Answers
The list that contains three equivalent expressions is given as follows:
KT/KS, KN/KL, cos K.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For triangle KLN, we have that:
KL is the hypotenuse.KN is adjacent to angle K.Hence:
cos(K) = KN/KL.
For triangle KTS, we have that:
KS is the hypotenuse.KT is adjacent to angle K.Hence:
cos(K) = KT/KL.
As the two triangles are similar, they have the same trigonometric ratios.
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Related Questions
Systematic sampling and cluster sampling are examples of which type of sampling method used in human research
Answers
Systematic sampling and cluster sampling are examples of probability sampling methods used in human research. These methods are employed to ensure that each participant in the population has a known, non-zero chance of being selected, which helps in obtaining representative samples and drawing more accurate conclusions.
Systematic sampling and cluster sampling are both examples of probability sampling methods used in human research.
Probability sampling methods involve randomly selecting participants from a larger population, giving each individual an equal chance of being selected.
Systematic sampling involves selecting every nth participant from a list of the population, while cluster sampling involves dividing the population into clusters or groups and then randomly selecting entire clusters to include in the study.
These methods are considered to be more representative and unbiased than non-probability sampling methods, which do not involve random selection and may not accurately reflect the characteristics of the population.
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given x+3y=k and x-k=y which of the following is equal to x
Answers
To solve the system of equations the value of k must be:
x = k
How to find the value of x in terms of k?Here we have the system of equations:
x + 3y = k
x - k = y
We want to solve the equation for x in terms of k, so let's do that.
We can see that y is isolated in the second equation, so let's replace that in the first equation:
x + 3*(x - k) = k
Now we need to isolate x.
x + 3x - 3k = k
4x = k + 3k
4x = 4k
x = 4k/4 = k
x = k
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Answer:
K.
Step-by-step explanation:
To find the value of x, we can substitute x-k for y in the first equation: x + 3(x-k) = k. Simplifying, we get 4x - 3k = k. Adding 3k to both sides, we get 4x = 4k, or x = k. Therefore, x is equal to k.
For ð inputs, there are ___ subsets of those features!
Answers
For ð inputs, there can be an infinite number of subsets of those features. This is because a subset is a collection of some or all of the features within the inputs. Therefore, the number of possible subsets is determined by the number of possible ways in which we can choose from the available features.
For instance, if we have three features within an input, we can create subsets of one, two, or all three features. This gives us a total of seven possible subsets. However, this is not the only way in which we can create subsets. We can also create subsets that contain no features or any combination of features, which increases the number of possible subsets even further.
Therefore, the total number of possible subsets for ð inputs is limitless. It is important to note that not all subsets will be relevant or useful, but the more subsets we have, the more options we have for creating effective models or making informed decisions based on the inputs and features.
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For ð inputs, there can be an infinite number of subsets of those features. This is because a subset is a collection of some or all of the features within the inputs. Therefore, the number of possible subsets is determined by the number of possible ways in which we can choose from the available features.
For instance, if we have three features within an input, we can create subsets of one, two, or all three features. This gives us a total of seven possible subsets. However, this is not the only way in which we can create subsets. We can also create subsets that contain no features or any combination of features, which increases the number of possible subsets even further.
Therefore, the total number of possible subsets for ð inputs is limitless. It is important to note that not all subsets will be relevant or useful, but the more subsets we have, the more options we have for creating effective models or making informed decisions based on the inputs and features.
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A blue van and a red van, each having 9 passenger seats, have arrived to take ten people to the airport. In how many ways can the passengers be placed into the vans
Answers
There are 6,158,592 ways to place the passengers into the vans.
Since each van has 9 passenger seats and there are a total of 10 people, it is not possible to place all of them in one van.
Thus, we need to consider two cases:
9 people in the blue van, 1 person in the red van.
There are 10 ways to choose the person who will ride in the red van, and the remaining 9 people will go in the blue van.
There is only 1 way to arrange the passengers in the red van, and 9! ways to arrange the passengers in the blue van.
The total number of ways for this case is:
10 x 9! = 3,628,800
8 people in the blue van, 2 people in the red van.
There are 45 ways to choose the two people who will ride in the red van, and the remaining 8 people will go in the blue van.
There are 2 ways to choose which person will sit in which seat in the red van, and 8!/(2!6!) ways to arrange the passengers in the blue van.
The total number of ways for this case is:
45 × 2 × (8!/2!6!) = 45 × 2 × 28 × 7! = 2,529,792
The total number of ways to place the passengers into the vans is:
3,628,800 + 2,529,792 = 6,158,592
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When is a Greenhouse- Geisser correction required?
a. when you do not have homogeneity of variance.
b. whenever you do an LSD-t test.
c. when you find a significant interaction effect.
d. when you do not have sphericity
Answers
Greenhouse- Geisser correction required when you do not have sphericity.
The Greenhouse-Geisser correction is a statistical method used to adjust for violations of sphericity in repeated measures ANOVA.
Sphericity assumes that the variances of the differences between all possible pairs of repeated measures are equal. When this assumption is violated, the Greenhouse-Geisser correction can be used to adjust the degrees of freedom to account for the non-sphericity and provide more accurate p-values.
Therefore, the correction is required when you do not have sphericity.
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Conducting multiple t-tests on the same DV inflates the ______________________.
a. per comparision alpha
b. experiment wise alpha
c. joint power
d. ego of the statician
Answers
Conducting multiple t-tests on the same DV inflates the experiment wise alpha.
How to find the conducting multiple t-tests when comparing multiple groups on the same dependent variable?When conducting multiple t-tests on the same dependent variable, there is an increased probability of committing a Type I error, which is rejecting the null hypothesis when it is actually true. This is because the more tests that are performed, the more likely it is that one or more of them will produce a significant result by chance alone.
The per comparison alpha is the probability of committing a Type I error on a single test, which is typically set at 0.05 (or 0.01) level of significance. When multiple tests are conducted, the probability of committing a Type I error across all tests, known as the experiment-wise alpha, increases. This means that the overall likelihood of falsely rejecting at least one null hypothesis increases with each additional test.
Therefore, it is important to adjust the alpha level for multiple comparisons using appropriate statistical techniques, such as Bonferroni correction or False Discovery Rate (FDR) control. These methods help to maintain a desirable experiment-wise error rate and control the risk of falsely rejecting the null hypothesis.
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What is the distance between points (12,16) and (3,6)
Answers
THEOREM 5 If A is an invertible n x n matrix, then for each b in R", the equation Ax = b has the unique solution x = A-'b.
PROOF Take any b in R" A solution exists because if A-lb is substituted for x, then AX = A(A-1b) = (AA-))b = Ib = b. So A-1b is a solution. To prove that the solution is unique, show that if u is any solution, then u, in fact, must be A-'b. Indeed, if Au = b, we can multiply both sides by A- and obtain
A- Au = A-'b, Tu= A-'b, and u=A-'b
The Invertible Matrix Theorem
Let A be a square n x n matrix. Then the following statements are equivalent. That is, for a given A, the statements are either all true or all false.
a. A is an invertible matrix.
b. A is row equivalent to the n x n identity matrix.
c. A has n pivot positions. d. The equation Ax = 0 has only the trivial solution.
e. The columns of A form a linearly independent set.
f. The linear transformation x H Ax is one-to-one.
g. The equation Ax = b has at least one solution for each b in R".
h. The columns of A span R".
i. The linear transformation x # Ax maps R" onto R".
j. There is an n x n matrix C such that CA = I.
k. There is an n x n matrix D such that AD = I.
l. AT is an invertible matrix.
Because of Theorem 5 in Section 2.2, statement (g) in Theorem 8 could also be written as "The equation Ax = b has a unique solution for each b in R" " This statement certainly implies (b) and hence implies that A is invertible.
These are in David C. Lay's Linear Algebra fifth edition.
My question is: Why (g) and Theorem 5 are equivalent? I think (g) also include the infinite solutions case and unique solution case. So they are not equivalent.
Answers
(g) and Theorem 5 are not equivalent.
Are (g) and Theorem 5 equivalent?
You are correct. Statement (g) in Theorem 8, which states that the equation Ax = b has at least one solution for each b in R", includes both the case of a unique solution and the case of infinitely many solutions.
Therefore, (g) is not equivalent to Theorem 5, which specifically states that the equation Ax = b has a unique solution x = A^(-1)b when A is an invertible matrix. The equivalence mentioned in the text seems to be an error or a misinterpretation.
The correct interpretation is that Theorem 5 implies statement (g) in Theorem 8, but the converse is not necessarily true.
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hello guys! is these questions correct?
if you can NOT see :
1 ) 47•
2 ) 44•
3 ) 65 •
4 ) 32•
5 ) 55•
6 ) 15•
7 ) 69•
8 ) 65•
9 ) 29•
10 ) 19 •
11 ) 161•
12 ) 36
thanks! have a good day
Answers
Answer:
you are correct but
the 11th is not 90-71 = 19°
True or false: The central limit theorem tells us about the sampling distribution of the sample standard deviation.
Answers
Answer:
Step-by-step explanation:
false
2.1.17
Solve the equation AB=BC for​ A, assuming that​ A, B, and C are square matrices and B is invertible.
A=_?_
Answers
The solution for the equation AB=BC is A = B(CB⁻¹), given that B is invertible.To solve the equation AB=BC for A, assuming that A, B, and C are square matrices and B is invertible, follow these steps:
1. Since B is invertible, it means it has an inverse matrix, denoted as B⁻¹.
2. To isolate A, you can multiply both sides of the equation by the inverse of B.
3. Multiply B⁻¹ to the right side of both equations: (AB)B⁻¹= (BC)B⁻¹.
4. Remember that matrix multiplication is associative, so you can rearrange the parentheses: A(BB⁻¹) = B(CB⁻¹).
5. Since the product of a matrix and its inverse is the identity matrix (I), we have AI = B(CB⁻¹).
6. As multiplying by the identity matrix doesn't change the original matrix, we can simplify the equation to A = B(CB⁻¹).
Now, you have isolated A, and the solution for the equation AB=BC is A = B(CB⁻¹).
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Given the root of a Binary Search Tree (BST), convert it to a Greater Tree such that every key of the original BST is changed to the original key plus the sum of all keys greater than the original key in BST.
As a reminder, a binary search tree is a tree that satisfies these constraints:
The left subtree of a node contains only nodes with keys less than the node's key.
The right subtree of a node contains only nodes with keys greater than the node's key.
Both the left and right subtrees must also be binary search trees.
Answers
We recursively call `reverseInorder` on the left child of the current node. This ensures that we visit all the nodes in the tree.
so be binary search trees.
To convert the BST to a Greater Tree, we can perform a reverse inorder traversal of the tree. In a normal inorder traversal, we visit the nodes in ascending order of their keys. However, in a reverse inorder traversal, we visit the nodes in descending order of their keys.
During the reverse inorder traversal, we maintain a running sum of all keys greater than the current key. For each node, we add this running sum to the node's key and update the running sum to include the current node's key.
Here is the Python code to perform the above algorithm:
```
class TreeNode:
def __init__(self, val=0, left=None, right=None):
self.val = val
self.left = left
self.right = right
class Solution:
def convertBST(self, root: TreeNode) -> TreeNode:
self.sum = 0
self.reverseInorder(root)
return root
def reverseInorder(self, node: TreeNode) -> None:
if not node:
return
self.reverseInorder(node.right)
node.val += self.sum
self.sum = node.val
self.reverseInorder(node.left)
```
We first initialize a running sum variable `self.sum` to 0 and call the `reverseInorder` function on the root node. The `reverseInorder` function is a recursive function that performs the reverse inorder traversal.
In the `reverseInorder` function, we first check if the current node is None. If it is, we return without doing anything.
Next, we recursively call `reverseInorder` on the right child of the current node. This ensures that we visit the nodes in descending order of their keys.
After visiting the right subtree, we add the current node's value to the running sum and update the node's value to the new sum. This effectively converts the node to its new value in the Greater Tree.
Finally, we recursively call `reverseInorder` on the left child of the current node. This ensures that we visit all the nodes in the tree.
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Simon makes 30 cakes
He gives 1/5 of the cakes to Sali
He gives 10% to Jane
What fraction of the 30 cakes does Simon have left?
ANSWER:
1/5 of 30 = 6
10% of 30 = 3
30 - 9 = 21
21/30 = 7/10
Answers
So Simon has [tex]7/10[/tex] of the original cakes left.
What fraction of does Simon have left?Simon gives 1/5 of the cakes to Sali:
= 30 * 1/5
= 6 cakes.
Simon gives 10% of the cakes to Jane:
= 10% * 30
= 3 cakes.
The total number of cakes Simon gives away is:
= 6 + 3
= 9 cakes.
So, Simon is left with 30 - 9 = 21 cakes.
To express this as a fraction of the original 30 cakes, we will simplify as:
= 21/30
= 7/10.
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During a sale, a store advertised that every item in the store was 35 percent off the marketed price. During this sale, what was the cost, in dollars, of an item that was marked x dollars
Answers
Step-by-step explanation:
35 % means you pay 65% or .65
if x is the original price the discounted price is $ .65 x
Use long division to divide 
Answers
Answer:
3682÷7 = 526
Step-by-step explanation:
7×5 = 35 minus it equal 1 put down the 8 and 7×2=14 minus the 18 equal 4 put down the 2 equal 42 so 7×6 is 42 minus it equal 526.
How do we solve this question
In a class of 31 students, 16 play football, 12 play table tennis and 5 play both games
(1) find the number of student who play
(i) at least one of the games
(ii) none of the games
Answers
Answer:
Step-by-step explanation:
Using the inclusion-exclusion principle, we can find the number of students who play at least one of the games as follows:
Number of students who play at least one of the games = number of students who play football + number of students who play table tennis - number of students who play both games
= 16 + 12 - 5
= 23
Therefore, 23 students play at least one of the games.
To find the number of students who play none of the games, we can subtract the number of students who play at least one of the games from the total number of students:
Number of students who play none of the games = total number of students - number of students who play at least one of the games
= 31 - 23
= 8
Therefore, 8 students play none of the games.
The city park is in the shape of a parallelogram. Mowers cut the grass along the base first for 50m. If the company cuts 1000m of grass, what is the height of the parallelogram.
Answers
The height of the parallelogram is equal to 20 meters.
How to calculate the area of this parallelogram?In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = b × h
Where:
b represents the base area of a parallelogram.h represents the height of a parallelogram.By substituting the given parameters into the formula for the area of a parallelogram, we have the following;
Area of a parallelogram, A = b × h
1000 = 50 × h
Height, h = 1000/50
Height, h = 20 meters.
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Washington Street and N. South St. is 3.2 km long from the north there are no cross streets for the first 1.2 km then there are four cross streets each an equal distance apart how far apart are the cross streets
A.50 meters
B.80meters
C.500 meters
D.800 meters
Answers
Each cross street is 500 m far apart from each other.
Given that a scenario of three streets, Washington Street and N. South St. is 3.2 km long from the north.
There are no cross streets for the first 1.2 km then there are four cross streets each an equal distance apart,
So,
We need to find the distance between each street,
3.2-1.2 = 2 km
Therefore, all the 4 streets collectively are of length 2 km,
Since, each of them have equal distance so,
4s = 20 [say s is the length of one street]
s = 0.5 km
s = 500 meters
Hence, each cross street is 500 m far apart from each other.
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In the 1960 presidential election, 34,226,731 people voted for Kennedy; 34,108,157 for Nixon, and 197,029 for third-party candidates. Would it be appropriate to find a confidence interval for the proportion of voters choosing Kennedy
Answers
Answer:
Yes, it would be appropriate to find a confidence interval for the proportion of voters choosing Kennedy since we have the necessary information (number of people who voted for Kennedy, number of people who voted for Nixon, and number of third-party votes) and the sample size (total number of voters) is large enough to assume a normal distribution. A confidence interval can provide an estimate of the true proportion of voters who chose Kennedy and the level of uncertainty around that estimate.
IXL HELP FAST PLEASE
Answers
Answer:
i think its 18
Step-by-step explanation:
Determine the equation of a quadratic function that has a minimum at (-2,-3) and passes through (-1,1)
Answers
The equation of the quadratic function is:
f(x) = 4(x + 2)^2 - 3
To determine the equation of a quadratic function, we can start with the general form of a quadratic equation:
f(x) = ax^2 + bx + c
Given that the quadratic function has a minimum at (-2, -3), we know that the vertex of the parabola is at (-2, -3). The x-coordinate of the vertex gives us the value of the line of symmetry, which is also the value of the x-coordinate at the minimum point. Thus, we have:
x = -2
To find the coefficient "a" of the quadratic function, we can use the fact that the vertex form of a quadratic function is given by:
f(x) = a(x - h)^2 + k
where (h, k) is the vertex. Substituting the values of the vertex (-2, -3) into the vertex form, we get:
f(x) = a(x - (-2))^2 + (-3)
f(x) = a(x + 2)^2 - 3
Now, we can use the fact that the quadratic function passes through the point (-1, 1). Substituting these coordinates into the equation, we get:
1 = a(-1 + 2)^2 - 3
1 = a(1)^2 - 3
1 = a - 3
a = 4
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52. On average, 400 people a year are
struck by lightning in the United States (The Boston Globe, July 21,2008)
a. What is the probability that at most 425 people are
struck by lightning in a year? b. What is the probability that at least 375 people are struck by lightning in a year?
Answers
To solve this problem, we can use the Poisson distribution, which models the number of events that occur in a fixed period of time, given the average rate of occurrence.
a. To find the probability that at most 425 people are struck by lightning in a year, we can use the Poisson distribution with a mean of 400. The formula for the Poisson distribution is:
P(X ≤ k) = e^-λ ∑_(i=0)^k (λ^i/i!)
where X is the random variable (the number of people struck by lightning in a year), λ is the mean (400), and k is the maximum number of people we're interested in (425). Plugging in the values, we get:
P(X ≤ 425) = e^-400 ∑_(i=0)^425 (400^i/i!) = 0.8855
So the probability that at most 425 people are struck by lightning in a year is 0.8855, or about 88.55%.
b. To find the probability that at least 375 people are struck by lightning in a year, we can use the complement rule: the probability of an event happening is 1 minus the probability of the event not happening. So in this case, we want to find the probability that fewer than 375 people are struck by lightning, and subtract that from 1 to get the probability of at least 375 people being struck.
P(X ≥ 375) = 1 - P(X < 375) = 1 - e^-400 ∑_(i=0)^374 (400^i/i!) = 0.9369
So the probability that at least 375 people are struck by lightning in a year is 0.9369, or about 93.69%.
It's important to note that these probabilities are based on the assumption that the number of people struck by lightning in a year follows a Poisson distribution with a mean of 400. This may not be a perfect model, but it's a reasonable approximation based on the available data. Additionally, the chances of being struck by lightning are still relatively low - even at the high end of our estimates, only about 0.1% of the US population would be affected.
Based on the given information of 400 people being struck by lightning in the United States on average each year, we can calculate the probabilities for the scenarios you mentioned.
a. The probability that at most 425 people are struck by lightning in a year:
To calculate this, we'll need to know the distribution of people being struck by lightning, which isn't provided. However, let's assume it follows a normal distribution with a mean of 400 and some standard deviation. In this case, we would calculate the z-score for 425 people and find the corresponding probability from the z-table. Unfortunately, without the standard deviation, we cannot compute the exact probability.
b. The probability that at least 375 people are struck by lightning in a year:
Similarly, to calculate this probability, we'd need the standard deviation to find the z-score for 375 people and then find the corresponding probability from the z-table. Again, without the standard deviation, we cannot compute the exact probability.
In conclusion, without knowing the standard deviation or the distribution of people being struck by lightning, we cannot provide a precise probability for the given scenarios.
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Continuity correction x = fewer than 8 (doesn't include 8)
Answers
The main answer, incorporating the continuity correction, is P(X < 8.5), where X represents a random variable.
How to use continuity correction method?To calculate the probability of X being fewer than 8 (excluding 8) with continuity correction, we can use the normal approximation to the binomial distribution.
Assuming X follows a binomial distribution, we can approximate it with a normal distribution by adjusting the boundaries of the interval. In this case, since we want fewer than 8 (excluding 8), we use the continuity correction and consider the interval as (X < 8.5).
We can then calculate the probability using the cumulative distribution function (CDF) of the normal distribution for X = 8.5. The resulting probability represents the likelihood of observing fewer than 8 (excluding 8) occurrences.
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Write the output when the input is n input 6 8 9 n output 1 3 4
Answers
The output for the given inputs 6, 8, and 9 is 1, 3, and 4 respectively.
Based on the given input-output relationship, we can see that the output is obtained by subtracting 5 from the input. Let's apply this rule to the given inputs:
Input: 6
Output: 6 - 5 = 1
Input: 8
Output: 8 - 5 = 3
Input: 9
Output: 9 - 5 = 4
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Lisette is saving money from her part-time job
to buy a car. Which of the following equations
represents this situation if y represents the
total amount of money that Lisette has saved
after x pay checks?
Lisette's Savings
X
у
3
1032
5
1072
7
1112
9
1152
y = 20x - 972
y - 1112 =
20 (x-7)
= 20x +972
Y
y =
-20x - 972
y = -20x +972
y + 1112 = 20 (x + 7)
Answers
The equation that represents the situation is y = 2x + 1062
Identifying the equation that represents the situationFrom the question, we have the following parameters that can be used in our computation:
x y
3 1032
5 1072
7 1112
9 1152
A linear equation is represented as
y = mx + c
Using the points, we have
3m + c = 1032
5m + c = 1072
So, we have
2m = 40
Divide
m = 2
Next, we have
5(2) + c = 1072
This gives
c = 1062
So, the equation is
y = 2x + 1062
Hence, the equation that represents the situation is y = 2x + 1062
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5
Fancy is building a toy house where 2 inches on the plan is equivalent to 11 inches on the actual toy house.
If the house is to be 35.75 inches tall, what will the height be on the plan? Show your work using the scratchpad.
The height in the plan will be
inches.
Answers
2 inches on plan / 11 inches on toy house = x inches on plan / 35.75 inches on toy house
To solve for x, we can cross-multiply:
(2/11) * 35.75 = x
6.5 = x
Therefore, the height on the plan will be 6.5 inches.
#6
Find the area of the sector formed by ZKJL. Round your
answer to the nearest hundredth.
M
9m
40°
Brevious
K
L
The areas of the small and large sectors are about
square meters, respectively.
3
C
&
3
square meters and
Answers
Area of small sector is 1620 square meters and Area of large sector is 12960 square meters
Area of sector = 1/2r²θ
r is the radius of the circle which is 9cm
The area of small and large sectors we have to find
Small sector has θ value of 40 degrees
and large sector has 320 degrees
Area of small sector = 1/2(9)²×40
=1/2×81×40
=1620 square meters
Area of large sector = 1/2(9)²×320
=81×160
=12960 square meters
Hence, area of small sector is 1620 square meters and Area of large sector is 12960 square meters
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Given H0: P = 0.25, Ha: P â 0.25, and P-value = 0.094. The test rejected the null hypothesis. Which LaTeX: \alpha α (level of significance) was used for making a decision in this hypothesis testing?
A. alpha = 1%
B. alpha = 10%
C. alpha = 5%
D. alpha = 4%
Answers
The level of significance chosen for this hypothesis testing is 5%. In this hypothesis testing scenario, the null hypothesis (H0) is that the population proportion (P) is equal to 0.25 and the alternative hypothesis (Ha) is that P is not equal to 0.25.
The P-value is 0.094, which is the probability of observing a sample proportion at least as extreme as the one obtained if the null hypothesis were true.
Since the test rejected the null hypothesis, it means that the P-value is less than the chosen level of significance (alpha), indicating that the data provides enough evidence to reject the null hypothesis. Therefore, the alpha level chosen for this test must be greater than 0.094.
The only answer choice that satisfies this condition is C, where alpha = 5%. This means that there is a 5% chance of rejecting the null hypothesis when it is actually true. In other words, the level of significance chosen for this hypothesis testing is 5%.
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At Woodbridge Middle School’s annual concert, for every 2 popular tunes played 3 classical tunes were played, for a ratio of popular to classical of 2: 3. If they played 10 popular and classical tunes in all, how many classical tunes were played?
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At Woodbridge Middle School's annual concert, 6 classical tunes were played.
The given ratio of popular to classical tunes played is 2:3, which means that for every 2 popular tunes played, 3 classical tunes were played. Let's assume that the number of popular tunes played is '2x' (since the ratio of popular to classical tunes is 2:3) and the number of classical tunes played is '3x'. Therefore, the total number of tunes played is:
2x + 3x = 5x
We are given that the total number of popular and classical tunes played is 10, so we can write:
5x = 10
Dividing both sides by 5, we get:
x = 2
Therefore, the number of popular tunes played is:
2x = 2 x 2 = 4
And the number of classical tunes played is:
3x = 3 x 2 = 6
So, at Woodbridge Middle School's annual concert, 6 classical tunes were played.
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How many home runs would Homer need to hit next season to have a 12-year mean of 60?
Answers
The number of home runs that Homer would need to hit next season to have a 12-year mean of 60 is given as follows:
98.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
The sum of the observations, considering next year's amount as x, is given as follows:
25 + 49 + 51 + 52 + 56 + 58 + 62 + 64 + 65 + 68 + 72 + x = 622 + x.
Hence, for a mean of 60, the value of x is obtained as follows:
(622 + x)/12 = 60
622 + x = 720
x = 98.
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