Earth science is made of many branches of knowledge concerning all aspects of the Earth system. The main branches are geology, meteorology, climatology, oceanography, and environmental science. Astronomy uses principles understood from Earth to learn about the solar system, galaxy, and universe.
Overview of Earth Science:Only recently have humans begun to understand the complexity of our planet Earth. We have only known for a few hundred years that Earth is just a tiny part of an enormous galaxy, which in turn is a tiny part of an even greater universe.
An important component of experiments is the different variables involved. A variable is any parameter in the experiment that can change. This could be a parameter like temperature, weight or height, or it could be more complex, such as life expectancy or growth rate. Depending on how you set up your experiment, you will use different kinds of variables. There are three basic types to be familiar with.
Independent variable:The first type is the independent variable. This is the variable that is manipulated during an experiment. For example, when experimenting with how fertilisers affects plant growth, the fertiliser is the independent variable because this is the variable that you change. It might help to think of the independent variable as the cause of change in the experiment.
Dependent variable:In contrast to this, the dependent variable is the variable that is affected during an experiment. In our experiment, our dependent variable would be plant growth since this is affected by the amount of fertiliser applied. If you think of the independent variable as the cause, then the dependent variable is the effect.
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the angle of depression from the top of the tower to a boulder on the ground is 38 degrees if the tower is 25 m high how far from the base of the tower is the boulder
Check the picture below.
Make sure your calculator is in Degree mode.
Instead of recording the number 1.23 cm for the radius of 2 tube, a student recorded 1.32cm.find the percentage error, correct to 1.DP
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
○ [tex]F = \frac{S + 24}{3}[/tex]
Step-by-step explanation:
We know that:
[tex]S = 3F -24[/tex],
where F is the length of the foot of a person, and S is their shoe size.
To solve for the length of a person's foot, we have to rearrange the given equation to make F the subject:
[tex]S = 3F -24[/tex]
⇒ [tex]S + 24 = 3F[/tex] [adding 24 to both sides]
⇒ [tex]\frac{S + 24}{3} = F[/tex] [dividing both sides by3]
⇒ [tex]F = \frac{S + 24}{3}[/tex] [swapping the sides]
Coordinates of G=(,),() and H=(,)(,)
Help Me please! Thankss
The coordinates of the missing points G. and H are G(a, y) and H(a,0) respectively
What is a right angles triangle?A right angled triangle is a triangle that has 3 sides and angle with one of its angles to be 90 degrees.
From the given triangle, the measure of the x-coordinate point of G and H will be equal.
Since the line GH intersects the x-axis and the point where the line intersects the x-axis is where y = 0, hence the coordinate H is (a, 0) and the measure of G is (a, +y)
The y-value of G can be any positive value on the y-axis
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Find the dimensions of a rectangle with an area of 2x^2-7x-10
Answer:
Step-by-step explanation:
I gotcha my dude.......
x-5 and 2x+3
How did doves view the conflict in Vietnam?
O As a vital Cold War battleground in the fight for democracy
O As a localized civil war that should not include the US
O As the first step in acquiring territory in Southeast Asia
O As a means to achieving Johnson's Great Society
The view of war doves with respect to the Vietnam War was that: B. as a localized civil war that should not include the United States of America (US).
What is the Vietnam War?The Vietnam War is also referred to as Second Indochina War or the Vietnam conflict and it can be defined as a short, costly, protracted and divisive conflict between the communist government of North Vietnam and South Vietnam, which ended on the 30th of April, 1975.
Based on historical information and records, the Vietnam War officially started on the 1st of November, 1955 in the following locations:
VietnamCambodiaNorth VietnamSouth VietnamLaosSouth East AsiaIn conclusion, we can infer and logically deduce that the view of war doves with respect to the Vietnam War was that it is a a localized civil war and as such should not include the United States of America.
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Find the area of the figure with the coordinates, S(-3, 5), A (1, 5), L(2, 1) and T(-6, 1).
Answer: a = 24 units²
Step-by-step explanation:
Let us graph the figure given. This shape appears to be a trapezoid. Now, we can solve for the area. This shape also has a height of 4, which I forgot to show in the picture.
In the formula, h is the height, a is a base, and b is the other base.
[tex]\displaystyle a=\frac{a+b}{2} h[/tex]
[tex]\displaystyle a=\frac{4+8}{2} 4[/tex]
[tex]\displaystyle a=\frac{12}{2} 4[/tex]
[tex]\displaystyle a=(6)4[/tex]
[tex]\displaystyle a=24\; \text{units}^{2}[/tex]
What is the exact value of cos (67.5°)?
OA.
OB.
OC. -√2+√2
√2+√2
2
-
√2-√2
2
OD. √2+ √2
4
first off, make sure you have a Unit Circle, if you don't do get one, you'll need it, you can find many online.
let's double up 67.5°, that way we can use the half-angle identity for the cosine of it, so hmmm twice 67.5 is simply 135°, keeping in mind that 135° is really 90° + 45°, and that whilst 135° is on the 2nd Quadrant and its cosine is negative 67.5° is on the 1st Quadrant where cosine is positive, so
[tex]cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\\\ cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}} \\\\[-0.35em] ~\dotfill\\\\ cos(135^o)\implies cos(90^o+45^o)\implies cos(90^o)cos(45^o)~~ - ~~sin(90^o)sin(45^o) \\\\\\ \left( 0 \right)\left( \cfrac{\sqrt{2}}{2} \right)~~ - ~~\left( 1\right)\left( \cfrac{\sqrt{2}}{2} \right)\implies -\cfrac{\sqrt{2}}{2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]cos(67.5^o)\implies cos\left( \frac{135^o}{2} \right)\implies \pm \sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}\implies \stackrel{I~Quadrant}{+\sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}} \\\\\\ \sqrt{\cfrac{ ~~ \frac{2-\sqrt{2}}{2} ~~ }{2}}\implies \sqrt{\cfrac{2-\sqrt{2}}{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{\sqrt{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{2}[/tex]
In a local shop some items are being sold at a third off. They now cost the following amounts. What was the original full price? 40 POINTS AND BRAINLIEST
1.£6.46
2.£58.24
3.£114.28
4.£12.50
5.£10.86
Answer:
1) 9.69
2) 87.36
3) 171.42
4) 18.75
5) 16.29
Step-by-step explanation:
Treat each value's full price as x. then, all of the values are (2/3)x. To get (2/3)x back to x, we must multiply (2/3)x*(3/2)=x. Multiply each of the questions given by 3/2 or 1.5
For the same sample data and null hypothesis, how does the p-value for a two-tailed test of μ compare to that for a one-tailed test?.
A one-tailed test's p-value is half that of a two-tailed test.
What is the difference between the p-value for a two-tailed test and a one-tailed test?Whether it is positive or negative, when you find your test statistic, you also find a tail probability to the right or left of that test statistic. What is the likelihood that, if the null hypothesis is correct, you will obtain a value that is more extreme (far out in the tail) than the observed test statistic? If the test is two-tailed, the phrase "probability...more extreme" applies to both tails, beyond the positive and negative values of your test statistic. Your calculations will fall either on the right or left, but if the test is two-tailed, it will also apply to both tails.
What is null hypothesis ?Two possibilities sharing similarities is the null hypothesis. That the observed discrepancy is solely the result of chance is the null hypothesis. Calculating the probability that the null hypothesis is correct using statistical testing is achievable.
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A circle is shown. Points Q, U, A, D are on the circle. Lines connect the points to form a quadrilateral. Angle Q U A is 111 degrees. Arc Q U is 88 degrees.
What is the measure of Arc A U?
44°
50°
64°
92°
The measure of Arc AU of the given Circle Geometry is; 50°
How to find the measure of arc angle?The circle theorem we will apply to solve for the arc measure states that “Measure of angles subtended to any point on the circumference of the circle from the same arc is equal to half of the angle subtended at the center by the same arc.”
We can express the above theorem as;
Angle at the center = 2 × Angle at the circumference
From the attached image below and from the given statement in the question, we are given that; ∠QUA = 111°
Therefore, applying the circle theorem earlier quoted, we can say that; m∠QDA = 2 × ∠QUA
m∠QDA = 2 × 111° = 222°
Which gives;
∠QOA = = 360° - 222° = 138°
∠QOA = ∠QOU + ∠UOA (by angle addition property)
Thus;
∠QOA = 138° = 88° + ∠UOA
∠UOA = 138° - 88° = 50°
Thus, the measure of Arc AU is;
Arc AU = ∠UOA = 50°
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Answer: b
Step-by-step explanation:
find the gradient of 15y-6x=8
Answer:
2/5 or 0.4
Step-by-step explanation:
First we have to make equation into the gradient slope form :
y=mx+c m is gradient and c is y-intercept
15y-6x=8
First we add 6x to both sides :
15y = 6x+8
Now we divide both sides by 15 :
y = 6x+8 / 15
Split the fraction on the right :
y = 6x/15 + 8/15
6x/15 = 6/15x
Our gradient will be 6/15 = 2/5 or 0.4
Hope this helped and have a good day
I don't get the minutes part
A gardener has 520 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing.
garden bordered by a river
What dimensions would guarantee that the garden has the greatest possible area?
shorter side: _____ft (feet)
longer side: ____ft (feet)
greatest possible area: ___ft2 (square-feet)
The shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet
What dimensions would guarantee that the garden has the greatest possible area?The given parameter is
Perimeter, P = 520 feet
Represent the shorter side with x and the longer side with y
One side of the garden is bordered by a river:
So the perimeter is:
P = 2x + y
Substitute P = 520
2x + y = 520
Make y the subject
y = 520 - 2x
The area is
A = xy
Substitute y = 520 - 2x in A = xy
A = x(520 - 2x)
Expand
A = 520x - 2x^2
Differentiate
A' = 520 - 4x
Set to 0
520 - 4x = 0
Rewrite as:
4x= 520
Divide by 4
x= 130
Substitute x= 130 in y = 520 - 2x
y = 520 - 2 *130
Evaluate
y = 260
The area is then calculated as:
A = xy
This gives
A = 130 * 260
Evaluate
A = 33800
Hence, the shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet
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In accordance with the marshaling of assets provision of the uniform partnership act, the correct ranking of the following liabilities of a partnership in order of payment is: $20,000 loan from a partner. $30,000 of profits from the last year of operations. $3,000 payable to a supplier. $100,000 in capital balances of the partners.
The correct order is 3,1,4,2.
(3) $3,000 payable to a supplier. (1) $20,000 loan from a partner. (4) $100,000 in capital balances of the partners.(2) $30,000 of profits from the last year of operations. What is the uniform partnership act?The Uniform Partnership Act (UPA) governs corporate partnerships in various states in the United States. When a partner dissociates, the UPA provides regulations for the dissolution of the partnership. Several revisions to the Uniform Partnership Act have been made over the years (UPA). The Revised Uniform Partnership Act refers to the revised act and changes (RUPA).The Uniform Partnership Act also governs partnership formation, liabilities, assets, and fiduciary obligations.Marshaling of assets:
The process of organizing the balance sheet elements (assets and liabilities) in a specified sequence is referred to as the marshaling of assets and liabilities. In other words, it is the process of organizing the various assets and liabilities on a balance sheet in a particular order.The order is the amount owed to a supplier, the amount of a loan from a partner, the amount of the partners' capital balances, and the number of profits from the previous year of operations.Therefore, the correct order is 3,1,4,2.
(3) $3,000 payable to a supplier. (1) $20,000 loan from a partner. (4) $100,000 in capital balances of the partners.(2) $30,000 of profits from the last year of operations.Know more about the uniform partnership act here:
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The correct question is given below:
In accordance with the marshaling of assets provision of the uniform partnership act, the correct ranking of the following liabilities of a partnership in order of payment is:
(1) $20,000 loan from a partner.
(2) $30,000 of profits from the last year of operations.
(3) $3,000 payable to a supplier.
(4) $100,000 in capital balances of the partners.
Using f(x), what is the equation that represents g(x)?
Og(x) = log5 (x) - 3
O
g(x) = log5 (x) +3
Og(x) = log5 (x-3)
Og(x) = logs(x + 3)
The equation that represents the function g(x) is g(x) = log₅(x - 3)
How to determine the equation that represents g(x)?The equation of the function f(x) is given as:
f(x) = log₅(x)
From the graph, we can see that the function g(x) is 3 units to the right of the function f(x)
This means that
g(x) = f(x - 3)
The function f(x - 3) is calculated as follows
f(x - 3) = log₅(x - 3)
Substitute f(x - 3) = log₅(x - 3) in g(x) = f(x - 3)
g(x) = log₅(x - 3)
Hence, the equation that represents the function g(x) is g(x) = log₅(x - 3)
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determine what type of model best fits the given situation: An Internet phone company presently provides service to 5,000 customers at a monthly rate of $20 per month. After a market survey, it was determined that for each $1 decrease in the monthly rate an increase of 500 new customers would result.
A. none of these
B. quadratic
C. linear
D. exponential
The option c is correct. The linear representation model is best for this situation out of the exponential, quadratic model.
According to the statement
we have given that:
Monthly Rate = $20, Number of customers = 5000
If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.
And we have to find that The type of model that best fits the given situation.
So, according to the linear representation model
Monthly Rate = $20, Number of customers = 5000
Let us decrease the monthly rate by $1.
Monthly Rate = $20 - $1 = $19, Number of customers = 5000 + 500 = 5500
Let us decrease the monthly rate by $1 more.
Monthly Rate = $19 - $1 = $18, Number of customers = 5500 + 500 = 6000
Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.
We have 2 pair of values here,
x = 20, y = 5000
x = 19, y = 5500
Let us write the equation in slope intercept form:
y = mx + c
And Slope of a function is
m = y₂ - y₁ / x₂ - x₁
Then
m = 5500 - 5000 / 19 - 20
m = -500
So, the equation become
y = -500x +c
And find the value of by putting the values.
So, c = 15000
And the equation become
y = -500x + 15000.
According to this linear model is perfect for this situation.
So, The linear representation model is best for this situation.
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help please!! show work if possible thank you!!
Round each fraction to help you estimate the solution for the following equation:
nine tenths minus eight tenths equals
0
one half
1
one and one half
Answer:
Step-by-step explanation:
answer is 1/2
No links, provide full answer
The value of M is:
M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.
What are the family of solutions behind an equation of the form p · q = k?
In this question we have a product of two nonzero real numbers equal to 5, whose mathematical form is:
p · q = 5, where p = 2 · x + √(4 · x² + 5) = k and q = 2 · y + √(4 · y² + 5) = 5 / k
Then, we proceed to find the solutions for x and y in terms of k:
2 · x + √(4 · x² + 5) = k
2 · x = k - √(4 · x² + 5)
4 · x² = k² - 2 · k · √(4 · x² + 5) + 4 · x² + 5
2 · k · √(4 · x² + 5) = k² + 5
4 · k² · (4 · x² + 5) = (k² + 5)²
4 · x² + 5 = (k² + 5)² /(4 · k²)
4 · x² = (k² + 5)² /(4 · k²) - 5
x = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5], for k ≠ 0.
2 · y = 5 / k - √(4 · y² + 5)
4 · y² = 25 / k² - (10 / k) · √(4 · y² + 5) + 4 · y² + 5
(10 / k) · √(4 · y² + 5) = 25 / k² + 5
(100 / k²) · (4 · y² + 5) = (25 / k² + 5)²
4 · y² + 5 = (k² / 100) · (25 / k² + 5)²
4 · y² = (k² / 100) · (25 / k² + 5)² - 5
y = ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5], for k ≠ 0.
Therefore, the value of M is:
M = ± (1 / 2) · √[(k² + 5)² /(4 · k²) - 5] ∓ (1 / 2) · √[(k² / 100) · (25 / k² + 5)² - 5] + √3, for k ≠ 0.
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I need help with this math question.
Answer:
23 children and 9 adults
p <= 70/9
Step-by-step explanation:
Let x = # of adults and y = # of children. The number of children is 5 more than twice the number of adults, so x = 2y + 5. The total cost of entrance is $6525, so 225x + 150y = 6525.
x = 2y + 5
225x + 150y = 6525
x - 2y = 5
225x + 150y = 6525
75x - 150y = 375
225x + 150y = 6525
300x = 6900
x = 23
x = 2y + 5
23 = 2y + 5
18 = 2y
y = 9
225p + 3750 <= 5500
225p <= 1750
p <= 70/9
Ashley has two equations that she found to be valuable models for her research. She thinks that if she can find the intersection of the two graphs, she will be able to identify a key point to her studies. At what point do these equations intersect?
4y –x = 9
y = 2x − 3
(3,3)
(3,-3)
(-3,-3)
(-3,3)
The equations intersect at the point (3 ,3 ).
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:
a= the slope
b=constant term that represents the y-intercept.
System of Linear EquationsSystem of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.
The question gives:
4y –x = 9 (1)
y = 2x − 3 (2)
You should replace the variable y of equation 1 to equation 2. Then, you will have:
4*(2x-3)-x=9
8x-12-x=9
8x-x=9+12
7x=21
x=3
If x=3, from equation 2 you can find the value of y. Thus, y=2*3-3=6-3=3
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please help 20 points and brainlyist
a) 1. The backpack weight sample mean is 6.375 pounds.
a) 2. The backpack weight sample mean is 6.375 pounds.
a) 3. The backpack weight sample mean is 6.625 pounds.
b) The range of the sample means is between 6.375 and 6.625, which approaches 0.250 pounds, plus or minus.
c) Since the students are using the sample means to estimate the mean backpack weight of their schoolmates, the true statements are A. and D.
The farther the range of the sample means is from O, the less confident they can be in their estimate.
What is a sample mean?A sample mean is a statistic computed from a sample of data or variables.
The sample mean represents the average value of the sample data.
What is a range in statistics?The range describes the difference between the largest number and the smallest number.
Thus, based on the range of the sample means, the farther it is from 0, the less confident the students can be in their estimate.
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Evaluate the following integral or state that it does not exist (Calculus 2) Please show step by step explanation!
Answer:
[tex]\displaystyle \int^1_0 \dfrac{e^{\sqrt{x}}}{\sqrt{x}}\:\:\text{d}x=2(e-1)[/tex]
Step-by-step explanation:
Given definite integral:
[tex]\displaystyle \int^1_0 \dfrac{e^{\sqrt{x}}}{\sqrt{x}}\:\:\text{d}x[/tex]
Integration by substitution:
Substitute u for one of the functions to give a function that's easier to integrate.
[tex]\textsf{Let }u=\sqrt{x}[/tex]
Find the derivative of u and rewrite it so that dx is on its own:
[tex]\implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{2\sqrt{x}}[/tex]
[tex]\implies \text{d}x=2 \sqrt{x}\:\text{d}u}[/tex]
[tex]\implies \text{d}x=2u\:\text{d}u[/tex]
Use the substitution to change the limits of the definite integral from x-values to u-values:
[tex]\textsf{When }x=0 \implies u=\sqrt{0}=0[/tex]
[tex]\textsf{When }x=1 \implies u=\sqrt{1}=1[/tex]
Therefore, the limits are unchanged.
[tex]\boxed{\begin{minipage}{3 cm}\underline{Integrating $e^x$}\\\\$\displaystyle \int e^x\:\text{d}x=e^x+\text{C}$\end{minipage}}[/tex]
Substitute everything into the original integral and solve:
[tex]\begin{aligned}\implies \displaystyle \int^1_0 \dfrac{e^{\sqrt{x}}}{\sqrt{x}}\:\:\text{d}x & =\displaystyle \int^1_0 \dfrac{e^u}{u} \cdot 2u\:\:\text{d}u \\\\ & = \displaystyle \int^1_0 2e^u\:\:\text{d}u \\\\ & = 2 \int^1_0 e^u\:\:\text{d}u\\\\ & = 2 \left[ e^u\right]^1_0\\\\ & = 2 \left[e^1-e^0\right]\\\\& = 2(e-1)\end{aligned}[/tex]
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David reflects the word 'MOM' over the y-axis and notices
that is still reads the same. Is the same true for the word
'DAD'? Use letter symmetry to explain why or why not.
The reflection of the word DAD across the y-axis is not the same
How to determine the true statement?The statement is given as:
MOM, when reflected over the y-axis = MOM
The above is true because the letters M and O have reflectional symmetry across the y-axis
However, the letter D do not have a reflectional symmetry across the y-axis
So, the letters would not remain the same when reflected
Hence, the reflection of the word DAD across the y-axis is not the same
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The area of a square is 400 square units. If the length of each side of the
square increased by one unit, would its area be a rational number? Explain.
yes it will be a rational number.
square having area 400 sq units will have a length of 20 on each side by increasing the length of each side by 1 we get 21 then the area will be
21 ^ 2=441
Then we will have a rational number.
find the perimeter and area of the polygons
Answer:
Below in bold.
Step-by-step explanation:
This figure is a trapezoid.
We can find the missing side length by applying the Pythagoras Theorem to the right triangle on the left of the figure.
The dotted line has length 12 cm and the base of the triangle = 25 - 18 = 7 cm
So x^2 = 12^2 + 7^2 (where x = missing length)
= 144 + 49
= 189
x = √189
= 13.75 to nearest hundredth
So the perimeter
= 18 + 12 + 25 + 13.75
= 68.75 cm.
Area of a trapezoid = 1/2 (a + b) * h.
Area = 1/2 *(18 + 25) * 12
= 258 cm^2.
To select the correct student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?
The correct student's t- distribution requires knowing the degrees of freedom. The degrees of freedom are there for a sample of size n is B) n-1.
Distribution is described as the technique of having items to consumers. An instance of distribution is rice being shipped from Asia to the USA. The frequency of occurrence or quantity of lifestyles.
Distribution manner to spread the product for the duration of the market such that a big quantity of humans should purchase it. Distribution involves doing the following matters. An amazing delivery machine to take the goods into one-of-a-kind geographical regions.
Distribution is one of the four elements of the advertising and marketing mix. Distribution is the method of creating a service or product available for the consumer or enterprise user who needs it. this may be executed without delay through the manufacturer or service company or the usage of indirect channels with vendors or intermediaries.
Disclaimer: The question is incomplete. Please read below to find the missing content.
Question: To select the correct Student's t-distribution requires knowing the degrees of freedom. How many degrees of freedom are there for a sample of size n?
A) n
B) n-1
C) n+1
D) [X - μ / (s / n)]
The degrees of freedom depends on the number of parameters you are estimating.
8=
i-1
In student t distribution we estimate the population mean through sample mean and population standard deviation through sample standard deviation
So here both parameters depend on the sample mean i.e. we just calculate from a sample of size n so
Degrees of freedom for students t distribution is B) n-1
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Find the term that must be added to the equation x2 6x=1 to make it into a perfect square.
The value added to the equation [tex]$x^2-6x=1[/tex] exists [tex]$x^2-6x+9=10[/tex].
What is a perfect square?
A perfect square exists as a number that can be described as the product of an integer by itself or as the second exponent of an integer.
The perfect square trinomial exists
[tex](a[/tex] ± [tex]b)^2[/tex] = [tex]a ^2[/tex] ± 2ab + [tex]b ^2[/tex]
[tex]$x^2-6x=1[/tex]
[tex]x^2-2*3x=1[/tex]
then [tex]$2ab = 2 * 3*x = 2 * x *3[/tex]
The value of a = x and b = 3
[tex]$b^2=3^2=9[/tex]
[tex]$x^2-6x+9=1+9[/tex]
[tex]$x^2-6x+9=10[/tex]
The value added to the equation [tex]$x^2-6x=1[/tex] exists [tex]$x^2-6x+9=10[/tex].
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Julia is casting a play with 4 main roles. Six students
have tried out. How many different combinations of 4
students can Julia cast from the 6 students?
Using the combination formula, it is found that Julia can take 15 combinations.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For this problem, 4 students are taken from a set of 6, hence the number of combinations is given as follows:
[tex]C_{6,4} = \frac{6!}{4!2!} = 15[/tex]
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