You want to test whether the population variance differs from 50. From a sample of 25 observations drawn from a normally distributed population, you calculate s2-80, when conducting this test at the 5% significance level, the, χ2df critical value is Multiple Choice 5.625 12.401 14.400 39.364.
Answers
Therefore, the correct option is 39.364.
When conducting a test at the 5% significance level, the critical value of\( χ2df is 39.364\).
The χ2 distribution is a continuous probability distribution that is commonly used in statistics to determine the variance of a population or the goodness of fit of a sample to an anticipated distribution. In the given question, we have to calculate the critical value of χ2df when conducting the test at the 5% significance level.The formula for calculating χ2 is:χ2=(n−1)s2σ2
Where, n is the sample size, s2 is the sample variance, and σ2 is the population variance .The null hypothesis H0 of this test is:H0:σ2=50The alternative hypothesis Ha of this test is:Ha:σ2≠50So, the degrees of freedom are:\(df=n−1=25−1=24\)The χ2 critical value with 24 degrees of freedom at the 5% significance level is:χ2df=39.364
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Related Questions
How would I go about solving this?
Answers
The required answer of given fractional problem is \(\frac{12\sqrt{8a}-24a\sqrt{6} }{128a^{2} }\)
What is rationalizatoin?Rationalization is the mathematical operation, in which denominator get multiply with the numerator and denominator.
According to the given data:⇒ \(\frac{3-3\sqrt{3a} }{4\sqrt{8a} }\)
⇒ \(\frac{3-3\sqrt{3a} }{4\sqrt{8a} }\) × \(\frac{4\sqrt{8a} }{4\sqrt{8a} }\)
⇒ \(\frac{12\sqrt{8a}-24a\sqrt{6} }{128a^{2} }\)
In maths, under root is not allow in denominator, so calculated answer best.
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How is this A? Or is it wrong? This is polynomials
Answers
Answer:
D
Step-by-step explanation:
The volume for a rectangular prism is given by the formula:
\(V=lwh\)
The length is 2h, the width is 9-h, and the height is h. So:
\(V=2h(h)(9-h)\)
Multiply the first two terms:
\(V=2h^2(9-h)\)
Distribute:
\(V=18h^2-2h^3\)
Our answer is D.
I hope this helps!
An amount of $290000 is borrowed for a period of 25 years at an interest rate of 4%
Answers
Answer:
nice
Step-by-step explanation:
Solve dy/dx=1/3(sin x − xy^2), y(0)=5
Answers
The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5
To solve this differential equation, we can use separation of variables.
First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:
dy/dx = 1/3(sin x − xy^2)
dy/(sin x - xy^2) = dx/3
Now we can integrate both sides:
∫dy/(sin x - xy^2) = ∫dx/3
To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:
∫dy/(sin x - xy^2) = ∫du/(sin x - u)
= -1/2∫d(cos x - u/sin x)
= -1/2 ln|sin x - xy^2| + C1
For the right side, we simply integrate with respect to x:
∫dx/3 = x/3 + C2
Putting these together, we get:
-1/2 ln|sin x - xy^2| = x/3 + C
To solve for y, we can exponentiate both sides:
|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)
|sin x - xy^2| = 1/e^(2C/3 - x/3)
Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.
Case 1: sin x - xy^2 > 0
In this case, we have:
sin x - xy^2 = 1/e^(2C/3 - x/3)
Solving for y, we get:
y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]
Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:
y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5
Squaring both sides and solving for C, we get:
C = 3/2 ln(1/25)
Putting this value of C back into the expression for y, we get:
y = √[(sin x - e^(x/2)/25)/x]
Case 2: sin x - xy^2 < 0
In this case, we have:
- sin x + xy^2 = 1/e^(2C/3 - x/3)
Solving for y, we get:
y = ±√[(e^(2C/3 - x/3) - sin x)/x]
Again, using the initial condition y(0) = 5 and solving for C, we get:
C = 3/2 ln(1/25) + 2/3 ln(5)
Putting this value of C back into the expression for y, we get:
y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]
So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:
y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5
y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5
Note that there is no solution for y when sin x - xy^2 = 0.
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The data are the ages that collected from a neighborhood 30, 35, 8, 12, 48, 70, 50, 62, 78 Find the mean, variation, standard deviation, first quartile, median, third quartile and 65% percentile.
Answers
According to the question, the mean, variation, standard deviation, quartiles, median, and percentile for the given data set are:
Mean = 43.33
Variation = 9646.22
Standard Deviation = 98.21
First Quartile (Q1) = 12
Median = 48
Third Quartile (Q3) = 70
65th Percentile = 50
To find the mean, variation, standard deviation, quartiles, median, and percentile for the given data set, we can follow these steps:
Step 1: Sort the data in ascending order: 8, 12, 30, 35, 48, 50, 62, 70, 78.
Step 2: Calculate the mean:
\(Mean = \frac{8 + 12 + 30 + 35 + 48 + 50 + 62 + 70 + 78}{9} = 43.33\) (rounded to two decimal places).
Step 3: Calculate the variation:
\(\text{Variation} = \frac{{\sum((x_i - \text{mean})^2)}}{n}\\\\= \frac{{((8 - 43.33)^2 + (12 - 43.33)^2 + \ldots + (78 - 43.33)^2)}}{9}\\\\= 9646.22 \quad\)
Step 4: Calculate the standard deviation:
Standard Deviation = \(\sqrt{(Variation)} = \sqrt{(9646.22)} = 98.21\) (rounded to two decimal places).
Step 5: Calculate the quartiles:
First Quartile (Q1) = 12 (since it is the median of the lower half of the data).
Third Quartile (Q3) = 70 (since it is the median of the upper half of the data).
Step 6: Calculate the median:
The median is the middle value of the sorted data set, which is 48.
Step 7: Calculate the percentile:
To find the 65th percentile, we need to determine the value that separates the lowest 65% of the data from the highest 35%. Since the data set has 9 elements, 65% of 9 is 5.85. Rounding up, we get 6. The 6th element in the sorted data set is 50, which represents the 65th percentile.
Hence, the mean, variation, standard deviation, quartiles, median, and percentile for the given data set can be represented in LaTeX as follows:
\(\text{Mean} &= 43.33 \\\text{Variation} &= 9646.22 \\\text{Standard Deviation} &= 98.21 \\\text{First Quartile (Q1)} &= 12 \\\text{Median} &= 48 \\\text{Third Quartile (Q3)} &= 70 \\\text{65th Percentile} &= 50 \\\)
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what is 3456 x 3 hundreds
Answers
Answer:
3456 × 300 is equal to 1036800.
Answer:
1036800 right or did i miss read the question?
Step-by-step explanation:
which statistical term is a representation of the frequency of the event, measured in a standard year?
Answers
The statistical term is a representation of the frequency of the event, measured in a standard year is ARO
The predicted frequency with which a risk or hazard is expected to materialise is referred to as the Annualized rate of occurrence, or ARO. Probability Determination is another name for ARO.
In theory, calculating the Annualized rate of occurrence is rather simple, but in fact, it can be much more challenging.
Applying the formula will allow you to approach a problem in a methodical and mathematical manner. But when you take into account all the variables that can truly affect the likelihood of anything happening, things get complicated.
The difficulty of the ARO calculation rises as the number of variables does.
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find a ratio that compares the relative sizes of the quantities
24 ounces to 9 pounds
Answers
Answer:
1 : 6
Step-by-step explanation:
1 ounce = 0.0625 pounds
24 ounces
= 24 x 0.0625
= 1.5 pounds
24 ounces to 9 pounds
= 24 ounces : 9 pounds
= 1.5 pounds : 9 pounds
= 1.5 : 9
= 1.5 / 9
= 15 / 90
= 1 / 6
= 1 : 6
use the sum of the first 10 terms to approximate the sum s of the series. (round your answers to five decimal places.) [infinity] 11 1 3n n = 1 s ≈
Answers
using the sum of the first 10 terms, the approximation for the sum of the series ∑(1/(3n)) from n = 1 to infinity is approximately 18.33333.
To approximate the sum of the series ∑(1/(3n)) from n = 1 to infinity using the sum of the first 10 terms, we can calculate:
s ≈ ∑(1/(3n)) from n = 1 to 10
s ≈ 1/3(1) + 1/3(2) + 1/3(3) + ... + 1/3(10)
s ≈ (1/3)(1 + 2 + 3 + ... + 10)
To find the sum of the arithmetic series 1 + 2 + 3 + ... + 10, we can use the formula:
Sum = (n/2)(first term + last term)
Sum = (10/2)(1 + 10)
Sum = 5(11) = 55
Substituting this value back into the original equation:
s ≈ (1/3)(55)
s ≈ 55/3 ≈ 18.33333
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What is 1/5 of 40,000
Answers
Answer:
8000
Step-by-step explanation:
\(\frac{1}{5}*40000=\frac{40000}{5}=8000\)
Good luck
Problem 2:
The lifespan of a particular brand of light bulb follows a normal distribution with a mean of 1000 hours and a standard deviation of 50 hours.
Find:
a) the z-score of light bulb with a mean of 500 hours.
b) If a customer buys 20 of these light bulbs, what is the probability that the average lifespan of these bulbs will be less than 980 hours?
c) the probability of light bulbs with the mean of 400 hours.
d) the number of light bulbs with the mean less than 1000 hours
Answers
The answers are:
a) The z-score for a light bulb that lasts 500 hours is -10.
b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.
c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.
d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.
How to solve the problema) The z-score is calculated as:
z = (X - μ) / σ
Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,
z = (500 - 1000) / 50 = -10.
The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.
b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is
50/√20
≈ 11.18 hours.
z = (980 - 1000) / 11.18 ≈ -1.79.
The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.
c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:
z = (400 - 1000) / 50 = -12.
The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.
d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.
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1. A candy cane company has 2,683 candy canes to package. How many
packs of 12 candy canes will the company be able to make?
Answers
Evan is going to use a computer at an internet cafe. The cafe charges an initial fee to use the computer and then an additional price per minute of usage. Let C represent the total cost of using a computer for t minutes at the internet cafe. A graph of C is shown below. Write an equation for C then state the slope of the graph and determine its interpretation in the context of the problem.
Answers
An equation for C is C = 0.1t + 4.
An interpretation of the slope of the graph is that the total cost of using a computer increases by 0.1 per minute.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (5 - 4.5)/(10 - 5)
Slope (m) = 0.5/5
Slope (m) = 0.1
At data point (10, 5) and a slope of 0.1, a linear equation for C can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = 0.1(x - 10)
y = 0.1x + 5 - 1
y = 0.1x + 4 ≡ C = 0.1t + 4
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What is the definition of an irrational number?
A.
a number that can be written as a fraction but not as a decimal
B.
a negative number
C.
a number that can be expressed as a fraction, , where p and q are integers and q is not equal to zero
D.
a number that cannot be expressed as a fraction, , where p and q are integers and q is not equal to zero
Answers
A.
a number that can be written as a fraction but not as a decimal I think
State the slope of the line shown below (help ASAP)
Is it a, b, c or d?
Answers
Answer:
D
Step-by-step explanation:
(the above graph depicts a horizontal line that intersects the y axis at -2)
(so, y = -2)
Answer:
0
Step-by-step explanation:
Horizontal line x axis is 0 while the vertical y axis is undefined.
What is the midpoint formula of quadratic equation?
Answers
The midpoint formula of a quadratic equation is given by: x = -b/(2a), where a, b and c are the coefficients of the quadratic equation ax2 + bx + c = 0.
This formula is used to determine the midpoint of the roots of a quadratic equation. It works by taking the coefficients of the equation and plugging them into the formula. The result of the formula will be the x-coordinate of the midpoint of the two roots.
This formula is useful when solving quadratic equations, because it allows us to quickly find the midpoint of the two roots without having to solve for both roots first. It is also useful for graphing the quadratic equation, as it reveals the location of the vertex of the parabola. Knowing the midpoint of the two roots also makes it easier to determine the nature of the roots, whether they are real or imaginary.
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Compute the maximum rate of change of ff at the given point and the direction in which it occurs.
f(x,y)=8y√x,(16,5)
Answers
y
of the two points over the change in
x
of the two points.
Point
(16,5)
does not fall on the graph
Approximately <0.301,0.959> is the direction in which the maximum rate of change of f occurs at (16,5).
To compute the maximum rate of change of f at the given point (16,5), we need to find the gradient vector of f at that point and then take its magnitude. The direction in which this maximum rate of change occurs will be given by the direction of the gradient vector.The gradient of a function is defined to be a vector field. Generally, the gradient of a function can be found by applying the vector operator to the scalar function. (∇f (x, y)). This kind of vector field is known as the gradient vector field. Now, let us learn the gradient of a function in the two dimensions and three dimensions.First, we need to find the partial derivatives of f with respect to x and y:∂f/∂x = 4y/√x
∂f/∂y = 8√xNext, we evaluate these partial derivatives at the given point (16,5):
∂f/∂x(16,5) = 4(5)/√16 = 10
∂f/∂y(16,5) = 8√16 = 32So the gradient vector of f at (16,5) is:
∇f(16,5) = <10,32>The magnitude of this gradient vector is:
|∇f(16,5)| = sqrt(10^2 + 32^2) = 33.166
Therefore, the maximum rate of change of f at (16,5) is 33.166, and it occurs in the direction of the gradient vector:
<10,32>/33.166 = <0.301,0.959> (approximately)
So the direction in which the maximum rate of change of f occurs at (16,5) is approximately <0.301,0.959>.
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CAN SOMEBODY PLEASE HELP ME!!! I WILL GIVE BRAINLY
Answers
Answer:
the angles are all the same
Step-by-step explanation:
that means they are sim
Answer:
BA is congruent to ZY
BC is congruent to ZX
Step-by-step explanation:
Since they are similar we can see that they have congruent parts due to there similarity
A hotel has a budget of $16,000 to buy 84 new mattresses. Each mattress costs $209. The hotel manager says, "Since 80 × $200 = $16,000, I can stay within the budget." Part A Use the drop-down box to tell whether the manager's reasoning is logical. The hotel manager's reasoning Choose... logical. Part B Use the drop-down boxes to explain why the manager's reasoning is or is not logical. Since the manager rounded 84 to 80 and $209 to $200, she found an Choose... . So, the actual total cost is Choose... $16,000.
Answers
Answer:
One
Step-by-step explanation:
Translate to words
6.4 - 3x + 8
Answers
Hope it works... not sure if it asked for that, I’d put that unless explained otherwise
Good luck!
The function used in excel to find the "line of best fit" is trendline dataline sales residual plot
Answers
The function used in Excel to find the "line of best fit" is called "Trendline". To add a trendline to a chart, you can right-click on a data series in the chart and select "Add Trendline" from the drop-down menu.
A trendline is a line that shows the general pattern or direction of a set of data. It's also known as a line of stylish fit or a retrogression line. A trendline can be added to a map in Excel to help fantasize the relationship between two variables and to make prognostications grounded on the data.
When you add a trendline in Excel, you have the option to choose from several different types of retrogression models, similar as direct, exponential, logarithmic, polynomial, power, and moving average. Each type of model fits a different type of data pattern, and it's important to choose the applicable model for your data. In addition to adding a trendline, Excel also provides a residual plot to help you assess the virtuousness of fit of the trendline.
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Repeated multiplication is used for converting a decimal fraction to binary. In this operation, which digit is produced as a product of the first multiplication? Is it the least significant digit of the answer or the most significant digit of the answer?
Answers
The first multiplication in the process of converting a decimal fraction to binary using repeated multiplication produces the least significant digit of the binary representation.
When converting a decimal fraction to binary using repeated multiplication, the first multiplication will produce the least significant digit of the binary representation.
To convert a decimal fraction to binary using repeated multiplication, the decimal fraction is multiplied by 2 repeatedly. The integer part of the product is the binary digit, and the fractional part is used for the next iteration. The process is repeated until the desired precision is achieved.
The multiplication starts with the fractional part of the decimal fraction, and the first multiplication determines the least significant bit (LSB) of the binary representation. Subsequent multiplications will determine the remaining bits from least significant to most significant.
Therefore, the first multiplication produces the least significant digit of the answer in the binary representation.
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Please help me ASAP and i mean ASAP
Answers
Answer:
no
Step-by-step explanation:
no
A basketball team played six games. In those games, the team won by 7 points, lost by 12, won by 8 , won by 11 , lost by 1 , and won by 5. What was the mean difference in game scores over the six games?
Answers
find x , y , sin alpha, tg beta and area of triangle
Answers
Answer:
Step-by-step explanation:
In the figure below, o ll k . Find the values of x and z .
Answers
Answer:
x = 110°, z = 32°
Step-by-step explanation:
x + 70 = 180 (Exterior angles)
x = 110
4z - 58 + 110 = 180 ( Linear pair)
4z = 128
z = 32
Pls mark as brainliest if possible and cheers!
Answer:yo mom
Step-by-step explanation:
Joe was in charge of lights for a dance. The red light blinks every two seconds, the yellow light every three seconds, and the blue light every five seconds. If we include the very beginning and very end of the dance, how many times during a seven minute dance will all the lights come on at the same time
Answers
Answer:
We consider:
T1 = 2s
T2 = 3s
T3 = 5s
We calculate the least common multiple of the Ts:
Ttot = 30 s.
During a seven minute dance the lights will come on at the same time:
7*60 s / 30 = 14 times.
In a span of 7 minutes, the lights will blink together 14 times.
What is LCM?LCM of two or more than two given numbers is the smallest common multiple that is divisible by two or more than two given numbers.
Given, Joe was in charge of lights for a dance.
The red light blinks every two seconds, the yellow light every three seconds, and the blue light every five seconds.
∴ LCM of 2, 3, and 5 is 30 so the lights blink together after every 30 seconds.
So, in 7 minutes or (7×60) = 420 seconds the lights will blink together
(420/30) = (42/3) = 14 times.
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for every positive integer $ k $ that divides the order of g, there exists a subgroup $ h $ of $ g $ of order $ k $.
Answers
The proof of every positive integer k that divides the order of g, there exists a subgroup h of g of order k is shown below:
What is Subgroup?A subgroup is a group nested inside another group. The subgroup test is used on subsets of a group to determine if they are subgroups. A proper subgroup is a subgroup that does not contain all of the original group, while a trivial subgroup contains only the identity.
Suppose k ∣ g ⟹n=dk:
If h(g)=⟨g⟩ is cyclic then
clearly K:=|⟨g^d⟩|=k .
Suppose now we have
1≠H≤h(g),
|H|=k and
let r>0 be the minimal natural number s.t.
g^r ∈ H , then
1=(g ^ r)^k = g^(r k)
⟹n ∣ r k ⟹ r k=ns =d ks ⟹ r= ds ⟹ s ∣ d
and from here we have
g^ r=(g^ d)^ s ∈K
Also, |H|=||K|
we get equality and thus uniqueness of K.
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how many pouds of blue berryes can you buy for 13.00
Answers
Answer: 3.25 pounds
Step-by-step explanation:
Answer:
$13.00 / $4.00 per pound = 3.25 pounds
hope that helped <3
1 pts
Graph the linear function y +8 = 2(x + 2)
-8
4
8
o
IA
2,8)
(014)
Answers
Answer: In the picture
please give me a brainliest answer
