A 4.0kg box slides with an initial speed of 3.0 m/s, end fraction towards a spring on a frictionless horizontal surface. when the box hits the spring, the spring compressed by 0.30m. what is the spring constant.
Answers
The spring constant is 180 N/m.
To solve for the spring constant, we can use the equation: k = (m * g) / x
where k is the spring constant, m is the mass of the box, g is the acceleration due to gravity (9.8 m/s^2), and x is the compression distance of the spring.
First, let's get the final velocity of the box when it hits the spring. We can use the equation:
v^2 = u^2 + 2as
where v is the final velocity (0 m/s), u is the initial speed (3.0 m/s), a is the acceleration (which is constant and equal to -k/m since the force from the spring is in the opposite direction of the box's motion), and s is the compression distance of the spring (0.30 m).
Rearranging the equation, we get:
k/m = (u^2 - v^2) / (2s)
k/4.0 = (3.0^2 - 0^2) / (2 * 0.30)
k/4.0 = 45
k = 180 N/m
Therefore, the spring constant is 180 N/m.
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Related Questions
what kind of polynomial is this -1/9x⁵+1
Answers
Answer: Binomial
Step-by-step explanation:
There are two terms in the polynomial so we ca say that it is binomial
in a distribution with a mean of 100 and a standard deviation of 15, what is the probability that the score will be 120 or higher
Answers
0.0912 is the probability that the score will be 120 or higher .
What is probability explain with an example?
The likelihood that something will occur is the foundation of it. The justification for probability serves as the basic foundation for theoretical probability. A coin is tossed, for instance, and the theoretical likelihood of getting a head is 1 in 2.Zlower = X₁ - μ/σ = 120 - 100/15 = 1.33
the probability is compared as
Pr ( X ≥ 120 ) = Pr(X - 100/15 ≥ 120 - 100/15)
= Pr(Z ≥ 120 - 100/15
= Pr( Z ≥ 1.33)
= 0.0912
Since 0.0912 > 0.05 i.e. this IQ score is not unusual and hence I can believe the claim.
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Choose the equation for the line shown on the graph.
Answers
Answer:
it's A
Step-by-step explanation:
Answer:
its A
Step-by-step explanation:
u can find the y-intercept by substituting 0 in place of Y so it will be;
Y= 2
hence, the co-ordinate will be (0,2) so the equation must be y=2/3x+2
Which angle is supplementary to the
Please helppp
Answers
Answer:
\(\angle FCB\)
Step-by-step explanation:
Supplementary angles are angles that sum to \(180^{\circ}\). In this case, \(\angle FCB\) is supplementary to \(\angle DCF\) since they add up to the angle of a straight line which is \(180^{\circ}\).
Hope this helps :)
Select all of the choices that are equal to (-5) - (-12)
-7
7
(-5)+12
(-5)+(-12)
Answers
Answer:
the awnser is. (-5) + (-12)
Answer: 7, -5+12
Step-by-step explanation:
Minus a negative is just like adding so -5 -( -12) would be the same as -5+12 which is 7
A population of Australian Koala bears has a mean height of 21 inches and a standard deviation of 4.5 inches. You plan to choose a sample of 64 bears at random. What is the probability of a sample mean between 21 and 22.
Answers
The probability of the sample mean being between 21 and 22 inches is approximately 47.72%.
To find the probability of a sample mean between 21 and 22 inches, we'll use the z-score formula for sample means. The z-score is calculated as:
Z = (X - μ) / (σ / √n)
where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
First, we'll find the z-scores for the sample means of 21 and 22 inches:
Z₁ = (21 - 21) / (4.5 / √64) = 0
Z₂ = (22 - 21) / (4.5 / √64) ≈ 2.01
Now, we'll find the probability between these z-scores using a standard normal distribution table. The probability corresponding to Z₁=0 is 0.5, and for Z₂≈2.01, it's approximately 0.9772.
So, the probability of the sample mean being between 21 and 22 inches is:
P(21 ≤ X ≤ 22) = P(Z₂) - P(Z₁) ≈ 0.9772 - 0.5 = 0.4772
Therefore, the probability of the sample mean being between 21 and 22 inches is approximately 47.72%.
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Find a formula for the
n
th term,
T
n
, of the following arithmetic equence:
−
13
,
−
25
,
−
37
,
−
49
,. . . Hence, or otherwie, find the value of the 60th term,
T
60
Answers
The value of the 60th term is -721 in given arithmetic progression.
What is arithmetic progression?
The difference between every two successive terms in a sequence is the same; this is known as an arithmetic progression (AP). It is possible to obtain a formula for the nth term of the AP using this kind of development. A good example of an arithmetic progression (AP) is the series 2, 6, 10, 14,..., which follows a pattern in which each number is created by adding 4 to the previous term. The nth term in this series equals 4n-2. You can get the sequence's terms by inserting n=1,2,3,...Given:
-13, -25, -37, -49,..
a = -13
d = t₂ - t₁
= -25 - (-13)
= -25 + 13
d = -12
tₙ = a +(n-1) d
t₆₀ = -13 + (60-1) (-12)
= -13 + (59) (-12)
= -13 - 708
t₆₀ = -721
Hence, the value of the 60th term is -721 in given arithmetic progression.
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M
Y
(4x - 1)
(2x +5)
Р
W
M
Answers
Step-by-step explanation:
(4x-1) × (2x+5)
3x × 7x
21x
The answer is = 21x
PLEASE HELP IF YOU KNOW THE ANSWER!!!
i need the domain and range
Answers
Answer:
domain: -1<x range:y<-1
Step-by-step explanation:
seeing as how the x value seems to start at -1, but keeps going past that to the right, we can get the equation x>-1. seeing as how the y value seems to start at -1, but keeps going down, we can get the equation y<-1.
If you have 2 coins, with one being fair and the other having two heads, and you then pick one of the two coins at random with equal probability out of an urn and without looking at both sides to see whether it is fair or not, and then flip it to determine whether you get heads or tails, and then repeating such a process 100 times, for a total of 100 flips. a) Compute the probabilities of getting exactly 60 heads. b) Generalize the result for getting exactly m heads after n flips.
Answers
a) Overall probability of getting exactly 60 heads in 100 flips is given by: 0.5 * P(X = 60 | coin A) + 0.5 * P(X = 60 | coin B) = 0.5 * P(X = 60 | coin A). b) The overall probability of getting exactly m heads in n flips is given by: 0.5 * P(X = m | coin A) + 0.5 * P(X = m | coin B).
a) In this scenario, you have two coins: a fair coin (coin A) with a 50% chance of getting heads, and a two-headed coin (coin B) with a 100% chance of getting heads. When picking a coin from the urn, you have an equal probability (50%) of choosing either coin.
Let's compute the probability of getting exactly 60 heads after 100 flips:
1. If you choose coin A (fair coin): The probability of getting 60 heads in 100 flips follows a binomial distribution with parameters n = 100 and p = 0.5. The probability is given by the formula: P(X = 60) = C(100, 60) * (0.5)^60 * (0.5)^40, where C(100, 60) is the number of combinations of 100 flips taken 60 at a time.
2. If you choose coin B (two-headed coin): Since it always lands heads, getting 60 heads in 100 flips is impossible.
Now, we need to consider the probability of selecting either coin A or B. Since there's a 50% chance of selecting either coin, the overall probability of getting exactly 60 heads in 100 flips is given by: 0.5 * P(X = 60 | coin A) + 0.5 * P(X = 60 | coin B) = 0.5 * P(X = 60 | coin A).
b) To generalize the result for getting exactly m heads after n flips, we can follow the same approach:
1. If you choose coin A (fair coin): The probability of getting m heads in n flips follows a binomial distribution with parameters n and p = 0.5. The probability is given by the formula: P(X = m) = C(n, m) * (0.5)^m * (0.5)^(n-m).
2. If you choose coin B (two-headed coin): The probability of getting m heads in n flips is 1 if m = n (as all flips result in heads) and 0 otherwise (if m < n).
The overall probability of getting exactly m heads in n flips is given by: 0.5 * P(X = m | coin A) + 0.5 * P(X = m | coin B).
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At the local farmer’s market it costs $6.00 for a 4-pound basket of pears. What is the price per pound?
Answers
Answer:
$1.50 per pound
Step-by-step explanation:
You divide 6 by 4 to get 1.5
You online store only sells one item, in either regular or deluxe version.
Because of high demand and restricted supply, you restrict each customer to buying 1 item - either buying the regular version of that item, or the deluxe version of that item, but not both.
On a typical day, you have 177 customers visit your online store. Each customer has a 0.29 chance of purchasing an item. If a customer purchases an item, there is a 9% chance they buy the regular item for $5.08 and if they do not buy the regular item, then they buy the deluxe item for $23.34.
Assume each customer makes their purchase decision independently of all other customers, and each customer has the same chance of purchasing the item.
What is your expected daily sales?
Answers
The expected daily sales for your online store are approximately $1196.28.
To calculate the expected daily sales, we need to multiply the number of customers by the probability of each customer purchasing an item and then sum up the expected sales for each type of item.
Given:
- Number of customers: 177
- Probability of a customer purchasing an item: 0.29
- Probability of buying the regular item: 0.09
- Probability of buying the deluxe item: 1 - 0.09 = 0.91
- Price of the regular item: $5.08
- Price of the deluxe item: $23.34
Let's calculate the expected daily sales:
Expected sales of regular items = Number of customers * Probability of purchasing * Probability of buying the regular item * Price of the regular item
Expected sales of deluxe items = Number of customers * Probability of purchasing * Probability of buying the deluxe item * Price of the deluxe item
Expected daily sales = Expected sales of regular items + Expected sales of deluxe items
Expected sales of regular items = 177 * 0.29 * 0.09 * $5.08 ≈ $85.74
Expected sales of deluxe items = 177 * 0.29 * 0.91 * $23.34 ≈ $1110.54
Expected daily sales = $85.74 + $1110.54 ≈ $1196.28
Therefore, the expected daily sales for your online store are approximately $1196.28.
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find four consecutive even integers whose sum is -84
Answers
Answer:
18, 20, 22, 24
Step-by-step explanation:
Suppose the integers are
n, n+2, n+4 and n+6
Then
84=n+(n+2)+(n+4)+(n+6)=4n+12
Subtract 12 from both ends to get 72=4n
Divide both ends by 4 to get n=18
So the integers are: 18, 20, 22, 24
Refer to the Johnson Filtration problem introduced in this section. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary, the managers obtained a list showing which repairperson performed the service. The revised data follow.
Repair Time in Hours Months Since Last Service Type of Repair Repairperson
2.9 2 Electrical Dave Newton
3 6 Mechanical Dave Newton
4.8 8 Electrical Bob Jones
1.8 3 Mechanical Dave Newton
2.9 2 Electrical Dave Newton
4.9 7 Electrical Bob Jones
4.2 9 Mechanical Bob Jones
4.8 8 Mechanical Bob Jones
4.4 4 Electrical Bob Jones
4.5 6 Electrical Dave Newton
a) Ignore for now the months since the last maintenance service (x1) and the repairperson who performed the service. Develop the estimated simple linear regression equation to predict the repair time (y) given the type of repair (x2). Recall that x2 = 0 if the type of repair is mechanical and 1 if the type of repair is electrical.
b) Does the equation that you developed in part (a) provide a good fit for the observed data? Explain.
c) Ignore for now the months since the last maintenance service and the type of repair associated with the machine. Develop the estimated simple linear regression equation to predict the repair time given the repairperson who performed the service. Let x3 = 0 if Bob Jones performed the service and x3 = 1 if Dave Newton performed the service.
d) Does the equation that you developed in part (c) provide a good fit for the observed data? Explain.
e) Develop the estimated regression equation to predict the repair time given the number of months since the last maintenance service, the type of repair, and the repairperson who performed the service.
f) At the .05 level of significance, test whether the estimated regression equation developed in part (e) represents a significant relationship between the independent variables and the dependent variable.
g) Is the addition of the independent variable x3, the repairperson who performed the service, statistically significant? Use α = .05. What explanation can you give for the results observed?
Answers
a. We can use the following equation y = b₀ + b₁ * x₂
b. The p-value indicates the significance of the relationship.
c. We can use the following equation y = b₀ + b₁ * x₃
d. Similar to part (b), we need to analyze the statistical measures such as R-squared and p-value to determine if the equation developed in part (c) provides a good fit for the observed data.
e. We can use the following equation y = b₀ + b₁ * x₁ + b₂ * x₂ + b₃ * x₃
f. A p-value below the significance level (0.05) would indicate a significant relationship.
g. The results and interpretation of this test can provide insights into the contribution of the repairperson to the overall model.
What is linear regression?The correlation coefficient illustrates how closely two variables are related to one another. This coefficient's range is from -1 to +1. This coefficient demonstrates the degree to which the observed data for two variables are significantly associated.
a) To develop the estimated simple linear regression equation to predict the repair time (y) given the type of repair (x₂), we can use the following equation:
y = b₀ + b₁ * x₂
where y represents the repair time and x₂ is the type of repair (0 for mechanical, 1 for electrical).
b) To determine if the equation developed in part (a) provides a good fit for the observed data, we need to analyze the statistical measures such as R-squared and p-value. R-squared measures the proportion of variance in the dependent variable (repair time) explained by the independent variable (type of repair). The p-value indicates the significance of the relationship.
c) To develop the estimated simple linear regression equation to predict the repair time given the repairperson who performed the service (x₃), we can use the following equation:
y = b₀ + b₁ * x₃
where y represents the repair time and x₃ is the repairperson (0 for Bob Jones, 1 for Dave Newton).
d) Similar to part (b), we need to analyze the statistical measures such as R-squared and p-value to determine if the equation developed in part (c) provides a good fit for the observed data.
e) To develop the estimated regression equation to predict the repair time given the number of months since the last maintenance service (x₁), the type of repair (x₂), and the repairperson (x₃), we can use the following equation:
y = b₀ + b₁ * x₁ + b₂ * x₂ + b₃ * x₃
where y represents the repair time, x₁ is the number of months since the last maintenance service, x₂ is the type of repair, and x₃ is the repairperson.
f) To test whether the estimated regression equation developed in part (e) represents a significant relationship between the independent variables and the dependent variable, we can perform a hypothesis test using the F-test or t-test and examine the p-value associated with the test. A p-value below the significance level (0.05) would indicate a significant relationship.
g) To determine if the addition of the independent variable x₃ (repairperson) is statistically significant, we can perform a hypothesis test specifically for the coefficient associated with x₃. The p-value associated with this coefficient will indicate its significance. A p-value below the significance level (0.05) would suggest that the repairperson variable has a statistically significant effect on the repair time. The results and interpretation of this test can provide insights into the contribution of the repairperson to the overall model.
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Please help! Find the value of x in the diagram below, and show work.
Answers
The value of x is 93.
What is the exterior angles property of a quadrilateral?
The total of a quadrilateral's outside angles is 360°. Since all convex polygons share this property, their total exterior angles will always add up to 360 degrees.
In the given figure,
The sum of all outside angles=360°
x-11+x+10+31+2x-42=360
4x-12=360
4x=360+12=372
x=372/4 =93
So, the value of x is 93.
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the population in a particular country is growing at the rate of 1.6% per year. If 5,092,000 people lived there in 1999, how many will there be in the year 2003? Use f(x)=y 0^e^0.016t and round to the nearest ten-thousand.
Answers
The population in 2003 is 5,830,000.
The population in a particular country is growing at the rate of 1.6% per year. To calculate the population for 2003, we can use the formula f(x)=y\(0^e^0.016t\) .
Where y0 is the population in 1999 and t is the time in years.
Plugging in the numbers we have y0 = 5092000 and t = 4 for the year 2003, the formula looks like this: f(x)=5092000e0\(^{016(4)\).
Solving this equation, we get f(x)=5837280, which is the population in 2003. Rounding this number to the nearest ten-thousand, the population in 2003 is 5,830,000.
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I need help with ANGLES!!!!!!!!!
Answers
Answer:
joe mama tee hee
Step-by-step explanation:
Answer:
Look DB
Step-by-step explanation:
Since m1+m2=180 and m1=76, then m2=104
m2=m4, so m4 is also 104
m3=m1, so it is 76
Hope I helped!
A local appliance store advertised a “10% off sale” on ovens. Mrs. Jones found an oven she liked that cost $560 before the sale. What is the sale price of the oven?
Answers
Answer:
504 dollares 56 dollars off
Step-by-step explanation:
Answer:
$504
Step-by-step explanation:
560 ÷ 10(10%) = 56
560 - 56 = 504
Calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall.
Answer:
Logic - BMI formula
703*(lbs/inches^2)
703(118/64^2)=703(118/4096)
703*0.0288=20.2464
Answers
The BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.
BMI stands for Body Mass Index.
It's a measure of body fat based on height and weight that applies to both adult men and women.
BMI is an easy-to-perform screening tool for body fat levels that can help identify individuals who have health risks linked with excess body fatness.
It's important to keep in mind that the BMI measurement should not be used as a diagnostic tool for health conditions and is only one component in an overall evaluation of a person's health status.
Using the formula below, we can calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall: BMI = (weight in pounds / (height in inches x height in inches)) x 703
First, we need to convert the height into inches:5 feet 4 inches = 64 inches
Next, we plug the values into the formula and solve for the BMI:
BMI = (118 / (64 x 64)) x 703BMI = (118 / 4,096) x 703BMI = 0.0288 x 703BMI = 20.2464
Therefore, the BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.
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find the limit if it exists. if it does not exist, explain why. lim (x;y)→(0;0) y^2 sin^2 (x) x^4 + y4
Answers
An auto mechanic converts a metric part to 0.473 in. The part comes only in fractional sized given to the nearest 64th of an inch. What would be the closest size?
Answers
Answer:
30/64 inches.
Explanation:
The size of the converted metric part = 0.473 in.
Now, we know that:
\(\frac{1}{64}=0.015625\)Therefore:
\(\frac{0.473}{0.015625}=30.272\approx30\)Thus, we have that:
\(0.473\approx\frac{30}{64}\text{ inch}\)To the nearest 64th of an inch, the closest size will be 30/64 inches.
A company determines the mean and standard deviation of the employees' salaries in one year. What is the best description of the standard deviation?
Approximately the median distance between the individual salaries of employees and the mean of every employee's salary.
The amount of money separating the highest salary from the lowest salary when considering the middle 50% of the distribution.
The amount of money separating the highest salary from the lowest salary when considering all employees.
The distance between the salary of an employee and the mean salary of all the employees.
Approximately the mean distance between the individual salaries of employees and the mean of all employees' salaries.
Answers
The best description of the standard deviation is "Approximately the mean distance between the individual salaries of employees and the mean of all employees' salaries."
Standard deviation, denoted by σ, is defined as the measure which indicates the average distance of the observations from the mean of the data set. It tells how spread out numbers are. It is equal to the square root of the variance. Variance is the average of the squared differences from the mean.
For the given problem, the standard deviation can be describe as the average(mean) distance of the individual salaries of employees from the mean of all employees' salaries.
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the number of times a variable appears in a data set is called _____
Answers
Answer:
The number of times a variable appears in a date set is called a constant.
Which of the following is a power function? Select all correct answers.
a. f(x)=4.15x
b. f(x)=3.10x
c. f(x)=17 ⁵√x
d. f(x)=12 ¹⁰√x
e. f(x)= 8.2x
Answers
The correct answers are a) f(x)=4.15x, b) f(x)=3.10x, and e) f(x)= 8.2x, all of which are power functions.
In algebra, a power function is any function of the form y = axⁿ, where a and n are constants.
This function has a polynomial degree of n and is frequently used to model phenomena in science and engineering. Therefore, any of the following functions with variable x raised to a constant power can be considered a power function:
`y = x^2, y = x^3, y = x^4, y = x^0.5, etc.`
In the given options, f(x)=4.15x = power function, where a = 4.15 and n = 1;
therefore, this is a linear function.
b) f(x)=3.10x = power function, where a = 3.10 and n = 1;
therefore, this is a linear function.
c) f(x)=17 ⁵√x = not a power function, it is not in the form of y = axⁿ; rather it is a root function.
d) f(x)=12 ¹⁰√x = not a power function, it is not in the form of y = axⁿ; rather it is a root function.
e) f(x)= 8.2x = power function, where a = 8.2 and n = 1; therefore, this is a linear function.
Therefore, the correct answers are a) f(x)=4.15x, b) f(x)=3.10x, and e) f(x)= 8.2x, all of which are power functions.
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Solving One Step Equations. SHOW YOUR WORK
x - 7 = 13 solve to find x
Answers
Answer:I'm guessing 2
Step-by-step explanation:
Answer:
X=20
Step-by-step explanation:
x-7=13
x=13+7
X=20
The sum of the digits of a two-digit number is seventeen. The number with the digits reversed is thirty more than 5 times the tens' digit of the original number. What is the original number?
Answers
Therefore, the original number is 10x + y = 10(10) + 7 = 107.
Given that the sum of the digits is seventeen, we have the equation:
x + y = 17 (equation 1)
The number with the digits reversed is thirty more than 5 times the tens' digit of the original number. The number with the digits reversed would be 10y + x.
According to the given information, we have the equation:
10y + x = 5x + 30 (equation 2)
To solve the system of equations, we can substitute equation 1 into equation 2:
10(17 - x) + x = 5x + 30
Expanding and simplifying:
170 - 10x + x = 5x + 30
170 - 30 = 5x + 10x - x
140 = 14x
x = 10
Substituting the value of x back into equation 1:
10 + y = 17
y = 7
Therefore, the original number is 10x + y = 10(10) + 7 = 107.
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Rai compares two cable plans from different companies. Which equation gives the correct value of m, the number of months for which Plans A and B cost the same?
Answers
Answer:
D. 75m = 50(12)+125(m-12)
Step-by-step explanation:
m = months.
Equation for which Plans A and B cost the same.
In Plan A:
No initial fees.
$75 per month
1 month = $ 75
then;
for m month =$75 m
Total cost for plan A = 75m
In Plan B:
$50 per month for first 12 month.
1 month = $50
12 months = 50(12)
Similarly,
$125 per month for each additional month after that.
additional month= (m-12)
Plan B additional month
= 125(m-12)
Total cost for plan B = 50(12)+ 125(m-12)
Since, Plans A and B cost the same.
75m = 50(12)+125(m-12)
1. g(x) = f(x) - 7
how do u solve these?
Answers
Answer:
g' (×)=f
Step-by-step explanation:
g (×)=f×-7
g' (×)= d÷d× (f×-7)
d÷d×(f+g)=d÷d×(f)+d÷d=(g)
g' (×)=d÷d×(f×)-d÷d×(7)
g'(×)=f-d÷d×(7)
g'(×)=f-0
g'(×)=f
when comparing more than two condition means, why should an analysis of variance be used instead of multiple t tests? a. using multiple t tests increases the risk of a type i error. b. using multiple t tests increases the risk of a type ii error. c. the analysis of variance is more likely to detect statistical significance. d. there is no advantage to using an analysis of variance instead of multiple t tests. a. there are no differences between any of the population means. b. at least one of the three population means is different from another population mean. c. all three of the population means are different from each other. d. one population mean is different from one of the other population means, but not the other population mean. a. r2
Answers
When comparing means of three or more conditions, an analysis of variance (ANOVA) should be used instead of multiple t-tests. This is because using multiple t-tests increases the risk of a type I error, where a significant difference is found when there is none. ANOVA controls for this by using a single test to determine if there is a significant difference between the means. Additionally, using multiple t-tests increases the risk of a type II error, where a significant difference is not found when there is one.
ANOVA is also more likely to detect statistical significance between the means because it takes into account the variability within each condition as well as the variability between conditions. This increases the power of the test and reduces the chances of missing a significant difference between the means.
When using ANOVA, the results can indicate that there are no differences between any of the population means (option a), that at least one of the three population means is different from another population mean (option b), that all three of the population means are different from each other (option c), or that one population mean is different from one of the other population means, but not the other population mean (option d).
Finally, ANOVA provides a measure of effect size, typically reported as r2, which indicates the proportion of variability in the data that can be attributed to the differences between the conditions. This can be useful in determining the practical significance of the results.
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A limited edition Pringles can (cylinder shape) has a radius of 5 inches and a height of 15 inches. What is the volume of the can?
PLS HELP I AM GIVING ALL OVER MY POINTS EVERYTHING I HAVE
Answers
Answer:
V ≈ 1178.1
Step-by-step explanation:
btw the equation is
V=πr²h