The decision to reject or not reject the null hypothesis depends on the chosen significance level. The smaller the significance level, the stronger the evidence needed to reject the null hypothesis.
In hypothesis testing, the significance level is the probability of rejecting the null hypothesis when it is true. It is usually set at 0.05 or 0.01. The P-value is the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.
For a P-value of 0.081, we can say that there is some evidence against the null hypothesis but not strong enough to reject it.
If the significance level is set at 0.05, we should not reject the null hypothesis because the P-value is greater than the significance level.
However, if the significance level is set at 0.10, we may choose to reject the null hypothesis because the P-value is equal to or less than the significance level.
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For part a, since the alpha level is 0.10, the null hypothesis should be rejected if the P-value is less than or equal to 0.10. Since the P-value is 0.081, which is greater than 0.10, we do not reject the null hypothesis. Therefore, the answer is B.
For part b, since the alpha level is 0.05, the null hypothesis should be rejected if the P-value is less than or equal to 0.05. Since the P-value is 0.081, which is greater than 0.05, we do not reject the null hypothesis. Therefore, the answer is C. In hypothesis testing, the null hypothesis is a statement that assumes there is no significant difference between the sample data and the population data. The hypothesis test is used to determine the validity of the null hypothesis by calculating the probability of observing the sample data if the null hypothesis is true. The significance level is the threshold value used to determine whether to reject the null hypothesis. It is usually set to 0.05 or 0.01. The P-value is the probability of obtaining a test statistic as extreme as or more extreme than the one observed, assuming the null hypothesis is true. If the P-value is less than or equal to the significance level, we reject the null hypothesis. Otherwise, we do not reject it.
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miggy ask to solved the given quadratic equation x²+8x-20=0 using the quadratic formula,Help miggy to determine the following
Answer:
x = -10 or 2
Step-by-step explanation:
Kelsey knit a total of 6 centimeters of scarf over 2 nights. After 4 nights of knitting, how many centimeters of scarf will Kelsey have knit in total? Assume the relationship is directly proportional.
Answer:
\(12\) cm
Step-by-step explanation:
If Kelsey knit a total of \(6\) cm of scarf over \(2\) nights, then we know that she can knit \(\frac{6}{2}=3\) cm each night. Therefore, after \(4\) nights of knitting, Kelsey would have knit a total of \(3*4=12\) cm of scarf in total. Hope this helps!
Simplify: 1/6x + 42 + 2/5x - 8/3 -19
A: 97/30x + 23
B: 21/10x - 23
C: -21/10x + 23
D: 97/30x - 23
Answer:
A: 97/30x + 23
Find the value of x and y.
Answer:
x= 73
y= 13
Step-by-step explanation:
The sum of the angles opposite the exterior angle = the exterior angle so
x= 141-68
x= 73
The angle sum of a triangle= 180.
180-68-73= 39
since there are 3 "y"s we need to divide 39 by 3
39/3= 13
how many 1/3 minutes are there in 5 minutes
Answer: 15
Step-by-step explanation:
3 1/3ds in 1 minute, multiply 3 by 5
Answer:
15
Step-by-step explanation:
15 thirds contain 5 integers:
\(\frac{5}{\frac{1}{3} } =\frac{(5)(3)}{1} =\frac{15}{1} =15\)
Hope this helps
Compute the flux of F⃗ =3(x+z)i⃗ +2j⃗ +3zk⃗ through the surface S given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0, oriented toward the xz-plane
It seems there is an error in the given vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ as it does not have a component along the y-axis. Please double-check the vector field or provide the correct vector field to proceed with the calculation.
To compute the flux of the vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ through the surface S given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0, oriented toward the xz-plane, we can use the surface integral.
The surface integral of a vector field F⃗ over a surface S is given by the formula:
∬S F⃗ · dS = ∬S F⃗ · (n⃗ dS)
where F⃗ is the vector field, dS is the differential area vector, and n⃗ is the unit normal vector to the surface.
In this case, the surface S is given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0. We can parameterize this surface as:
r(x, z) = xi⃗ + yj⃗ + zk⃗ = xi⃗ + (x^2+z^2)j⃗ + zk⃗
To find the normal vector n⃗ to the surface, we can take the cross product of the partial derivatives of r(x, z) with respect to x and z:
n⃗ = ∂r/∂x × ∂r/∂z
= (1i⃗ + 2xj⃗) × (0i⃗ + 2zj⃗)
= -2xz i⃗ + 2zj⃗ + 2xk⃗
Now, we can calculate the flux:
∬S F⃗ · (n⃗ dS) = ∬S (3(x+z)i⃗ + 2j⃗ + 3zk⃗) · (-2xz i⃗ + 2zj⃗ + 2xk⃗) dS
= ∬S (-6x^2z - 4xz + 6xz^2 + 6xz) dS
= ∬S (-6x^2z + 2xz + 6xz^2) dS
To evaluate this integral, we need to determine the limits of integration for x, y, and z.
Since the surface is defined by 0≤y≤16, x≥0, z≥0, we have:
0 ≤ y = x^2 + z^2 ≤ 16
Simplifying the inequality, we get:
0 ≤ x^2 + z^2 ≤ 16
From this, we can see that x and z both range from 0 to 4.
Now, we can evaluate the flux:
∬S (-6x^2z + 2xz + 6xz^2) dS = ∫∫ (-6x^2z + 2xz + 6xz^2) dA
where dA is the differential area.
Integrating over the limits 0 ≤ x ≤ 4 and 0 ≤ z ≤ 4, we can calculate the flux.
However, it seems there is an error in the given vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ as it does not have a component along the y-axis. Please double-check the vector field or provide the correct vector field to proceed with the calculation.
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Find the value of f(-6)
Answer:
-8
Step-by-step explanation:
pls help asap! i will give brainliest
Answer:
G
Step-by-step explanation:
I did this assignment yesterday
Answer:
x = 91
y = 98
Your answer is F.
Step-by-step explanation:
Since a straight angle is 180° you have to subtract 89 from 180 and 82 from 180.
180 - 89 = 91
180 - 82 = 98
Hope this helps, and have a wonderful day! :)
The sculpture consists of four identical prisms. Jane says the surface area of the sculpture is 4 times the surface area of one prism. Which statement about jane's method is true?
Options:
A.) Jane should multiply volumes, not areas.
B.) Jane should also subtract the areas of six hidden surfaces.
C.) Jane should also add the areas of six hidden surfaces.
D.) Jane is correct.
Answer:
B.) Jane should also subtract the areas of six hidden surfaces.
Step-by-step explanation:
When three-dimensional solids are joined together to form a solid, some surfaces will be visible while others won't.
When calculating the surface areas of such shapes, we only consider the visible parts (i.e. the areas of the hidden parts will be subtracted from the total areas of the individual shapes).
Since the sculpture is not attached to this question, we can assume that there are 6 hidden surfaces (as suggested by the options). The areas of these 6 hidden surfaces must be subtracted to get the actual surface area.
Answer:
Jane should also subtract the areas of six hidden surfaces.
Step-by-step explanation:
I just did it on Imagine Math
Sam's uncle is 6 years older than 4 times his age. If his uncle is 30, how old is Sam
is 0.9 greater,least than, or equal to 95%
Answer:
Less
Step-by-step explanation:
Answer:
if 1 represents 100% then it would be less than
Step-by-step explanation:
that would make the .90 90% and thus less than 95%
Which two numbers on the number line have an absolute value of 2.75?
Select the location of both numbers on the number line.
Two numbers on the number line have an absolute value of 2.75 is -2.75 and 2.75
number line - A line on which numbers are marked at intervals and used to illustrate simple numerical operations.
center of the number line is called origin i.e. 0 (zero) positive numbers are on the right side of zero. negative numbers are on the left side of the zero.absolute value - absolute value of real number is its distance from the zero.
The absolute value of 2.75 is 2.75 and the absolute value of -2.75 is 2.75
Two numbers on the number line have an absolute value of 2.75 is -2.75 and 2.75
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how do you find y=-4x+3 on a table
please help ! matching for 21-32 and please explain ! thanks :) preparing for exam
Answer:
I'm very sorry, but there is no questions 21-23, if you give me the picture, I'll do it.
Step-by-step explanation:
the branch of statistics that involves organizing, displaying, and describing data.
Answer:
descriptive statistics
Step-by-step explanation:
show that among any group of five (not necessarily consecutive) integers, there are two with the same remainder when divided by 4. (Hinpigeonhole principle)
Two of them have the same remaining. The proof using the pigeonhole principle is now complete.
When an integer is divided by 4, there are four potential remainders: 0, 1, 2, or 3. Take any set of five numbers as an example.
If at least three of them have the same remainder when divided by 4, then we are done, since two of them will have the same remainder. This is because if three integers have the same remainder, then we can subtract that remainder from all of them, and the resulting three integers will all be divisible by 4, which means that two of them will have the same remainder when divided by 4.
So suppose that at most two of the integers have the same remainder when divided by 4. Then there are at most two integers with remainder 0, at most two integers with remainder 1, at most two integers with remainder 2, and at most two integers with remainder 3. This means that there are at most 8 integers in total, which is a contradiction since we started with 5 integers. Therefore, there must be at least three integers with the same remainder when divided by 4, and hence there are two with the same remainder. This completes the proof by the pigeonhole principle.
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3(2x+3)-x = x-23 solve for x and if you show me good step by step explanation ill give you brainliest
Answer:
x= -8
Step-by-step explanation:
First distribute: 3(2x+3)-x is equal to 6x+9-x, or 5x+9
Rewrite: 5x+9=x-23
Add 23 to both sides to get rid of it on one: 5x+32=x
Subtract 5x from both sides to get rid of it on one: 32= -4x
Divide by -4: -8=x
Answer:
x = -8
Step-by-step explanation:
\(3(2x + 3) - x = x - 23\)
➡️ \(6x + 9 - x = x - 23\)
➡️ \(5x + 9 = x - 23\)
➡️ \(5x - x = - 23 - 9\)
➡️ \(4x = - 32\)
➡️ \(x = - 8\) ✅
simplify the question
Answer:
=−4√2
I got this when simplified.
6,8,10,11. 12, 14, 18, 18,30
Create a box plot to display the data.
Answer:
dunny but 4950
Step-by-step explanation:
4960-
Pls give simple working out
Answer:
x = 33
Step-by-step explanation:
∡ CBE = ∡DBA = 57°
The sum of the interior angles of a triangle results 180°
∡BDA = it´s a right angle = 90°
Then:
57° + 90° + x = 180°
147° + x = 180°
x = 180° - 147°
x = 33°
If the sum of the number and five is tripled, the result is one less than twice the number. Find the number.
Answer:
see below
Step-by-step explanation:
5 + y x 3 = 2y - 1
What is an example of a left skewed distribution?
Age at natural death is an example of a real-world variable with a left-skewed distribution (heart disease, cancer, etc.). Most of these deaths occur in older people and a minority in younger people.
What are some examples of right-skewed distributions?Salary is an example of a real-world variable with a right-skewed distribution. If there are a few outliers (CEOs, professional athletes, etc.), most individuals have incomes in the low/mid range, with a wide range of higher numbers (a long "tail"). A long left tail indicates that the distribution is skewed to the left. A negatively skewed distribution is similar to a left skewed distribution. This is because the number line has a long tail in the negative direction. The average is also to the left of the peak. The left side of a left-skewed distribution is longer than the right side. That is, a left-skewed distribution has a long tail on the left.
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a pool with dimensions of 10 ft radius and 4 ft height fill with water at a rate of 20 gallons a minutes. about how many hours will it take to fill the pool if 1 cubic foot of water is about 7.5 gallons?
It will take approximately 7.85 hours to fill the pool.
To determine the time needed to fill the pool, first calculate the volume of the pool, then convert the volume to gallons, and finally, divide by the fill rate.
The pool is a cylinder with a radius of 10 ft and a height of 4 ft. The volume of a cylinder is given by the formula V = πr²h.
V = π(10 ft)²(4 ft) = 400π cubic feet ≈ 1256.64 cubic feet
Next, convert the volume to gallons using the given conversion factor:
1256.64 cubic feet * 7.5 gallons/cubic foot ≈ 9424.8 gallons
Now, divide the total gallons by the fill rate of 20 gallons/minute to find the time in minutes:
9424.8 gallons ÷ 20 gallons/minute ≈ 471.24 minutes
Finally, convert the time to hours:
471.24 minutes ÷ 60 minutes/hour ≈ 7.85 hours
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Alicia records the total number of points scored in two games by 10 players on her basketball team.
28, 13, 4, 8, 15, 10, 22, 7, 11, 15
which box plot represents the data
The first option in the second row, Option(C) represents the data.
In order to solve the problem,
First, we need to arrange the numbers in ascending order.
4, 7, 8, 10, 11, 13, 15, 15, 22, 28
Median = 11+13/2
= 12
From the first range ( 4,7,8,10,11 ) , we can find Q1 also known as first quartile where Q1 = 8 ( middle-most number).
Similarly, from the second range ( 13,15,15,22,28 ) , we can find Q2 also known as third quartile where Q3 = 15 (middle-most number ).
Now, for the box plot,
We need to draw a number line from 0 to 32.
Next, we need to draw a box from Q1 to Q3 with a vertical line through the median.
Next, we put dots above 4 and 28 since our numbers start from 4 and end with 28.
Finally we join the dots and the box plot with a straight line.
Hence, option C is the correct choice.
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Solve the following system of equations graphically on the set of axes y= x -5 y=-/x -8
Answer:
(-3/2, -13/2)
Step-by-step explanation:
To solve the system of equations graphically, we need to plot the two equations on the same set of axes and find the point of intersection.
To plot the first equation y = x - 5, we can start by finding the y-intercept, which is -5. Then, we can use the slope of 1 (since the coefficient of x is 1) to find other points on the line. For example, if we move one unit to the right (in the positive x direction), we will move one unit up (in the positive y direction) and get the point (1, -4). Similarly, if we move two units to the left (in the negative x direction), we will move two units down (in the negative y direction) and get the point (-2, -7). We can plot these points and connect them with a straight line to get the graph of the first equation.
To plot the second equation y = -x - 8, we can follow a similar process. The y-intercept is -8, and the slope is -1 (since the coefficient of x is -1). If we move one unit to the right, we will move one unit down and get the point (1, -9). If we move two units to the left, we will move two units up and get the point (-2, -6). We can plot these points and connect them with a straight line to get the graph of the second equation.
The point of intersection of these two lines is the solution to the system of equations. We can estimate the coordinates of this point by looking at the graph, or we can use algebraic methods to find the exact solution. One way to do this is to set the two equations equal to each other and solve for x:
x - 5 = -x - 8 2x = -3 x = -3/2
Then, we can plug this value of x into either equation to find the corresponding value of y:
y = (-3/2) - 5 y = -13/2
So the solution to the system of equations is (-3/2, -13/2).
7 Given S - sum of the digits in the number M, find
the values of S when
(a) M461
(b) M17 (c) M
Answer:
the answer is 45%.
Step-by-step explanation:
if you add 5% divided by 3 = 15%.
So if you add all of those plus the 30% you will be getting 45%.
Suppose A is a symmetric n x n matrix. Show that all of the following statements are true. (a). (2 pts) There exists a diagonal matrix D and an orthogonal matrix Q with A = QDQT; (b). (2 pts) There exists n eigenvectors of A that form an orthonormal set, and the eigenvalues of A are real numbers; (c). (2 pts) A is positive definite if and only if all the eigenvalues of A are positive
Explanation:-
Let A be a symmetric n × n matrix. The following statements are true:
(a) There exists a diagonal matrix D and an orthogonal matrix Q with A = QDQT.
(b) There exists n eigenvectors of A that form an orthonormal set, and the eigenvalues of A are real numbers.
(c) A is positive definite if and only if all the eigenvalues of A are positive.Proof:Let λ1, λ2,..., λn be the eigenvalues of A, and let {v1, v2,..., vn} be a set of orthonormal eigenvectors of A. Because A is symmetric, its eigenvectors are orthonormal. Then: (i) AQ = [Av1, Av2,..., Avn] = [λ1v1, λ2v2,..., λnvn] = QD, where D is the diagonal matrix [λ1, λ2,..., λn]
.(ii) QTQ = I; this implies that QQT = I. Now we have A = QDQT. Because QQT = I, we see that Q-1 = QT and that Q-1QT = I
.(iii) Now let x be any nonzero vector. Let y = QTx. Then yTy = xTQ-1QTQ-1Tx = xTx = ||x||2. Therefore, y is nonzero, and A = QDQT is positive definite if and only if λ1, λ2,..., λn are all positive.
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four less than three times a number is 20
Answer:
3x-4
Step-by-step explanation:
Have a good day!!
Answer:
3x-4
Step-by-step explanation:
Multiply and simplify if possible. (2sqrt3x -2)(3sqrt3x +5)
show work
The expression is simplified to give 2(9x + 2√3x - 5)
How to determine the valueFirst, we need to know that surds are mathematical forms that can no longer be simplified to smaller forms
From the information given, we have that;
(2√3x - 2)(3√3x + 5)
expand the bracket, we get;
6√9x² + 5(2√3x) - 6√3x - 10
Find the square root factor
6(3x) + 10√3x - 6√3x - 10
collect the like terms, we have;
18x + 4√3x - 10
Factorize the expression, we have;
2(9x + 2√3x - 5)
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help asap + 27 points
Answer:
J'= (-4,-1) K'= (-2,-4) L'= (4,-3)
P'= (-3,0) Q'= (1,3) R'= (0, -1)
Step-by-step explanation: