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▹ Answer
3,298,076 is written as three million two hundred ninety eight thousand seventy six.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
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Answer:
Three million, two hundred and ninety-eight thousand and seventy-six.
ANSWERR THISSS ASAPPPPP
(21points)
Answer:
the answer is C......
Step-by-step explanation:
!!!!!!!!!!!
HELP - 100 POINTS AND BRAINLIEST!! Find the area and volume - a square has a side length of 6.25 Please show your work! Thank you!
Step-by-step explanation:
Area: bh
The shape is a square in which the side lengths are the same, so we multiply the number squared.
A = 6.25(6.25)
A = 39.06
Volume: lwh
6.25^3 = V
V = 244.14
Hope this helps:)
Step-by-step explanation:
Area: bh
The shape is a square in which the side lengths are the same, so we multiply the number squared.
A = 6.25(6.25)
A = 39.06
Volume: lwh
6.25^3 = V
V = 244.14
I hope I contributed
Polygons in the coordinate
In order to know if a triangle is a right triangle on a coordinate plane, you can find the lengths of all three sides of the triangle using the distance formula and apply the Pythagorean theorem.
How to know if it's a triangleFind the lengths of the three sides of the triangle using the distance formula.
Once you have the lengths of the sides, check if any of the three sides satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In other words, if a² + b² = c², where c is the longest side, then the triangle is a right triangle.
If one of the sides satisfies the Pythagorean theorem, then the triangle is a right triangle.
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The perimeter of the rectangle below is 94 units. Find the length of side WX.
Write your answer without variables.
Answer:
24units
Step-by-step explanation:
2(4y + 3) + 2(5y - 1) = 94
18y + 4 = 94
y = 5
WX = 5y - 1 = 5(5) - 1 = 24units
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First we need to find the value of y .
\(Perimeter = 2 \times ( \: (4y + 3) + (5y - 1) \: ) \\ \)
\(Perimeter = 2 \times (9y + 2)\)
\(Perimeter = 18y + 4\)
Question told us that perimeter is 94 ,
Thus :
\(94 = 18y + 4\)
\(18y + 4 = 94\)
Subtract sides 4
\(18y + 4 - 4 = 94 - 4\)
\(18y = 90\)
Divide sides by 18
\( \frac{18y}{18} = \frac{90}{18} \\ \)
\(y = 5\)
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The face sides in the rectangular are same.
Thus :
\(VY = WX\)
So ;
\( WX = 5y - 1\)
\(WX = 5(5) - 1\)
\(WX = 25 - 1\)
\(WX = 24\)
Done...
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Show that 7x + 1 is equivalence to 2(2x - 1) + 3(x + 1)
Answer with Step-by-step explanation:
2 ( 2x -1 ) + 3 ( x + 1 )
First, let us find the value of the above expression.
2 ( 2x -1 ) + 3 ( x + 1 )
4x - 2 + 3x + 3
Combine like terms
4x + 3x - 2 + 3
7x + 1
Therefore, it is clear that the given expression is equal to 7x + 1.
∴ 7x + 1 = 2 ( 2x -1 ) + 3 ( x + 1 )
given tannen's perspective on gender differences in communication, what would you expect to find regarding salary negotiation and gender
Given tannen's perspective on gender differences in communication, Men far more than women negotiate for higher starting salaries because salary is a sign of status. So, correct option is C.
Based on Tannen's perspective on gender differences in communication, it is likely that you would find that men negotiate for higher starting salaries far more than women because salary is a sign of status.
Tannen argues that men are socialized to use language as a way to establish and maintain their status in society, and negotiating for a higher salary is one way for men to assert their status.
Women, on the other hand, are socialized to use language as a way to build and maintain relationships, and negotiating for a higher salary may be perceived as aggressive or confrontational, which goes against societal expectations for women's communication style.
Therefore, option (c) is the most likely answer.
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Complete question is:
Given tannen's perspective on gender differences in communication, what would you expect to find regarding salary negotiation and gender
answer choices:
a. Women negotiate for higher starting salaries far more than men because they wish to prove their worth
b. Men and women negotiate for higher starting salaries about equally
c. Men far more than women negotiate for higher starting salaries because salary is a sign of status
d. None of the above is true
Help please! Greatly appreciated if you do!
Answer:
i think its D because fun isn't 25%. food is 25% and fun is smaller than food
Answer:
B
The blue plus the yellow makes the half mark all the way across the circle. Just for example the red, green, and purple make the other half.
Hope that helps!! Have a good day!! :)
ow many different phone numbers are possible in the area code 503, if the first number cannot start with a 0 or 1? do not use commas in your answer. answer:
Your answer: 8000000 different phone numbers are possible in the area code 503, with the first number not starting with a 0 or 1.
In an area code like 503, phone numbers have the format 503-XXX-XXXX. Since the first number cannot start with a 0 or 1, we have 8 choices (2-9) for the first digit. The remaining six digits can be any number from 0-9, giving us 10 choices for each.
To calculate the total possible combinations, multiply the choices together: 8 (for the first digit) * 10 (for the second digit) * 10 (for the third digit) * 10 (for the fourth digit) * 10 (for the fifth digit) * 10 (for the sixth digit) * 10 (for the seventh digit).
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Can someone solve this for me ill mark brainliest
What integer represents √ 4
Answer:
2 is the answer
Step-by-step explanation:
the square root of 4 is 2... right?
Alexa is researching a cure for the coronavirus. She needs 14 test tubes for 4 experiments. The first experiment requires 2 test tubes, and the remainder of the tubes are used evenly over the rest of the experiments. How many test tubes did she use for the last experiment?
Answer:
She used 4 test tubes for the last experiment
Step-by-step explanation:
Total test tubes needed = 14
Experiment 1 = 2 test tubes
Total test tubes remaining = total - used
= 14 - 2
= 12 test tubes
Remaining experiment = 4 - 1
= 3
Test tubes used for the remaining experiment = test tubes remaining / Experiment remaining
= 12 / 3
= 4 test tubes
How many test tubes did she use for the last experiment?
She used 4 test tubes for the last experiment
What's the surface area of the pyramid?
The Answer is C 226.8 ft
I remember doing this not to long ago
Find two nontrivial functions \( f(x) \) and \( g(x) \) so \( f(g(x))=\frac{1}{(x-9)^{4}} \) \[ \begin{array}{l} f(x)= \\ g(x)= \end{array} \] Question Help: MMessage instructor
Let's assume that f(x) and g(x) are nontrivial functions such that \(f(g(x))=1/(x-9)\)⁴.
We have to find out the values of f(x) and g(x).Here's the solution:Let, \($y=g(x)$\)Thus, \($f(y)=\frac{1}{(y-9)^4}$\) Let's integrate both sides w.r.t y by assuming u=y-9,
$du=dy$ and limits are from\($g(a)$\)to \($g(x)$\).So,\($\int _{ g(a) }^{ g(x) }{ f(y)dy } =\int _{ g(a)-9 }^{ g(x)-9 }{ \frac { 1 }{ u^{ 4 } } du }\) \($$=-\frac { 1 }{ 3u^{ 3 } } $\) [from the formula of the definite integral]\($=-\frac { 1 }{ 3(g(x)-9)^{3} } +\frac { 1 }{ 3(g(a)-9)^{3} }$\)\($f(y)\)=\(-\frac { 1 }{ 3(y-9)^{3} } +\frac { 1 }{ 3(g(a)-9)^{3} }$$g(x)$ lies between $a$ and $b$\),
so the function $g$ is not trivial, since we have chosen the lower bound a<9 and the upper bound b>9.
Hence,\($g(x)=a+{\frac { b-a }{ 1+(x-9)^{12} } }$ and $f(x)=-\frac { 1 }{ 3(x-9)^{3} } +\frac { 1 }{ 3(g(a)-9)^{3} }$\) .
The values of \($a$\) and \($b$\) depend on the specific nontrivial functions you choose. Hence, the solution is complete.
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as part of video game, the point (5,2) is rotated counterclockwise about the origin through an angle of 5 degrees. find the new coordinates of this point
The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).
To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.
Converting the angle of rotation from degrees to radians:
theta = 5 degrees * (pi/180) ≈ 0.08727 radians
Plugging in the values into the rotation formula:
x' = 5 * cos(0.08727) - 2 * sin(0.08727)
y' = 5 * sin(0.08727) + 2 * cos(0.08727)
Evaluating the trigonometric functions and simplifying:
x' ≈ 4.993
y' ≈ 2.048
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define a transformation t:[3->[2by t(x)=ax. find t(u), the image ofuunder the transformation t.
The transformation t is defined as t(x) = ax, where a is a constant.
To find the image of u under the transformation t, we need to substitute u for x in the expression t(x).
The transformation t:[3 ≥ [2 is defined as t(x)=ax, where a is a constant.
This means that for any given value of x in the domain [3,
the transformation t maps it to a corresponding value of ax in the codomain [2.
To find the image of u under the transformation t
t(u) = au.
This means that the image of u under the transformation t is the value of au in the codomain [2.
For example, if u = 4 and a = 2, then t(u) = 2(4) = 8, which is the image of u under the transformation t.
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How would the dx2−y2 orbital in the n=5 shell compare to the dx2−y2 orbital in the n=3 subshell?
a) The contour of the orbital would extend further out along the x and y axes.
b) The value of ℓ would increase by 2.
c) The radial probability function would include two more nodes.
d)The orientation of the orbital would be rotated 45∘ along the xy plane.
e) The mℓ value would be the same.
**Which statements above are correct?
A. The contour of the orbital would extend further out along the x and y axes and the mℓ value would be the same.
The dx2−y2 orbital in the n=5 shell will have a higher principal quantum number (n=5) than the dx2−y2 orbital in the n=3 subshell (n=3). This means that the contour of the orbital in the n=5 shell will extend further along the x and y axes, as the orbital size increases with increasing n.
However, the mℓ value will remain the same, as the angular momentum quantum number (ℓ) remains constant at two and mℓ can only take values between -ℓ and +ℓ.
The value of ℓ will not increase by two, as stated in option B, and the radial probability function will not include two more nodes, as stated in option C. Furthermore, the orientation of the orbital will not be rotated 45∘ along the xy plane, as stated in option D.
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Find the absolute maximum and absolute minimum values of f on the given interval
1) f(t) = 2cost + sin2t , [0,pi/2]
2) f(x) = xe^-x^2/8 , [-1,4]
(1) The values are given below:
Absolute maximum: \(3\sqrt\dfrac{(3)}{2}\)Absolute minimum: 0(2) The values are given below:
Absolute maxima are (2,\(\dfrac{2}{e}\))
Absolute minima are (-1,\(\dfrac{-1}{e^\frac{1}{8}}\)))
Part(1),
The given equation is,
\(f(t) = 2cos(t) + sin(2t) [0, \dfrac{\pi}{2}]\)
The absolute min/max is found by evaluating the function at
1) The endpoints, and
2) local minima/maxima
Let's start with the endpoints.
\(f(0) = 2cos(0) + sin(2\times 0) = 2(1) + 0 = 2\)
\(f(\dfrac{\pi}{2}) = 2cos(\dfrac{\pi}{2}) + sin(2\times \dfrac{\pi}{2})\)
\(f(\dfrac{\pi}{2}) = 2(0) + sin(\pi) = 0 + 0 = 0\)
Now, let's calculate the local minima/maxima. Take the derivative.
f'(t) = 2(-sin(t)) + cos(2t) (2)
f'(t) = -2sin(t) + 2cos(2t)
Make f'(t) = 0,
0 = -2sin(t) + 2cos(2t). Use the double-angle formula.
\(0 = -2sin(t) + 2[cos^2(t) - sin^2(t)]\)
\(0 = -2sin(t) + 2cos^2(t) - 2sin^2(t)\)
\(0 = -2sin(t) + 2[1 - sin^2(t)] - 2sin^2(t)\)
\(0 = -2sin(t) + 2 - 2sin^2(t) - 2sin^2(t)\)
\(0 = -2sin(t) + 2 - 4sin^2(t)\)
\(0 = -sin(t) + 1 - 2sin^2(t)\)
\(2sin^2(t) + sin(t) - 1 = 0\)
\([2sin(t) - 1] [sin(t) + 1] = 0\)
Obtain all solutions within [0, \(\dfrac{\pi}{2}\)].
2sin(t) - 1 = 0
2sin(t) = 1
\(sin(t) = \dfrac{1}{2}\)
\(t = { \dfrac{\pi}{6}, \dfrac{5\pi}{6} }\) but \(\dfrac{5\pi}{6}\) is outside of the interval, so reject it.
sin(t) + 1 = 0
sin(t) = -1
\(t = {\dfrac{3\pi}{2}}\) but reject this because it's outside of our interval.
Therefore, critical numbers are only
\(t = \dfrac{\pi}{6}\)
Plug this value into the function.
\(f(\dfrac{\pi}{6}) = 2cos(\dfrac{\pi}{6}) + sin(2\times\dfrac{\pi}{6})\)
\(f(\dfrac{\pi}{6}) = 2[\sqrt{(\dfrac{3}{2})} + sin(\dfrac{\pi}{3})\)
\(f(\dfrac{\pi}{6}) = \sqrt{(3)} + \sqrt{\dfrac{(3)}{2}\)
\(f(\dfrac{\pi}{6}) = [2\sqrt{(3)} + \sqrt{\dfrac{(3)}{2 }\)
\(f(\dfrac{\pi}{6}) = 3\sqrt\dfrac{(3)}{2}\)
Compare all values; endpoints and local extrema.
f(0) = 2
\(f(\dfrac{\pi}{2}) = 0\)
\(f(\dfrac{\pi}{6}) = 3\sqrt{\dfrac{(3)}{2}} = 2.59\)
The highest value among these values is the absolute maximum. The lowest value among these values is the absolute minimum.
Absolute maximum: \(3\sqrt{\dfrac{(3)}{2}}\)
Absolute minimum: 0
Part(2),
The given expression is,
\(f(x) = x e^{\dfrac{-(x^2)}{8}\)
To find the absolute maximum and minimum you need to find your local maxima and minima of the curve and then also check the endpoints of the interval.
Differentiating gives:
\(f'(x) = e^\dfrac{-(x^2)}{8}} -\dfrac{1}{4}(x^2 e^{\dfrac{-(x^2)}{8}\)
Which simplifies to:
\(=\dfrac{-1}{4} e^{\dfrac{(-(x^2)}{{8}}} [ x^2 - 4]\)
So the function has local maxima/minima at x = 2 and -2. -2 isn't on the interval so ignore that. Sub 2 in and you get the point (2,2/e) as local maxima.
Lastly find the end points.
\(f(-1) = \dfrac{-1}{e^(\dfrac{1}{8}) }= -0.882497\)
So absolute maxima are (2,\(\dfrac{2}{e}\))
And absolute minima is (-1,\(\dfrac{-1}{e^{(\dfrac{1}{8}})}\))
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joint and/or inverse variation. show you solution.
The force is 80,000 Dynes.
What is joint variation?We know that when we talk about the joint variation then we have a lot of variables that are being altered at the same time and this is what we are going to work on in the questions that we have here.
We are told that;
C α mr/t^2
Then;
C = kmr/t^2
k = Ct^2/mr
k = 6000 * 2^2/6 * 10
k = 400
Then, to find C;
C = 400 * 18 * 100/3^2
C = 80,000 Dynes
\
Hence, we can see from the calculation that the centrifugal force that is required is 80,000 Dynes.
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Evaluate Cₙ,ₓpˣqⁿ⁻ˣ for the values of n, x, and p given below.
n = 4, x = 1. p = 1/2
Cₙ,ₓpˣqⁿ⁻ˣ = ___ (Round to three decimal places as needed)
Using the combination formula, C₄,₁ = 4, and substituting p = 1/2, q = 1/2, and C₄,₁ into Cₙ,ₓpˣqⁿ⁻ˣ, we find that Cₙ,ₓpˣqⁿ⁻ˣ = 1/4.
To evaluate Cₙ,ₓpˣqⁿ⁻ˣ, we can use the combination formula and substitute the given values. The combination formula is given by:
Cₙ,ₓ = n! / (x!(n - x)!)
where n! represents the factorial of n.
Given:
n = 4
x = 1
p = 1/2
First, let's calculate q, which is the complement of p:
q = 1 - p
= 1 - 1/2
= 1/2
Now, let's substitute the values into the combination formula:
C₄,₁ = 4! / (1!(4 - 1)!)
= 4! / (1! * 3!)
Calculating the factorials:
4! = 4 * 3 * 2 * 1 = 24
1! = 1
3! = 3 * 2 * 1 = 6
Substituting the factorials back into the formula:
C₄,₁ = 24 / (1 * 6)
= 4
Now, let's substitute p, q, and C₄,₁ into Cₙ,ₓpˣqⁿ⁻ˣ:
Cₙ,ₓpˣqⁿ⁻ˣ = C₄,₁ * pˣ * q^(n - x)
= 4 * (1/2)^1 * (1/2)^(4 - 1)
= 4 * (1/2) * (1/2)^3
= 4 * 1/2 * 1/8
= 4/16
= 1/4
Therefore, Cₙ,ₓpˣqⁿ⁻ˣ evaluates to 1/4.
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help!! I’m very bad at rounding lol! What’s the number 45836 rounded to the hundreds place??
Answer:
45900
Step-by-step explanation:
that is rounding the hundreds place
Answer:
45,800
Rounded to the nearest 100 or
the Hundreds Place.
Step-by-step explanation:
Hope this helps. Sorry if its wrong
A survey was done that asked people to indicate whether they preferred to ride a
street bike or a mountain bike. The results of the survey are shown in the two-way
table.
Amjed is making a relative frequency table from this data.
What operation should Amjed perform to determine the relative frequency of a
person over 30 years old who prefers to ride a mountain bike? 1) Subtract 25 from 462, then divide by 462. 2) Divide 25 by 462. 3) Add 180 to 462, then divide by 463. 4) Divide 180 by 462
The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:
2) Divide 25 by 462.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.
The total number of people is given as follows:
58 + 164 + 215 + 25 = 462.
Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:
25/462.
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Write the number three-hundred-sixty-five-thousandths in standard form.
Answer:
365/1,000 or .365
Step-by-step explanation:
HTH :)
Three hundred sixty five thousand in standard form is 365000.
What is standard form and word form of numbers ?The standard form of numbers is when we have to write the number in digits according to it's place and face value.
Word form of numbers is that when we have to write numbers given in numerical form to words by determining place and face value.
According to the given question we have to write three thousand sixty five thousand in standard form.
We know thousand has three zeroes.Suppose we have to write one thousand in standard form which is 1000.
Given we have to write three hundred sixty five thousand in standard form which is 365000.
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do blood-building drugs help brain development in babies born prematurely? researchers randomly assigned 53 babies, born more than a month premature and weighing less than 3 pounds, to one of three groups. babies either received injections of erythropoietin (epo) three times a week, darbepoetin once a week for several weeks, or no treatment. results? babies who got the medicines scored much better by age 4 on measures of intelligence, language, and memory than the babies who received no treatment. what is the purpose of randomly assigning the babies to the three treatments? random assignment eliminates any bias in the experiment. random assignment helps to avoid confounding and reduces variation in responses. random assignment helps to create three groups of infants that are roughly equivalent at the beginning of the study. random assignment helps us distinguish the effects of the treatments form chance difference between the groups. random assignment allows us to show how different treatments cause different effects.
The correct option regarding the random assignment of babies in the treatment is given as follows:
Random assignment helps us distinguish the effects of the treatments form chance difference between the groups.
Randon AssignmentRandom assignment is used for control in experimental researches, to strengthen the validity of an experiment, distinguish the effects of the treatments form chance difference between the groups.
In these experiments, the effect of an independent variable is studied in one or multiple dependent variables in the study, and then the random assignment increases the validity of these effects.
Thus the correct option is given as follows:
Random assignment helps us distinguish the effects of the treatments form chance difference between the groups.
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finding roots from graph whats the answer?
Answer:
x=0, x=2, x=7
Step-by-step explanation:
The roots of graph are points with y = 0
Select the graph that shows the solution set of the linear inequality y 2 -2 + 3x.
A. A
B. B
C. C
D D
How many times will the following loop execute?
int x = 0;
do {
x++;
cout << x << endl;
}while(x < 5)
Answers:
a. - 5 times
b. - 4 times
c. - It doesn't
d. - Infinite times
e. - 6 times
Answer:
Step-by-step explanation:
The loop will run an infinite number of times
Need Help here Please!
Answer:
Step-by-step explanation:
To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:
a) To find the value of \(\sf 3(x - y) \\\):
\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)
b) To find the value of \(\sf 6x - 6y \\\):
\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)
c) To find the value of \(\sf y - x \\\):
\(\sf y - x = - (x - y) = -4 \\\)
Therefore:
a) The value of \(\sf 3(x - y) \\\) is 12.
b) The value of \(\sf 6x - 6y \\\) is 24.
c) The value of \(\sf y - x \\\) is -4.
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♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
calculate the lie factor of the following graph. do you think the concept of a lie-factor is useful or relevant in practice?
Therefore, The lie factor is a helpful tool to identify misleading graphs, but it should be used alongside critical thinking and contextual understanding.
The lie factor is a measure of how much a graph distorts the data it represents. It is calculated by dividing the size of the effect shown in the graph by the size of the effect in the data. A lie factor of 1 indicates no distortion, while a lie factor greater than 1 indicates distortion. In practice, the concept of a lie factor can be useful to identify misleading graphs that exaggerate or downplay the significance of the data. However, it should be used in conjunction with other critical thinking skills and contextual understanding to fully evaluate the accuracy and relevance of a graph's message.
Therefore, The lie factor is a helpful tool to identify misleading graphs, but it should be used alongside critical thinking and contextual understanding.
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In tests of significance about an unknown parameter of some population, which of the following is considered strong evidence against the null hypothesis?
A. The value of an estimate of the unknown parameter based on a simple random sample from the population is not equal to zero.
B. The value of an estimate of the unknown parameter lies within 2 units of the sample value.
C. We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very consistent with the null hypothesis
D. We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true.
In tests of significance about an unknown parameter of some population, "We observe a value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true" is considered strong evidence against the null hypothesis. The correct answer is Option (D).
We apply the principle of hypothesis testing to test a population's claims in inferential statistics. The null hypothesis (H₀) is always a statement about the population parameter that we believe to be true. However, we use the sample data to decide whether the null hypothesis is true or not. When we perform the hypothesis testing, we must consider the level of significance, the sample size, and the nature of the test.
The value of an estimate of the unknown parameter based on a simple random sample from the population that is very unlikely to occur if the null hypothesis is true is considered strong evidence against the null hypothesis. In other words, if the value of the test statistic is greater than the critical value, we can reject the null hypothesis. Consequently, we will have sufficient evidence to support the alternative hypothesis.
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There are three plants that manufacture the boots, two distribution centers, and five warehouses. We need to ship the boots to the warehouses at a minimum cost satisfying the constraints outlined in the spreadsheet. Namely, each plant can only produce so much product, the amount of boots passing through the distribution centers has to remain constant
The problem can be modeled as a linear programming problem. We need to minimize the total cost of shipping the boots, which can be represented as a linear combination of the shipment quantities.
Thus, the objective function to be minimized can be written as:
Minimize Z = 4x11 + 5x12 + 7x13 + 6
32 + y33 ≤ 40 (capacity limit at warehouse 3)
y41 + y42 + y43 ≤ 30 (capacity limit at warehouse 4)
y51 + y52 + y53 ≤ 45 (capacity limit at warehouse 5)
xij, yjk ≥ 0 (non-negativity constraint)
Thus, the complete linear programming problem can be formulated as:
Minimize Z = 4x11 + 5x12 + 7x13 + 6x21 + 4x22 + 5x23 + 4y11 + 3y12 + 6y13 + 5y21 + 5y22 + 4y23 + 6y31 + 7y32 + 5y33 + 4y41 + 6y42 + 5y43 + 5y51 + 4y52 + 6y53
Subject to:
x11 + x12 + x13 ≤ 60
x21 + x22 + x23 ≤ 90
x11 + x21 = y11 + y21 + y31 + y41 + y51
x12 + x22 = y12 + y22 + y32 + y42 + y52
x13 + x23 = y13 + y23 + y33 + y43 + y53
y11 + y12 + y13 ≤ 35
y21 + y22 + y23 ≤ 50
y31 + y32 + y33 ≤ 40
y41 + y42 + y43 ≤ 30
y51 + y52 + y53 ≤ 45
xij, yjk ≥ 0
Solving this linear programming problem using a suitable solver will provide us with the optimal values of xij and yjk, which will help us in determining the minimum cost required for shipping the boots while satisfying all the constraints.
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