find a cartesian equation for the curve and identify it. hyperbola parabola circle ellipse limaçon r cos(2theta)
Answers
The curve is an ellipse with the Cartesian equation x²/1 + y²/1 = 1.
To convert the given polar equation r² cos 2θ = 1 to a Cartesian equation, we can use the following relationships between polar and Cartesian coordinates:
x = r cos(θ)
y = r sin(θ)
Substitute these values into the given polar equation:
r² cos 2θ = 1
(r cos θ)² - (r sin θ)² = 1
use the identity cos² θ - sin² θ = 1 to simplify further:
(cos θ)² - (sin θ)² = 1
Replace (cos θ)² with x² and (sin θ)² with y²:
x² - y² = 1
Rearrange the equation to put it in standard form for an ellipse:
x²/1 - y²/1 = 1
The equation represents an ellipse with a major axis along the x-axis and a minor axis along the y-axis.
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Complete question:
Find a Cartesian equation for the curve and identify it.
r2 cos 2θ = 1
circle ellipse hyperbola limaçon parabola
Related Questions
Helpful conversions: 1 acre =43,560 square feet 1 hectare =10,000 square meters 1lb=454 grams 1 kg=2.2lbs=1000grams 1. Scouting for cover crop establishment in the field requires conversion of your massbased seeding rate (e.g., lbs/acre) to a population-based establishment rate (e.g., plants/f? ). Let's practice doing that. Convert the following seeding rates: a. Cereal rye - 60 ibs/acre = H seeds/square foot b. Crimson clover −15 kg/ha= H seeds/square meter 2. Convert the following population-based seeding rates to mass-based seeding rates. a. Oats −30 plants/square foot = Ibs seedlacre b. Hairy vetch −20 plants/square meter = kg seedsha 3. Your farm manager wants you to drill crimson clover seed, but the seed hasn't arrived yet and you don't know if it's coated or not. If the seed is not coated, the seeding rate is 20 blacre. Will you need to increase or decrease your seeding rate if the seed is coated?
Answers
Coating the seed typically improves seed quality and germination rates, so the same seeding rate can be maintained even with coated seed.
To convert mass-based seeding rates to population-based establishment rates, we need to consider the area conversion factors provided:
a. Given a seeding rate of 60 lbs/acre for cereal rye, we can convert it to seeds per square foot by using the conversion factor of 1 acre = 43,560 square feet.
b. Given a seeding rate of 15 kg/ha for crimson clover, we can convert it to seeds per square meter using the conversion factor of 1 hectare = 10,000 square meters.
To convert population-based seeding rates to mass-based seeding rates, we can use the given area conversion factors:
a. Given a seeding rate of 30 plants/square foot for oats, we can convert it to pounds of seed per acre.
b. Given a seeding rate of 20 plants/square meter for hairy vetch, we can convert it to kilograms of seed per hectare.
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4. What is the coefficient in the following term?
a²b²
A
B
2
1
Answers
Answer:
A and B
Step-by-step explanation:
The coeffiecent is the constant placed before the multiplying factor.
A telecommunication station is designed to receive a maximum of 10 calls per 1/2 second. If the number of calls to the station is modeled as a Poisson random variable with a mean of 9 calls per 1/2 second, what is the probability that the number of calls will exceed the maximum design constraint of the station
Answers
The probability that the number of calls will exceed the maximum design constraint of the station is approximately 0.038, or 3.8%
A telecommunication station is designed to receive a maximum of 10 calls per 1/2 second.
If the number of calls to the station is modeled as a Poisson random variable with a mean of 9 calls per 1/2 second, the probability that the number of calls will exceed the maximum design constraint of the station is approximately 0.038.
We can find this probability using the Poisson distribution formula and solving for the probability of having more than 10 calls in 0.5 seconds.
The Poisson distribution formula is:
P(X = k) = (e^-λ * λ^k) / k!
where X is the random variable (number of calls), λ is the mean of the distribution (9 calls per 0.5 seconds), k is the number of occurrences, e is Euler's number (approximately 2.71828), and k! is the factorial of k.
To find the probability of having more than 10 calls, we need to sum up the probabilities for
k = 11, 12, 13, and so on, up to infinity:
P(X > 10) = 1 - P(X ≤ 10)≈ 1 - 0.962≈ 0.038
Therefore, the probability that the number of calls will exceed the maximum design constraint of the station is approximately 0.038, or 3.8% (rounded to three decimal places).
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Given the function f(x) = 2|x + 6| – 4, for what values of x is f(x) = 6?
Answers
Answer:
20
Step-by-step explanation:
\(f(x) = 2|x + 6| -4\)
Step 1: Substitute \(x\) for the given function.
6 is the given function.
\(f(x) = 2|x + 6| -4\\=f(x) = 2|6 + 6| -4\\\\f(x) = 2|6 + 6| -4\\=24-4\\\\=20\)
Can u guys help me plz?
Answers
Does (2, 4) make the equation y = –6x true?
Answers
Answer:
No
Step-by-step explanation:
When \(x=2\), \(y=-6(2)=-12\), not \(4\).
find a basis for and the dimension of the solution space of the homogeneous system of linear equations −x y z = 0 2x − y = 0 2x − 3y − 4z = 0 (a) a basis for the solution space
Answers
The homogeneous system of linear equations has a solution space with a basis of {(1, 2, -1)}. The dimension of the solution space is 1.
To find a basis for the solution space of the given homogeneous system of linear equations, we need to solve the system and express the solutions in terms of a linear combination of vectors.
The system of equations is as follows:
Equation 1: -x + y - z = 0
Equation 2: 2x - y = 0
Equation 3: 2x - 3y - 4z = 0
We can start by using the equations to eliminate variables. From Equation 2, we can express y in terms of x as y = 2x. Substituting this into Equation 1 gives us -x + 2x - z = 0, which simplifies to x - z = 0. Rearranging this equation, we have x = z.
Now, we can express the variables in terms of a single parameter. Let's choose z as the parameter. Thus, x = z and y = 2x = 2z.
Now, we can express the solutions in vector form as (x, y, z) = (z, 2z, z) = z(1, 2, 1). This means that the solution space is spanned by the vector (1, 2, 1).
To find the basis for the solution space, we need to check if the vector (1, 2, 1) is linearly independent. Since it is the only vector spanning the solution space, it is linearly independent. Therefore, the basis for the solution space is {(1, 2, 1)}.
The dimension of the solution space is equal to the number of vectors in the basis, which in this case is 1. Therefore, the dimension of the solution space is 1.
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The cytoskeletal structure(s) that are composed of actin and regulate cell shape, cell movement, and muscle contraction include
Answers
The cytoskeletal structure composed of actin and involved in regulating cell shape, cell movement, and muscle contraction is called the actin cytoskeleton.
The actin cytoskeleton is a fundamental component of the cytoskeleton, a network of protein filaments within cells that provides structural support and plays essential roles in cellular processes. Actin filaments, also known as microfilaments, are polymers of actin protein subunits and form the main component of the actin cytoskeleton.
The actin cytoskeleton is involved in various cellular functions. It plays a crucial role in determining cell shape by providing structural support and contributing to the maintenance of cell integrity. Actin filaments are also responsible for generating the forces required for cell movement, including crawling, amoeboid movement, and migration of cells during processes such as wound healing.
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Find the area of the trapezoid
Answers
Answer:
1. 54ft^2 2. 48ft^2
Step-by-step explanation:
1. A=1/2h(a+b)
A= 1/2x6(10+8)
A=54
2. A=1/2x6(12+4
A=48
condense the expression to a single logarithm using the properties of logarithms. log(x)−1/2log(y) 3log(z)
Answers
the expression to a single logarithm using the properties of logarithms log(x) + log(z^3) - log(y^(1/2))
We can use the properties of logarithms to condense the expression. Firstly, we can use the rule that says log(a) - log(b) = log(a/b). Applying this rule to the first two terms gives us log(x/y^(1/2)). Next, we can use the rule that says nlog(a) = log(a^n).
Applying this rule to the last term gives us log(z^3). Finally, we can use the rule that says log(a) + log(b) = log(ab) to combine the first and last terms, giving us log(xz^3/y^(1/2)).
Therefore, the condensed expression using the properties of logarithms is log(xz^3/y^(1/2)).
The condensed expression is log(x * z^3 / y^(1/2)).
To condense the given expression using properties of logarithms, we need to apply the following rules:
1. log(a) - log(b) = log(a/b)
2. log(a^n) = n * log(a)
So, let's apply these rules to the given expression:
log(x) - (1/2)log(y) + 3log(z)
First, apply rule 2:
log(x) - log(y^(1/2)) + log(z^3)
Next, apply rule 1:
log(x * z^3 / y^(1/2))
The expression log(x) - (1/2)log(y) + 3log(z) can be condensed to a single logarithm as log(x * z^3 / y^(1/2)).
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what are the zeros of this function. f(x)=x^2+3x-40
Answers
By solving the given equation f(x) = \(x^{2} +3x-40\), the zeroes are -3 and 5.
To solve the given equation we have to do the factorization.
What is factorization: Factorization is the method of writing numbers as the product of their factors or divisors. In other words, we can say finding what to multiply together to get an expression.
To do the factorization, we have to follow the steps as shown below:
\(x^{2} +3x-40\) \(= 0\)
\(-40 = 8 * -5\\\) [ multiplication of 8 and -5 is -40]
\(x^{2}+8x-5x -40\) \(= 0\)
\(x(x+8) -5(x+8)\) \(= 0\)
\((x-5)(x+8)\) \(= 0\)
\(x = 5\) and \(x = -8\) [ The roots or zeroes]
From the above solution, we can conclude that the zeros of the given function \(x^{2} +3x-40\) are 5 and -8.
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Deandra is doing her math homework. She completed the first 6 problems in 2 hours and the last 12 problems in 3 hours.
Which best describes Deandra’s rate for completing her homework?
Deandra completed the first 6 problems at a rate of 6 problems per hour and the last 12 at a rate of 2 problems per hour.
Deandra completed the first 6 problems at a rate of 3 problems per hour and the last 12 at a rate of 4 problems per hour.
Deandra completed the first 6 problems at a rate of 2 problems per hour and the last 12 at a rate of 6 problems per hour.
Deandra completed the first 6 problems at a rate of 4 problems per hour and the last 12 at a rate of 3 problems per hour.
Answers
Answer:
Deandra completed the first 6 problems at a rate of 3 problems per hour and the last 12 at a rate of 4 problems per hour.
Step-by-step explanation:
6 problems ÷ 2 hours = 3 problems per hour
12 problems ÷ 3 hours = 4 problems per hour
Answer B is the answer
The number name of 70080067
In Indian System
Answers
Answer:
Seven crore eighty thousands sixty-seven.
Step-by-step explanation:
70080067
Seven crore eighty thousands sixty-seven.
What are the three common elements of an optimization problem? a. objectives, resources, goals.
b. decisions, constraints, an objective. c. decision variables, profit levels, costs.
d. decisions, resource requirements, a profit function.
Answers
The three common elements of an optimization problem are b. decisions, constraints, and an objective.
Decisions refer to the choices or actions that can be taken in order to achieve a specific goal. Constraints are the limitations or restrictions that must be considered when making decisions. An objective is the goal that needs to be achieved, and it can be either maximizing or minimizing a specific quantity. In an optimization problem, the task is to find the optimal decision variables that satisfy the given constraints and achieve the objective.
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How to factor x^2-2x
Answers
Answer:
x(x-2)
Step-by-step explanation:
Compute the directional derivative of the functionf(x,y)=2xy−3y2,at the point P0=(5,5)in the direction of the vector u = 4i + 3j.
Answers
The directional derivative of the function f(x,y) = 2xy - 3y^2 at the point P0 = (5,5) in the direction of the vector u = 4i + 3j is 6√2.
Explanation:
The directional derivative measures the rate of change of a function in a specific direction. It is denoted by ∇_u f(x,y), where u is the unit vector in the direction of interest. To compute the directional derivative, we need to take the dot product of the gradient of f with the unit vector u.
First, we need to find the gradient of f(x,y).
∇f(x,y) = [2y, 2x - 6y]
Next, we need to normalize the vector u to get the unit vector in the direction of interest.
|u| = √(4^2 + 3^2) = 5
u^ = (4/5)i + (3/5)j
Taking the dot product of the gradient of f with the unit vector u, we get:
∇_u f(x,y) = ∇f(x,y) · u^ = [2y, 2x - 6y] · (4/5)i + (3/5)j
At the point P0 = (5,5), we have:
∇_u f(5,5) = [2(5), 2(5) - 6(5)] · (4/5)i + (3/5)j = 10(4/5) + (-6)(3/5) = 8 - 3.6 = 4.4
Therefore, the directional derivative of f(x,y) at the point P0 = (5,5) in the direction of the vector u = 4i + 3j is:
∇_u f(5,5) = 4.4
Finally, we need to scale the result by the magnitude of the vector u to get the directional derivative in the direction of u.
Directional derivative = ∇_u f(5,5) / |u| = 4.4 / 5 = 0.88 * √(2)
Directional derivative = 6√2.
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if 4 -letterwords'' are formed using the letters a, b, c, d, e, f, g, how many such words are possible for each of the following conditions:(a) no condition is imposed.
Answers
The number of 4-letter words that can be formed without any condition imposed is 8,064.
To determine the number of 4-letter words that can be formed without any conditions, we can use the concept of permutations. Since we have 8 options (a, b, c, d, e, f, g) for each letter position, we can multiply the number of options for each position to find the total number of possibilities.
For the first letter position, we have 8 options to choose from. Similarly, for the second, third, and fourth positions, we also have 8 options each. Therefore, the total number of possibilities is:
8 options for the first position × 8 options for the second position × 8 options for the third position × 8 options for the fourth position = 8 × 8 × 8 × 8 = 8,064.
Hence, there are 8,064 possible 4-letter words that can be formed without any conditions imposed.
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i need answer please
Answers
Answer:
Below in bold.
Step-by-step explanation:
Radius of the pizza = 1/2 * 8 = 4 in.
Area of the whole pizza = π r^2
= π * 4^2
= 8 π
So if you take 1/8 away
the area left = 7/8 * 8 * π
= 7π
Taking π to be 22/7:
= 7 * 22/7
= approximately 22 in^2.
tina bought three pairs of jeans and three sweaters that were on sale she paid a total of 105.69 if the jeans were 26.93 how much was each sweater?
Answers
Answer:
Each sweater costs $8.30
Step-by-step explanation:
j = jeans
s = sweater
3j + 3s = 105.69
3(26.93) + 3s = 105.69
80.79 + 3s = 105.69
-80.79 -80.79
3s = 24.9
/3 /3
s = 8.3 ($8.30)
Check:
3j + 3s = 105.69
3(26.93) + 3(8.3) = 105.69
80.79 + 24.9 = 105.69
105.69 = 105.69
Hope this helps!
Find the volume of each cone. Round your answer to two decimal places.
Answers
Answer:
ABBBB
Step-by-step explanation:
graph the line with slope -1/2 passing through the point (5,-3)
Answers
Step-by-step explanation:
The graph is shown in the image above.
Answer: Draw a line through the two points (5,-3) and (7,-4)
See the diagram below.
=======================================================
Explanation:
Start at (5,-3). Then move down 1 and to the right 2 units to arrive at (7,-4)
The motion of "down 1, right 2" is from the slope of -1/2
slope = rise/run = -1/2
rise = -1 = go down 1 unit
run = 2 = go 2 units to the right
Two points are the minimum amount needed to draw any line. Plot the two points (5,-3) and (7,-4) and draw a straight line through them as shown in the diagram below. I used GeoGebra to make the graph. Desmos is another tool you could use.
What is the value of x?
Answers
Answer:
x = 25 unitsStep-by-step explanation:
they are two similar triangles, same shape but dimensions in proportion, and we solve, in fact, with a proportion between the corresponding values
24 : 15 = 40 : x
x = 15 × 40 : 24
x = 600 : 24
x = 25
In one month, the median home price in the west fell from $203,400 to $192,300. Find the percent decrease
Answers
(i’m not sure what to round it to)
subtract 192,300 from 203,400 to find the amount of change
(= 11,100)
then divide that amount from the original price (203,400)
then multiply that number by 100 to get a percent
finally round to a reasonable percent
11,100/203400= 5.46%
It decreased by 5.46%
your velocity is given by v(t)=1t2 8 in m/sec, with t in seconds. estimate the distance, s, traveled between t=0 and t=8. use the average of the left and right sums with 4 subdivisions
Answers
To estimate the distance traveled between t=0 and t=8 using the average of the left and right sums with 4 subdivisions, we can approximate the area under the velocity curve.
The average of the left and right sums is a numerical integration technique used to estimate the area under a curve. In this case, we want to estimate the distance traveled, which corresponds to the area under the velocity curve.
Given that the velocity function is v(t) = t^2 - 8, we can divide the interval [0, 8] into 4 equal subdivisions. Using the left and right sums, we evaluate the velocity at the left and right endpoints of each subdivision and multiply it by the width of each subdivision.
Calculating the estimates for each subdivision and summing them will give us an approximation of the total distance traveled between t=0 and t=8.
To perform the calculation, we evaluate the velocity at the left endpoints of each subdivision (0, 2, 4, 6) and the right endpoints (2, 4, 6, 8). Then, we multiply each velocity value by the width of the subdivision (2 units). Finally, we sum these estimated distances to obtain the approximation of the total distance traveled.
The detailed calculations would involve substituting the values into the velocity function, multiplying by the width, and summing the results.
Therefore, by using the average of the left and right sums with 4 subdivisions, we can estimate the distance traveled between t=0 and t=8 for the given velocity function.
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A pizza lover wants to compare the average delivery times for four local pizza restaurants. Over the course of a few weeks, he orders a number of pizzas from each restaurant, and he records the time it takes for each pizza to be delivered.
a) When performing an ANOVA with this data, what is the alternative hypothesis?
- All of the restaurants have different mean delivery times
- At least two of the restaurants have different mean delivery times
- Two of the restaurants have different mean delivery times
- One of the restaurants has a different mean delivery time than the others
b) A partial ANOVA table for his data is shown below. What is the value of B?
Source DF SS MS F P-value
Treatment B 19.31 D F G
Error C 15.667 E
Total 18 34.977
What is the value of C in the ANOVA table?
d) What is the value of D in the ANOVA table? Give your answer to three decimal places.
e) What is the value of E in the ANOVA table? Give your answer to three decimal places.
f) What is the value of F in the ANOVA table? Give your answer to two decimal places.
g) What is the value of G in the ANOVA table? Give your answer to four decimal places.
h) Using a 0.1 level of significance, what should his conclusion be in this case?
- He should conclude that at least two of the restaurants have different mean delivery times because the P-value is less than 0.1.
- He should fail to reject the claim that at all of the restaurants have the same mean delivery times because the P-value is greater than 0.1.
- He should conclude that at least two of the restaurants have different mean delivery times because the P-value is greater than 0.1.
- He should conclude that at all of the restaurants have the same mean delivery times because the P- value is less than 0.1.
Answers
(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.
(b)75.8
Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.
The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.
It is given that a pizza lover wants to compare the average delivery times.
Therefore the null hypothesis and alternate hypothesis implies that,
H₀ = all restaurants have equal mean delivery time
Hₐ = at least two restaurants have different two deliveries
Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.
The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.
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rectangle calc: find l, w=n/a, d=n/a
Answers
The length of the rectangle would be equal to the square root of 2 times "n/a".
To find the length (l) of a rectangle when you know the width (w) and the diagonal (d), you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (d) is equal to the sum of the squares of the other two sides (l and w). In this case, we're looking for the length (l), so we can rearrange the formula to solve for it:
d^2 = l^2 + w^2
l^2 = d^2 - w^2
l = sqrt(d^2 - w^2)
However, in your question, you say that the width (w) and the diagonal (d) are both equal to "n/a". This means that we don't actually know their specific values - we only know that they are the same.
So if we substitute "n/a" for both "w" and "d" in the Pythagorean theorem, we get:
(n/a)^2 = l^2 + (n/a)^2
2(n/a)^2 = l^2
l = sqrt(2)*n/a
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help help help helppppp
Answers
Answer:
Multiply by 2 on each side
Use distributive property to multiply x by 2 and-3 by 2.
The least expensive buttons cost
$0.28 each. Yellow bought all of
the buttons she could for $1.40 and
wore them proudly.
Answers
The number of buttons that she can wear proudly will be 5.
What are the ratio and proportion?The ratio is the division of the two numbers. In reality, ratios and proportions are only two sides of the same coin. A proportion is what results when two ratios are equal. Typically, fractions are used to define ratios and proportions. A ratio is created when we use the symbol ":" to denote a fraction, and a percentage is created when we use "::" to represent two ratios.
For example,
a/b, where a and b represent the numerator and denominator, respectively.
The relationship between two variables is called a proportion.
As per the given question,
Cost of one button = $0.28
The cost of buttons that she can wear = $1.40
A number of buttons = $1.40/$0.28 = 5
The number of buttons that she can wear proudly will be 5.
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a tree has degree sequence (6,6,6,6,4,...), where the rest of the vertex degrees are either 2 or 1. find the number of vertices with degree 1.
Answers
The tree has 11 vertices with degree 1.
To find the number of vertices with degree 1 in a tree with degree sequence (6,6,6,6,4,...), we can use the Handshaking Lemma. This lemma states that the sum of all vertex degrees in a graph is twice the number of edges. In a tree, the number of edges is one less than the number of vertices, so we can write:
6+6+6+6+4+...+2+2+1+1 = 2n-1
where n is the number of vertices. Simplifying this equation gives:
n = (6+6+6+6+4+...+2+2+1+1+1)/2 + 1
The term inside the parentheses is the sum of all vertex degrees, which we know from the degree sequence. Plugging in the values and simplifying, we get:
n = 18
So the tree has 18 vertices. Since we know that the rest of the vertex degrees are either 2 or 1, we can subtract the six vertices with degree 6 and the one vertex with degree 4 to get:
18 - 6 - 1 = 11
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A researcher conducted a one-sided hypothesis test for a proportion (Ha:p>po) and obtained a test statistic of 4.318. Which of the following are true? Check all that apply. - The observed sample proportion is 4.318 standard deviations above the claimed value po. - The large value of the test statistic means that our observed data are not surprising when the null hypothesis is true. - The researcher should fail to reject the null hypothesis. - When the null hypothesis is true, the test statistic comes from a standard normal distribution. - There is a 4.318% chance that the alternative hypothesis is true.
Answers
This statement is true, as the test statistic represents the number of standard deviations between the observed sample proportion and the claimed value (po) under the null hypothesis.
- The large value of the test statistic means that our observed data are not surprising when the null hypothesis is true. This statement is false. A large test statistic implies that the observed data is surprising when the null hypothesis is true, which means there is evidence against the null hypothesis.
- The researcher should fail to reject the null hypothesis. This statement is false. A large test statistic suggests evidence against the null hypothesis, so the researcher should reject the null hypothesis in favor of the alternative hypothesis.
- When the null hypothesis is true, the test statistic comes from a standard normal distribution. This statement is true, as the test statistic follows a standard normal distribution when the null hypothesis is true.
- There is a 4.318% chance that the alternative hypothesis is true. This statement is false. The test statistic does not directly provide the probability of the alternative hypothesis being true. Instead, we can use the test statistic to calculate the p-value, which represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.
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