelligence than left-handed siblings, a researcher pairs up right- and left-handed siblings.
This is a related-samples t test using a matched-pairs design, as the researcher is interested in comparing emotional intelligence scores of right-handed and left-handed siblings who are matched based on certain criteria (in this case, being siblings).
A local school's principal is curious to discover how much an honors class benefits the children there. He administers tests to honors English students before the start of the school year and again at the conclusion of the year to gauge their progress.
This is a related-samples t test using a repeated-measures design, as the principal is interested in comparing the test scores of the same group of students before and after taking the honors English class to measure how much they learned during the year.
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10. Which is the bigger portion, ½ of a 12 inch pizza, or % of a 9 inch pizza? Give a reason for your
answer.
½ of a 12 inches pizza represents the bigger portion.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle. Then the area of the circle will be
A = πr² square units
½ of a 12-inch pizza, then the area is given as,
A = (π / 2) x (12 / 2)²
A = 56.52 square inches
30% of a 9-inch pizza. Then the area is given as,
A = 0.30 x π (9 / 2)²
A = 19.0755 square inches
½ of a 12 inches pizza represents the bigger portion.
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a researcher for an organization that collects and reports on crime has data on the murder rates for 10 states from a certain year. the murder rate is the number of murders per 100,000 inhabitants. the murder rate sample data are reproduced below. use a ti-83, ti-83 plus, or ti-84 to calculate the sample standard deviation and the sample variance of the murder rates. round your answers to one decimal place. murders per 100k inhabitants 7.1 9 5.6 2.5 4.8 7 3.6 2.1 6.1 helpcopy to clipboarddownload csv provide your answer below: $$standard deviation
The sample standard deviation of murder rates is approximately 2.2, and the sample variance is approximately 4.9. The standard deviation and variance are measured in the same units as the original data (murders per 100,000 inhabitants), squared and unsquared.
We can use a TI-83, TI-83 Plus, or TI-84 to calculate the sample standard deviation and variance of the murder rates:
Enter the following information into a list: Enter the data into L1 by pressing STAT, then ENTER.Determine the standard deviation of the sample: STAT, CALC, and 1-VarStats are the commands. Enter L1 into the list and hit ENTER. The Sx value represents the standard deviation (s).Determine the sample variance: The sample variance is equal to the square of the sample standard deviation. To get the sample variance (s2), we can square the Sx value calculated in step 2.We get the following results using this method:
2.209 is the sample standard deviation (s).
4.877 sample variance (s2) (rounded to three decimal places)
As a result, the sample standard deviation of the murder rates is about 2.2, and the sample variance is about 4.9. It should be noted that the standard deviation and variance are measured in the same units as the original data (murders per 100,000 inhabitants), squared and unsquared.
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Please Help Me...
Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity.
$300 invested quarterly for 15 years at a 4.5% interest rate compounded quarterly.
The accumulated amount will be $_________?
(Round to the nearest cent as needed.)
In 15 years the investment will be worth $586.99.
What is compounding?Compound interest is the addition of interest to the principal sum of a loan or deposit or interest on interest plus interest.
It is the result of reinvesting interest, or adding it to the loaned capital, rather than paying it out or requiring payment from the borrower, so that interest is earned on the principal sum plus previously accumulated interest in the following period.
In finance and economics, compound interest is the norm.
To find how much will the investment be worth in 20 years:
Given -
Initial investment = $300.
Interest rate = 4.5%.
Interest applied = quarterly.
So, the table of 15 years will be as follows:
using the formula we get,
Therefore, in 15 years the investment will be worth $586.99
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i don’t know how to solve or die this please help
Officials at a metropolitan transit authority want to get input from people who use a certain bus route about a possible change in the schedule. They randomly poll 20 riders from each bus route. The type of sampling method used is: A. Simple random sample B. Stratified random sample C. Cluster sample D. Systematic sample
Answer: so u do 1 + n = 21
Step-by-step explanation:
21
Answer:
Step-by-step explanation:
SRS
Steps by steps to divide 44 divided by 2,876
Answer:
44 ÷ 2,876 = 0.01528 (rounded to five decimal places)
Step-by-step explanation:
To divide 44 by 2,876, we can use long division. Here are the steps:
Write 44 under the long division symbol (÷) and 2,876 outside the symbol.
___
2,876 | 44
Since 2 is smaller than 44, we can't divide 2,876 by 44, so we need to add a decimal point and a zero to the quotient and bring down the next digit of the dividend (4).
___
2,876 | 44.0
___
2,876 | 44.0
4
We see that 28 is the largest multiple of 2,876 that is less than or equal to 440. We write 28 above the line, and multiply 2,876 by 28 to get 80,528. We subtract 80,528 from 440, which gives us a remainder of 4.
28
___
2,876 | 44.0
4 4 0
- 3 4 2 8
-------
8 4
Since we have a remainder of 4, we can't bring down any more digits from the dividend, so we add a decimal point and a zero to the quotient and bring down a zero to make the dividend 40. We repeat the process of finding the largest multiple of 2,876 that is less than or equal to 400, writing it above the line, multiplying it by 2,876, subtracting the result from the dividend, and bringing down the next digit.
28. 0
___
2,876 | 44.0
4 4 0
- 3 4 2 8
-------
8 4
8 3 6
- 8 0 4
-------
3 2
We have a remainder of 32, and we can't bring down any more digits from the dividend, so we add a decimal point and a zero to the quotient and bring down another zero to make the dividend 320. We repeat the process of finding the largest multiple of 2,876 that is less than or equal to 3,200, writing it above the line, multiplying it by 2,876, subtracting the result from the dividend, and bringing down the next digit.
28. 00
___
2,876 | 44.0
4 4 0
- 3 4 2 8
-------
8 4
8 3 6
- 8 0 4
-------
3 2
2 8 2
- 2 8 7 6
-------
6
We have a remainder of 6, and we can't bring down any more digits from the dividend, so we have our final answer:
44 ÷ 2,876 = 0.01528 (rounded to five decimal places)
A number line goes from 0 to 10. A closed circle is shown at point 0 and 5. Point 0 is labeled Start and point 5 is labeled Finish.
A 5-mile race takes place along a straight course. The number line shows the distance, in miles, from start to finish. The race director would like to place a water station along the course such that the distance from the start to the water station and the water station to the finish line is in a 7:5 ratio. Where would the water station be located? Round to the nearest tenth of a mile, if necessary.
The water station will be placed about
miles from the start.
The water station would be located at 2.92 miles. Round to the nearest tenth of a mile, the answer is 2.9 miles.
What is the distance?Distance is a numerical value that quantifies "how much ground an object has traveled" while in motion. Distance is calculated as the sum of a person's movement and time.
Call the distance between the starting point and the water station x. 5 - x meters separate from the water station from the finish line.
We may write the following equation because we are aware that the ratio between these two lengths is 7:5.
x / (5 - x) = 7/5
Expanding and solving for x, we get:
5x = 7(5) - 7x
12x = 35
x = 35/12 = 2.92 miles
Therefore, the distance of the water station would be 2.9 miles.
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According to a survey, 56% of young Americans aged 18 to 29 say the primary way they watch television is through streaming services on the internet. Suppose a random sample of 350 Americans from this group is selected. Would it be surprising to find that more than 70% of the sample watched television primary through streaming services? (Include z-score)
Answer:
The z-score is a statistical measure that describes how far a sample estimate is from the population parameter in standard deviation units. It is calculated by taking the difference between the sample estimate and the population parameter, and dividing it by the standard deviation of the sampling distribution of the estimate. The resulting z-score can be used to calculate the probability of observing a sample estimate as extreme or more extreme than the one obtained, assuming the null hypothesis is true.
In this case, the sample estimate is the proportion of individuals who watch television primarily through streaming services, which is 70%, and the population parameter is the proportion of all individuals who watch television primarily through streaming services, which is 56%. The sample size is 350. The null hypothesis is that there is no difference between the sample and population proportions, and the alternative hypothesis is that the sample proportion is greater than the population proportion.
To calculate the z-score, we need to determine the standard error of the sampling distribution of the proportion. The standard error is a measure of the variability of sample estimates due to random sampling variation. It is calculated by taking the square root of the population proportion times one minus the population proportion, divided by the sample size. In this case, the standard error is:
standard error = sqrt[(0.56 * (1 - 0.56)) / 350] = 0.028
The z-score can now be calculated as:
z-score = (0.7 - 0.56) / 0.028 = 5.19
This z-score is quite large, indicating that the sample estimate is more than 5 standard errors away from the population parameter. This suggests strong evidence against the null hypothesis, as the probability of observing a sample estimate as extreme or more extreme than the one obtained is very low, assuming the null hypothesis is true.
In other words, the result of observing a sample proportion of 70% or above is highly unlikely to have occurred by chance alone, assuming that the true population proportion is 56%. This result provides evidence in support of the alternative hypothesis, which states that the sample proportion is greater than the population proportion.
Rewrite 92 and 146 as product of their prime factor
92 and 146 as product of their prime factor are 2^2 * 23 and 2 * 73
How to rewrite the expressionFrom the question, we have the following parameters that can be used in our computation:
92 and 146
Prime factorization of 92:
92 = 2 x 2 x 23
Prime factorization of 146:
146 = 2 x 73
So, we have
Product = 2 * 2 * 23 * 2 * 73
This gives
Product = 2^3 * 23 * 73
Hence, the expression is 2^3 * 23 * 73
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Please help !! I need help
Answer:
Step-by-step explanation:
197.97
[10 points] if u is a uniform random variable on [0,1], what is the distribution of the random variable x?
Answer:
x= ( 0,1 )
Step-by-step explanation:
your graph it
Adding and Subtracting Polynomials
Feb 09, 10:57:07 AM
Find the sum of 9x² + 5x + 8 and 9x – 7.
-
9x² + 14x +1 is the sum of polynomials 9x² + 5x + 8 and 9x – 7.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
We need to find the sum of 9x² + 5x + 8 and 9x – 7.
Summation is the addition of a sequence of any kind of numbers.
So add 9x² + 5x + 8 and 9x – 7.
9x² + 5x + 8 + 9x – 7.
Add the like terms
9x² + 14x +1
Hence, 9x² + 14x +1 is the sum of polynomials 9x² + 5x + 8 and 9x – 7.
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Alex and Tory are married and filing jointly. Their taxable income is $150,000. Based
on the table below, how much do they owe in federal taxes?
Note: For a married couple filing jointly, the standard deduction is $25,900.
With given percentages of taxes on income, Alex and Tory owe $18,882 in federal taxes.
what exactly is a percentage?
A percentage is a way of representing a number as a fraction of 100. It is often denoted by "%". For example, 50% means 50 out of 100, or 0.5 as a decimal. Percentages are commonly used to express rates, ratios, and proportions in many areas such as finance, statistics, and everyday life.
Now,
Since the couple is married and filing jointly, their standard deduction is $25,900. Thus, their taxable income is $150,000 - $25,900 = $124,100.
From the tax table, the tax on the first $19,750 is 10% and the tax on the next $60,500 ($80,250 - $19,750) is 12%. The remaining taxable income is $124,100 - $80,250 = $43,850, which falls into the 22% tax bracket.
Therefore, the tax owed on the first $19,750 is $1,975 (10% of $19,750), the tax owed on the next $60,500 is $7,260 ($1,975 plus 12% of $60,500 - $19,750), and the tax owed on the remaining $43,850 is $9,647 (22% of $43,850).
The total tax owed is the sum of these amounts: $1,975 + $7,260 + $9,647 = $18,882. Therefore, Alex and Tory owe $18,882 in federal taxes.
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The overhead reach distances of adult females are normally distributed with a mean of 205 cm and a standard deviation of 8.6 cm.
a. Find the probability that an individual distance is greater than 218.40 cm.
b. Find the probability that the mean for 20 randomly selected distances is greater than 203.20 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
a) The probability that an individual overhead reach distance is greater than 218.40 cm is about 0.0594.
b) The probability that the mean for 20 randomly selected overhead reach distances is greater than 203.20 cm is about 0.7930.
c) The central limit theorem applies and we can use the normal distribution to approximate the sampling distribution of the sample means.
What is Probability :Probability is a way to evaluate how likely something is to happen. Several things are difficult to forecast with absolute confidence.
Now in the given question ,
a. To find the probability that an individual distance is greater than 218.40 cm, we can use the z-score formula:
z = (x - μ) / σ
where x is the individual distance, μ is the mean overhead reach distance, and σ is the standard deviation of the overhead reach distances. Plugging in the values given, we have:
z = (218.40 - 205) / 8.6
z = 1.56
Using a standard normal table or calculator, we can find the probability that a z-score is greater than 1.56 to be approximately 0.0594. Therefore, the probability that an individual overhead reach distance is greater than 218.40 cm is about 0.0594.
b. To find the probability that the mean for 20 randomly selected distances is greater than 203.20 cm, we need to use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normal, with a mean of μ and a standard deviation of σ / sqrt(n), where n is the sample size. In this case, we have:
μ = 205
σ = 8.6
n = 20
So the standard deviation of the sample means is:
σ / sqrt(n) = 8.6 / sqrt(20) = 1.923
Next, we need to find the z-score corresponding to a mean of 203.20 cm:
z = (203.20 - 205) / 1.923
z = -0.82
Using a standard normal table or calculator, we can find the probability that a z-score is greater than -0.82 to be approximately 0.7930. Therefore, the probability that the mean for 20 randomly selected overhead reach distances is greater than 203.20 cm is about 0.7930.
c. The normal distribution can be used in part (b) because of the central limit theorem. Even though the sample size is less than 30, the sampling distribution of the sample means will still be approximately normal if the population distribution is normal or if the sample size is large enough. In this case, we are told that the population distribution of overhead reach distances is normal, so the central limit theorem applies and we can use the normal distribution to approximate the sampling distribution of the sample means.
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For each conjecture below, you are to describe in words what the Null Hypothesis and Alternative Hypothesis are. Consider the decision that you have to make based upon your conjectures. Explain in words or with a chart what the Type I and Type II errors mean in context. Finally, describe the ramifications of making these errors within the context of the problem and describe which of the 2 errors are worse (in your opinion).
1. It is believed that a new drug can cure a cold.
2. The teacher will never check homework today.
3. In a big store like Wal-Mart, they will never catch me if I shoplift.
4. If I try to learn to ski, I will end up hurting myself.
Type I error is generally worse than a Type II error in all of these scenarios, as it can have more severe consequences.
The Null Hypothesis is a statement that assumes that there is no significant difference or effect between two groups or variables. The Alternative Hypothesis is a statement that assumes that there is a significant difference or effect between two groups or variables.
Conjecture: It is believed that a new drug can cure a cold.
Null Hypothesis: The new drug does not cure a cold.
Alternative Hypothesis: The new drug does cure a cold.
Type I error: We conclude that the drug cures a cold, but it does not.
Type II error: We conclude that the drug does not cure a cold, but it actually does.
Ramifications: If we make a Type I error, we may give the drug to people who do not need it, which can have negative side effects. If we make a Type II error, people who could have benefited from the drug will not receive it.
Conjecture: The teacher will never check homework today.
Null Hypothesis: The teacher will check homework today.
Alternative Hypothesis: The teacher will not check homework today.
Type I error: We conclude that the teacher will not check homework today, but they actually do.
Type II error: We conclude that the teacher will check homework today, but they actually do not.
Ramifications: If we make a Type I error, we may not do our homework and receive a lower grade. If we make a Type II error, we may waste time doing homework that will not be checked.
Conjecture: In a big store like Wal-Mart, they will never catch me if I shoplift.
Null Hypothesis: Wal-Mart will catch me if I shoplift.
Alternative Hypothesis: Wal-Mart will not catch me if I shoplift.
Type I error: We conclude that Wal-Mart will not catch us if we shoplift, but they actually do.
Type II error: We conclude that Wal-Mart will catch us if we shoplift, but they actually do not.
Ramifications: If we make a Type I error, we may shoplift and get caught, which can have legal consequences. If we make a Type II error, we may shoplift and get away with it, which can encourage further illegal behavior.
Conjecture: If I try to learn to ski, I will end up hurting myself.
Null Hypothesis: Trying to learn to ski does not result in injury.
Alternative Hypothesis: Trying to learn to ski does result in injury.
Type I error: We conclude that trying to learn to ski results in injury, but it actually does not.
Type II error: We conclude that trying to learn to ski does not result in injury, but it actually does.
Ramifications: If we make a Type I error, we may avoid skiing altogether and miss out on the experience. If we make a Type II error, we may attempt skiing and get injured, which can have physical and financial consequences
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Consider the polynomial interpolation for the following data points
x| 0 | 2 | 3 | 4 | y | 7 | 11| 28| 63| (a). Write down the linear system in matrix form for solving the coefficients a; (i = 0,...,n) of the polynomial pn(x). (b). Use the Lagrange interpolation process to obtain a polynomial to approximate these data points.
Lagrange interpolation process to obtain a polynomial to approximate these data points is L(x) = (7/6)x³ - (5/3)x² + (19/6)x + 7
The polynomial interpolation is a technique that is used to find a polynomial function that passes through a given set of points. This is particularly useful in situations where we have a set of data points, and we want to find a smooth function that connects these points.
The given set of data points can be represented as (x0, y0), (x1, y1), ... , (xn, yn), where xi and yi represent the x and y coordinates of the ith point. In our case, the data points are (0, 7), (2, 11), (3, 28), and (4, 63).
To find the polynomial function that passes through these points, we can use a method called linear system. In this method, we assume that the polynomial function has the form:
pn(x) = a0 + a1x + a2x^2 + ... + anxn
Alternatively, we can use the Lagrange interpolation process to obtain a polynomial to approximate these data points. In this process, we construct a polynomial that passes through the data points by using the Lagrange basis polynomials. The Lagrange basis polynomial Li(x) is defined as:
Li(x) = (x - xi) / (xi - xj)
where i and j are indices that range from 0 to n, and i is not equal to j.
Using the Lagrange basis polynomials, we can construct the Lagrange polynomial L(x) as:
L(x) = y0L0(x) + y1L1(x) + ... + ynLn(x)
where yi is the y-coordinate of the ith point. This polynomial L(x) is the polynomial that passes through the given set of data points.
In this one, the Lagrange polynomial can be written as:
L(x) = (7/6)x³ - (5/3)x² + (19/6)x + 7
This polynomial can be used to approximate the values of y for any x within the range of the data points.
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In the process of producing engine valves, the valves are subjected to a first grind. Valves whose thicknesses are within the specification are ready for installation. Those valves whose thicknesses are above the specification are reground, while those whose thicknesses are below the specification are scrapped. Assume that after the first grind, 75% of the valves meet the specification, 20% are reground, and 5% are scrapped. Furthermore, assume that of those valves that are reground, 90% meet the specification, and 10% are scrapped.
a)Find the probability that a valve is ground only once. Round the answer to two decimal places.
b)Given that a valve is not reground, what is the probability that it is scrapped?
c)Find the probability that a valve is scrapped. Round the answer to three decimal places.
d)Given that a valve is scrapped, what is the probability that it was ground twice?
e)Find the probability that the valve meets the specification (after either the first or second grind).
f)Given that a valve meets the specification (after either the first or second grind), what is the probability that it was ground twice?
g)Given that a valve meets the specification, what is the probability that it was ground only once?
The probabilities are (a) 0.8 (b) 0.125 (c) 0.12 (d) 0.1667 (e) 0.88 (f) 0.2045 (g) 0.795
Let A = meet specification, B = reground and C = scrapped
index 1 indicates the value was not reground and index 2 indicates that value was reground before obtaining the situation.
P(A₁) = 70% = 0.7
P(B) = 20% = 0.2
P(C₁) = 10% = 0.1
P(A₂/B) = 90% = 0.9
P(C₂/B) = 10% = 0.1
(a) Probability that a valve is ground only once = 1 - P(B)
= 1 - 0.2 = 0.8
(b) a valve is not reground, the probability that it is scrapped
P(A₁∪C₁)
P(A₁) + P(C₁) = 0.1 + 0.7 = 0.8
P(C₁/A₁∪C₁) = 0.1/0.8 = 0.125
(c) Probability that a valve is scrapped
P(C₁) + P(B) × P(C₂/B) = 0.1 + 0.2 × 0.1
= 0.12
(d) a valve is scrapped, the probability that it was ground twice
P(B/C) = P(B∩C)/P(C)
= [tex]\frac{0.2\times 0.1}{0.12}[/tex]
P(B/C) = 0.1667
(e) the probability that the valve meets the specification (after either the first or second grind)
P(A) = P(A₁) + P(B) × P(A₂/B)
P(A) = 0.7 + 0.2 × 0.9 = 0.88
(f) P(B/A) = P(A₂)/P(A)
= 0.18/0.88 = 0.2045
(g) valve meets the specification, probability that it was ground only once
1 - P(B/A) = 1 - 9/14
= 0.795
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Sam exercised 6 times as many hours as Alex last week. Sam exercised for 12 hours. How many hours did Alex exercise?
Answer:
alex exercised 2 hours
Answer: 2
Step-by-step explanation:
we know that samn excersided 6 TIME AS MANY as alex. and that he excersides 12 hrs (dudes buff)
so we must divide 6/12
6/12=2
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The second annual Airplane Etiquette Study commissioned by Expedia asked 1000 Americans to rank the most annoying on-board behaviors of fellow passengers. Rear seat kickers topped the list with 67% of those surveyed ranking this annoying behavior as number one. You create a 90% confidence interval and find the population proportion to be within 0.024 of 0.67, or between (0.646, 0.694). Which of the following statements gives a valid interpretation of this interval? O There is a 90% chance that between 64.6% and 69.4% of all Americans would rank rear seat kickers as the most annoying on-board behavior of fellow passengers. O You are 90% confident that between 64.6% and 69.4% of all Americans would rank rear seat kickers as the most annoying on-board behavior of fellow passengers. O There is a 67% chance that between 64.6% and 69.4% of all Americans would rank rear seat kickers as the most annoying on-board behavior of fellow passengers. O You are 90% confident that between 64.6% and 69.4% of the 1000 sampled passengers ranked rear seat kickers as the most annoying on-board behavior of fellow passengers.
Previous question
The correct statement is option (B) You are 90% confident that between 64.6% and 69.4% of all Americans would rank rear seat kickers as the most annoying on-board behavior of fellow passengers
The confidence interval created in the study was found to be between (0.646, 0.694), with a 90% level of confidence.
To interpret this interval, we can look at the options provided. Option A states that there is a 90% chance that the population proportion falls between 64.6% and 69.4%. This is not a correct interpretation, as it suggests that the proportion changes depending on the survey and is not fixed.
Option B, on the other hand, correctly states that we can be 90% confident that the true population proportion falls within the given range. This means that if we were to conduct the same survey many times, with different samples of 1000 Americans, we can expect the true population proportion to fall within this range in 90% of the surveys conducted.
Option C is incorrect, as it suggests that there is a 67% chance that the proportion falls within the given range, which is not the level of confidence used in the study.
Option D is also incorrect, as it only refers to the sample of 1000 passengers surveyed and not the entire population of Americans.
In summary, the confidence interval created in the Airplane Etiquette Study provides a range within which we can be 90% confident that the population proportion of Americans who rank rear seat kickers as the most annoying on-board behavior of fellow passengers falls. This interval does not change with repeated surveys and represents a fixed parameter of the population.
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Suppose annual salaries for sales associates from a particular store have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500. Refer to Exhibit 3-3. The z-score for a sales associate from this store who earns $37,500 is
With a mean of $32,500 and a standard deviation of $2,500. The z-score for a sales associate who earns $37,500 is 2.
The z-score, also known as a standard score, is a measure of how many standard deviations a given value is from the mean. It is used to standardize the data and make it easier to compare and interpret. The formula for the z-score is:
z = (x - μ) / σ
where x is the value of interest, μ is the mean, and σ is the standard deviation.
In this case, the mean annual salary for sales associates from a particular store is $32,500 and the standard deviation is $2,500. We want to find the z-score for a sales associate who earns $37,500. Plugging in the values, we get:
z = ($37,500 - $32,500) / $2,500 = 2
This means that the sales associate's salary is 2 standard deviations above the mean.
Interpreting the z-score can help us understand how unusual or typical a given value is in comparison to the mean. In this case, a z-score of 2 indicates that the sales associate's salary is relatively high compared to the mean, but it is not an extremely high salary.
We can use a standard normal table to find the proportion of the data that falls below a given z-score, or to find the corresponding value for a given proportion of the data.
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find the sum please helpppppp
The value of the sum notation is 729
How to determine the sum notationFrom the question, we have the following parameters that can be used in our computation:
The sum notation
From the notation, we have the following values
First term, a = 972
Common ratio, r = -1/3
The sum is then represented as
Sum = a/(1 -r)
So, we have
Sum = 972/(1 + 1/3)
Evaluate
Sum = 729
Hence. the sum is 729
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Kyle got into his car and steadily accelerated to the speed limit. After driving at a constant
rate of speed for a while, he slowed to a stop and parked in a store parking lot. Kyle spent
a few minutes shopping, and then reentered his car to drive home. He accelerated to the
speed limit, continued at that speed for a while, and then slowed to a stop and parked in
his driveway. Which graph best represents the scenario described? and why.
Answer:
Below
Step-by-step explanation:
Answer C
A spam filer is designed by screening commonly occurring phrases in spam. Suppose that 60% of email is spam. In 20% of the spam emails, the phrase "free gift card" is used. In non-spam emails, 99.5% of them do not mention "free gift card". What is the probability that a newly arrived email which does mention "free gift card", is not spam?
The probability that a newly arrived email which does mention "free gift card", is not spam is 0.0165.
Let S be the event that an email is spam, and let F be the event that an email mentions "free gift card". We want to find P(S' | F), the probability that the email is not spam given that it mentions "free gift card".
We can use Bayes' theorem to find P(S' | F):
P(S' | F) = P(F | S') P(S') / P(F)
We can calculate each of these probabilities as follows:
P(F | S') = the probability that a non-spam email mentions "free gift card". From the problem, we know that this probability is 0.005 (i.e., 99.5% of non-spam emails do not mention "free gift card").
P(S') = the probability that an email is not spam. From the problem, we know that this probability is 0.4 (i.e., 60% of emails are spam, so 40% are not spam).
P(F) = the probability that an email mentions "free gift card". This can be calculated using the law of total probability:
P(F) = P(F | S) P(S) + P(F | S') P(S')
= 0.20 × 0.60 + 0.005 × 0.40
= 0.121
In the first term, we use the given probability that 20% of spam emails mention "free gift card". In the second term, we use the probability that 0.5% of non-spam emails mention "free gift card".
Plugging these values into Bayes' theorem, we get:
P(S' | F) = 0.005 × 0.4 / 0.121 ≈ 0.0165
Therefore, the probability that a newly arrived email which does mention "free gift card" is not spam is approximately 0.0165 or 1.65%.
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Girl Scout cookies are available only for a few weeks every year. They are mostly sold door-to-door and from tables at strip malls. Some cookie flavors are very popular, while others don't sell as well and are changed from year to year.The following analysis of variance was made to compare the popularity of each type of cookie, based on sales of 4 cookie flavors by 8 girl scouts in the same troop.COOKIE.............N....Mean....StdevDo-si-dos..........8.....8.33......3.39Samoas.............8....23.00....15.23Tagalongs.........8......9.17......2.23ThinMints..........8....51.00.....26.11Pooled StDev = 11.02Compute the margin of error to compare all pairs of means with Bonferroni's procedure with 94% family confidence.
The margin of error to compare all pairs of means with Bonferroni's procedure with 94% family confidence are [9.17, 20.17], [-4.66, 6.34] and [37.17, 48.17]. The margin of error for the difference in means between Samoas and Tagalongs is approximately 14.97.
To compute the margin of error to compare all pairs of means with Bonferroni's procedure with 94% family confidence, we need to use the formula:
Margin of error = t* (Sqrt (MSE/n))
Where t* is the critical value for a two-tailed t-test with a significance level of alpha = (1 - 0.94)/2 = 0.03,
degrees of freedom (df) = N - k,
where N is the total sample size (N = n * k = 8 * 4 = 32)
and k is the number of groups (k = 4), and MSE is the mean square error from the analysis of variance (ANOVA).
To find the critical value t* from the t-distribution table or calculator,
we need to look up the value of t for alpha/2 = 0.03/2 = 0.015 and df = 32 - 4 = 28, which is approximately 2.5.
The mean square error MSE is calculated by dividing the residual sum of squares (SSR) by the degrees of freedom within (dfw), which is
N - k = 32 - 4 = 28.
From the ANOVA table, we have:
SSR = 3458.08
dfw = 28
MSE = SSR/dfw = 3458.08/28 = 123.50
Now we can compute the margin of error for each pair of means with a 94% family confidence level, which means that the overall family
error rate is alpha = 1 - 0.94 = 0.06, and
the individual error rate for each comparison is alpha/k(k-1)/2 = 0.06/6 = 0.01.
For Do-si-dos vs. Samoas, the difference in means is 23 - 8.33 = 14.67. The margin of error is:
t* (Sqrt (MSE/n)) = 2.5 * (Sqrt (123.50/8)) = 5.50
The 94% family confidence interval for this comparison is [14.67 - 5.50, 14.67 + 5.50] = [9.17, 20.17].
For Do-si-dos vs. Tagalongs, the difference in means is 9.17 - 8.33 = 0.84. The margin of error is:
t* (Sqrt (MSE/n)) = 2.5 * (Sqrt (123.50/8)) = 5.50
The 94% family confidence interval for this comparison is [0.84 - 5.50, 0.84 + 5.50] = [-4.66, 6.34].
For Do-si-dos vs. Thin Mints, the difference in means is 51 - 8.33 = 42.67. The margin of error is:
t* (Sqrt (MSE/n)) = 2.5 * (Sqrt (123.50/8)) = 5.50
The 94% family confidence interval for this comparison is [42.67 - 5.50, 42.67 + 5.50] = [37.17, 48.17].
For Samoas vs. Tagalongs, the difference in means is 9.17 - 23 = -13.83. The Margin of error = 2.326 * 11.02 * √(1/8 + 1/8) ≈ 14.97
Therefore, the margin of error for the difference in means between Samoas and Tagalongs is approximately 14.97.
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A rectangular pyramid has a volume of 525 cubic feet. It has a base of 25 feet by 18 feet. Find the height of the pyramid.
Volume of a Pyramid: V=1/3Bh
What is the height of the pyramid in cubic feet?
Answer: The height is 3.5 cubic feet
Step-by-step explanation:
We have to find the area of the base first so multiply 25 and 18 feet together. You will get 450
Now you can make an equation.
525 = (1/3)*450*h
Multiply the 1/3 and the 450 together to get 150
Your equation is now 525 = 150h
Divide 150 on both sides to isolate h
You now have 3.5 = h
Determine the number k so that there is a solution to the differential equation ky'- y = x that satisfies the conditions y(1) = 0 and y'(1) = 1
To solve for k, we first take the derivative of the differential equation to obtain:
ky'' - y' = 1
Then we substitute y = 0 and y' = 1 when x = 1, giving us:
k(1) - (1) = 1
k = 2
Therefore, the value of k that satisfies the given conditions is k = 2.