If an observed statistic from a study turns out to be a likely value under the chance model, then it is possible that the observed result occurred by chance.
What happens if an observed statistic from a study turns out to be a likely value under the chance model?In statistics, a chance model is a model that describes the distribution of outcomes that would be expected if there were no underlying effect of the variable being studied.
In other words, it represents the distribution of outcomes that would be expected purely by chance.
When conducting a hypothesis test, researchers compare the observed statistic (such as a mean, proportion) from their study to the distribution of values that would be expected under the chance model.
If the observed statistic is a likely value under the chance model, then this suggests that the observed result could plausibly have occurred by chance, and not due to the effect of the variable being studied.
For example, imagine a study that investigates whether a new drug is effective at reducing cholesterol levels in patients.
The researchers compare the mean cholesterol levels of patients who received the drug to those who received a placebo.
If the observed difference in means is a likely value under the chance model then this suggests that the observed difference could have occurred by chance, and not necessarily due to the drug's effect.
However, it's important to note that just because an observed statistic is a likely value under the chance model does not necessarily mean that the result was due to chance.
There may be other factors at play that are not accounted for in the chance model. That's why statistical inference is always probabilistic and subject to some degree of uncertainty.
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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.
Which null hypothesis would be correct for a single sample t-test?
a. μ=c
b. μâ = μâ
c. μâ c
d. μ is not related to c.
The correct null hypothesis for a single sample t-test is "a. μ=c".
What is a single sample t-test?A single sample t-test is used to determine whether the mean of a sample is significantly different from a hypothesized value, usually denoted by "c".
The test compares the sample mean to the hypothesized value and determines whether the observed difference is large enough to reject the null hypothesis.
The null hypothesis for a single sample t-test is always that the population mean is equal to the hypothesized value, which is expressed mathematically as:
H0: μ = c
where μ is the population mean and c is the hypothesized value.
The alternative hypothesis, which represents the opposite of the null hypothesis, is that the population mean is not equal to the hypothesized value, expressed as:
Ha: μ ≠ c
If the calculated t-value from the test is larger than the critical t-value at the chosen level of significance (usually 0.05), then we reject the null hypothesis and accept the alternative hypothesis.
This means that we have sufficient evidence to conclude that the sample mean is significantly different from the hypothesized value.
On the other hand, if the calculated t-value is smaller than the critical t-value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the sample mean is significantly different from the hypothesized value.
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How many home runs would Homer need to hit next season to have a 12-year mean of 60?
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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A farmer is pouring milk into a cylindrical tank with diameter 5m. If the level of milk is rising with the rate of 0.25m/min find at what rate milk is pouring into the tank. Round your answer to the nearest tenth.
The rate at which milk is pouring into the tank is approximately [tex]4.91 m^3/min[/tex], rounded to the nearest tenth.
We can begin by using the formula for the volume of a cylinder:
[tex]V = \pi r^2h[/tex]
where V is the volume of the milk in the tank, r is the radius of the tank (which is half the diameter), and h is the height of the milk in the tank.
Since the diameter of the tank is 5m, the radius is 2.5m. We can differentiate the formula for the volume of a cylinder with respect to time to find the rate at which the volume of milk is increasing:
[tex]dV/dt = \pi r^2 dh/dt[/tex]
where dV/dt is the rate at which the volume of milk is increasing and dh/dt is the rate at which the height of the milk is increasing.
We are given that dh/dt = 0.25m/min, so we can substitute in the values we know:
[tex]dV/dt =\pi (2.5)^2 (0.25)\\\\dV/dt =4.91 m^3/min[/tex]
Therefore, the rate at which milk is pouring into the tank is approximately [tex]4.91 m^3/min[/tex], rounded to the nearest tenth.
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given x+3y=k and x-k=y which of the following is equal to x
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.
Given a conditional statement p→q, find the converse of its inverse, the converse of its converse, and the converse of its contrapositive
The truth value of the inverse and converse may be different from the original statement and its contrapositive.
To find the different forms of a conditional statement, we first need to understand the different components of a conditional statement.
In the conditional statement "p → q," p is the hypothesis or antecedent, and q is the conclusion or consequent.
The inverse of "p → q" is "not p → not q."
The converse of "p → q" is "q → p."
The contrapositive of "p → q" is "not q → not p."
So, here are the different forms of the given conditional statement:
Inverse: The inverse of "p → q" is "not p → not q." The converse of the inverse is "not q → not p."
Converse: The converse of "p → q" is "q → p." The inverse of the converse is "not q → not p."
Contrapositive: The contrapositive of "p → q" is "not q → not p." The converse of the contrapositive is "not p → not q."
Note that the original conditional statement and its contrapositive always have the same truth value, as do the inverse and converse. However, the truth value of the inverse and converse may be different from the original statement and its contrapositive.
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True or false: The central limit theorem tells us about the sampling distribution of the sample standard deviation.
Answer:
Step-by-step explanation:
false
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.
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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How many times can 5 go into 11
Answer:
Step-by-step explanation:2
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?
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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Ignore my answer but I need help asap I’m confused
The amount of principal after one month would be B. 72. 67.
How to find the principal ?In order to ascertain the amount of principal after one month, we must compute both the interest and principal segments of the initial monthly payment.
Initially, let us derive the sum for the first month's interest. The yearly rate of interest culminates to 19%; thus, applying the relevant mathematical formula leads to determination of the ensuing monthly interest rate:
= 19 % / 12
= 0. 015833
The interest portion on the payment is:
= 1, 800 x 0. 015833
= $ 28. 50
The principal is therefore:
= 101. 06 monthly payment - 28. 50
= $ 72. 67
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For ð inputs, there are ___ subsets of those features!
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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You survey students about whether they like board games or video games. One hundred thirty of the students like board games, with 71 of them responding that they dislike video games. One hundred thirty-eight of the students dislike board games, with 53 of them responding that they like video games. Organize the results in a two-way table. Include the marginal frequencies
The results in a two-way table and the marginal frequencies are given below.
We have,
To organize the results in a two-way table:
Like Video Games Dislike Video Games Total
Like Board Games ? 71 130
Dislike Board Games 53 ? 138
Total 191 209 400
Since there are 130 students who like board games, we know that 71 of them dislike video games.
Like Board Games and Video Games
= Total who Like Board Games - Dislike Video Games
= 130 - 71
= 59
Similarly, since there are 138 students who dislike board games, and we know that 53 of them like video games,
So,
Dislike Board Games and Video Games
= Total who Dislike Board Games - Like Video Games
= 138 - 53
= 85
We can now fill in the missing cells in the table:
Like Video Games Dislike Video Games Total
Like Board Games 59 71 130
Dislike Board Games 53 85 138
Total 112 156 268
We can also calculate the marginal frequencies, which are the totals for each row and column:
Total who Like Board Games: 130
Total who Dislike Board Games: 138
Total who Like Video Games: 112
Total who Dislike Video Games: 156
Grand Total: 268 (which is the same as the total number of students surveyed)
Thus,
The results in a two-way table and the marginal frequencies are given above.
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MZYX=pi/3 radians. Covert this radian measure to its equivalent degree measure.
60°
120°
180°
300°
MZYX=pi/3 radians is equivalent to 60 degrees. To convert radians to degrees, we use the formula: degree measure = (radian measure) x (180/π)
So, to convert MZYX=pi/3 radians to degrees, we plug in the value:
degree measure = (pi/3) x (180/π)
The π in the numerator and denominator cancel out, leaving:
degree measure = (1/3) x 180
Simplifying, we get:
degree measure = 60
Therefore, MZYX=pi/3 radians is equivalent to 60 degrees.
It's important to understand the concept of radians and degrees when dealing with angles. Radians are a unit of measure for angles, just like degrees. However, while degrees divide a circle into 360 equal parts, radians divide a circle into 2π equal parts. One radian is the angle formed at the center of a circle when the length of the arc on the circumference is equal to the radius of the circle.
In summary, to convert radians to degrees, we use the formula: degree measure = (radian measure) x (180/π). We can use this formula to convert any angle given in radians to its equivalent measure in degrees.
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Ingrid and Harish were trying to solve the equation: x^2-3x=x+1
ngrid said, "First, I'll subtract x from both sides so I have x^2-4x=1. Then I can solve by completing the square. If I add 444 to each side, I can rewrite the equation as (x-2)^2=5
Harish said, "I'll isolate the x^2 term by adding 3x to both sides of the equation. Then I'll solve by taking the square root."
Whose solution strategy would work?
Both Ingrid's and Harish's solution strategies are correct and would work.
Ingrid's solution involves completing the square, which is a commonly used method to solve quadratic equations. By subtracting x from both sides and adding a constant to complete the square, she rewrites the equation in a form that allows her to take the square root of both sides and solve for x.
Harish's solution involves isolating the x^2 term by adding 3x to both sides of the equation, which also works. He would then have a quadratic equation in standard form that he can solve using the quadratic formula or factoring. Both methods have their advantages and disadvantages, and the choice of which method to use depends on the specific equation and the problem at hand.
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If there is no difference between what is observed and what is expected, your chi-square value will be ______. a. -1 b. 0 c. 1 d. impossible to determine
The answer is (b) 0.
what is observed and what is expected, your chi-square value will be a. -1 b. 0 c. 1 d. impossible to determineIf there is no difference between what is observed and what is expected, it means that the observed frequencies match the expected frequencies perfectly. In other words, the observed data fits the expected distribution perfectly, and there is no deviation from the expected values.In this case, the numerator of the chi-square formula, which is the sum of the squared differences between observed and expected values, will be equal to zero. Therefore, the chi-square value will also be equal to zero.So, if there is no difference between what is observed and what is expected, the chi-square value will be 0.
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If the F in Anova is NOT significant, then __________________.
a. the variability between the means is due to individual differences + error.
b. the variability within each group is due to individual differences + error
c. You should just do a post hoc test.
d. Who cares. I want to go home!
some of the group means are different, but not which pairs of groups.
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
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.
Use long division to divide 
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 can Adam use the scale factor to find the area of the actual electronics board? Remember, he uses a different method than Jason.
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.
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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Continuity correction x = fewer than 8 (doesn't include 8)
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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What dimensions would I need to find the volume of the following prism?
The dimensions which would be needed to find the volume of the following prism as required are; base of the triangle, height of the triangle and height of the prism.
Which dimensions would be needed to find the volume?It follows from the task content that the dimensions needed to find the volume of the given prism is to be determined.
On this note, since the given prism is a triangular prism. Its volume is a function of the triangular base area and the height of the prism.
Consequently, since the base area of the triangle depends on the base and height of.the triangle;
The required dimensions to calculate the volume of the prism are; base of the triangle, height of the triangle and height of the prism.
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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
Answer:
you are correct but
the 11th is not 90-71 = 19°
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%
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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What are the degrees of freedom for the F statistic for testing the null hypothesis that all five of the regression coefficients for the explanatory variables are zero
The degrees of freedom for the F statistic for testing the null hypothesis that all five of the regression coefficients for the explanatory variables are zero are (5, n-6).
What is the F statistic's degrees of freedom formula for a five-explanatory variable regression model?The degrees of freedom for the F statistic in a regression model with five explanatory variables can be calculated using the formula (5, n-6), where n is the sample size.
In a regression model, the F statistic is used to test the null hypothesis that all of the regression coefficients for the explanatory variables are zero.
When the null hypothesis is true, the F statistic follows an F distribution with degrees of freedom (5, n-6). The numerator degrees of freedom, 5, represent the number of restrictions on the coefficients, and the denominator degrees of freedom, n-6, represent the error degrees of freedom.
The F statistic compares the variability explained by the model to the variability that is not explained by the model.
If the calculated F statistic is larger than the critical value from the F distribution with (5, n-6) degrees of freedom at a given significance level, we reject the null hypothesis and conclude that at least one of the regression coefficients is not zero.
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Marjorie has 28 feet of trim to use as edging on a rectangular blanket she wants to make. What is the length and width of two blanket sizes she can make
Possible size for the blanket is 8 feet by 6 feet.
Let's assume the length of the blanket is L and the width is W.
The perimeter of a rectangle is given by the formula P = 2L + 2W.
In this case, Marjorie has 28 feet of trim, so we can set up the equation:
2L + 2W = 28
To find two different combinations of length and width that satisfy this equation, we can try different values. Here are two possibilities:
Let's assume L = 10 feet, then the equation becomes:
2(10) + 2W = 28
20 + 2W = 28
2W = 8
W = 4
So, one possible size for the blanket is 10 feet by 4 feet.
Let's assume L = 8 feet, then the equation becomes:
2(8) + 2W = 28
16 + 2W = 28
2W = 12
W = 6
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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
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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A pet store employee orders 4 boxes of cat treats. Each box is 26 inches high and has 21 bags of cat treats. Each bag has 16 ounces of cat treats. How many ounces of cat treats does the employee order?
1, 344 ounces of cat treats the employee order.
We have,
Each box is 26 inches high and has 21 bags of cat treats.
Each bag has 16 ounces of cat treats.
So, the ounce of cat treats order
= 4 x 21 x 16
= 84 x 16
= 1344 ounce
Thus, 1, 344 ounces of cat treats the employee order.
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what is the formal definition for the pythagorean theorem in english words?
The Pythagorean Theorem is a mathematical theorem that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In other words, a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides. This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. The Pythagorean Theorem is one of the most well-known and widely used theorems in mathematics and has numerous applications in fields such as architecture, engineering, and physics.
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