In the Maryland Lotto game, to win the grand prize the contestant must match six distinct numbers 1 through 49 randomly drawn by a lottery representative. What is the probability of choosing the winning numbers

Statistically meaningful results that make it possible for researchers to feel confident that they have confirmed their hypotheses is known as a statistically significant outcome.

statistically meaningful results that make it possible for researchers to feel confident that they have confirmed their hypotheses is known as statistical significance.

This means that the results are unlikely to be explained solely by chance or random factors. The p value, or probability value, tells you the statistical significance of a finding.

In most studies, a p value of 0.05 or less is considered statistically significant, but this threshold can also be set higher or lower depending on the context.

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The probability that Aaron selects a terrier, given Rebecka selects a poodle, is 1/3.

To find the probability that Aaron selects a terrier, given Rebecka selects a poodle, we need to use conditional probability.

First, we need to find the probability that Rebecka selects a poodle. Since there are four poodles out of seven puppies total, the probability that Rebecka selects a poodle is 4/7.

Next, we need to find the probability that Aaron selects a terrier, given that Rebecka has already selected a poodle. Now there are only three poodles and two terriers left in the store, so the probability that Aaron selects a terrier is 2/6 (or simplified, 1/3).

Putting it all together, we can use the formula for conditional probability:

P(Aaron selects a terrier | Rebecka selects a poodle) = P(Aaron selects a terrier and Rebecka selects a poodle) / P(Rebecka selects a poodle)

Since we know that Rebecka selects a poodle, the numerator is just the probability that Aaron selects a terrier given that there are three puppies left in the store. So:

P(Aaron selects a terrier and Rebecka selects a poodle) = (1/3) * (4/7) = 4/21

And we already calculated that P(Rebecka selects a poodle) = 4/7. So:

P(Aaron selects a terrier | Rebecka selects a poodle) = (4/21) / (4/7) = 1/3

Therefore, the probability that Aaron selects a terrier, given Rebecka selects a poodle, is 1/3.

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Ann has 21, Deandre has 31, and Bob has 42 in their wallets.

Let's start by using variables to represent the amount of money each person has:

Let A be the amount of money Ann has.

Let B be the amount of money Bob has.

Let D be the amount of money Deandre has.

We can then translate the problem into a system of equations:

A + B + D = 94 (the total amount of money they have is 94)

B = 2A (Bob has twice what Ann has)

A = D - 10 (Ann has 10 less than Deandre)

We can use the third equation to substitute A in terms of D in the first two equations:

A = D - 10

B = 2A = 2(D - 10) = 2D - 20

A + B + D = 94 => (D - 10) + (2D - 20) + D = 94 => 4D - 30 = 94 => 4D = 124 => D = 31

So Deandre has 31. We can use the third equation again to find that Ann has 21, and then we can use the second equation to find that Bob has 42.

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Answer:

31

Step-by-step explanation:

if the lenght is 10(×2), the width is 3 and the height is 4(×2). The sum of 20, 3,and 8 will be 31. That is the answer

To find the partial fraction expansion of the rational function:

f(s) = (6s^3 + 120s^2 + 806s + 1884) / (s^2 + 10s + 29)^2

We start by factoring in the denominator:

s^2 + 10s + 29 = (s + 5 - 2i)(s + 5 + 2i)

Since we have a quadratic factor repeated twice, we will have two partial fractions of the form:

A / (s + 5 - 2i) + B / (s + 5 + 2i) + C / (s + 5 - 2i)^2 + D / (s + 5 + 2i)^2

where A, B, C, and D are constants to be determined.

To find A and B, we can multiply both sides of the equation by (s + 5 - 2i)(s + 5 + 2i) and then set s = -5 + 2i and s = -5 - 2i, respectively. This gives us the equations:

A(s + 5 + 2i) + B(s + 5 - 2i) + C(s + 5 - 2i)^2 + D(s + 5 + 2i)^2 = 6s^3 + 120s^2 + 806s + 1884

Substituting s = -5 + 2i, we get:

A(3 + 2i) = -204 + 856i

Substituting s = -5 - 2i, we get:

B(3 - 2i) = -204 - 856i

Solving these equations for A and B, we get:

A = (356 + 144i) / 29

B = (-560 + 144i) / 29

To find C and D, we differentiate both sides of the equation with respect to s and then set s = -5 + 2i and s = -5 - 2i, respectively. This gives us the equations:

A + B + 2C(s + 5 - 2i) + 2D(s + 5 + 2i) = 6s^2 + 240s + 806

2C + 2D = 0

Substituting s = -5 + 2i, we get:

A + B + 4C = -176 - 264i

Substituting s = -5 - 2i, we get:

A + B + 4D = -176 + 264i

Solving these equations for C and D, we get:

C = (16 + 3i) / 58

D = (16 - 3i) / 58

Therefore, the partial fraction expansion of f(s) is:

f(s) = [(356 + 144i) / 29] / (s + 5 - 2i) + [(-560 + 144i) / 29] / (s + 5 + 2i) + [(16 + 3i) / 58] / (s + 5 - 2i)^2 + [(16 - 3i) / 58] / (s + 5 + 2i)^2

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It's important to note that correlation does not necessarily imply causation, and there may be other factors at play that contribute to the relationship between SAT scores and GPA.

The slope of 0.00362 represents the rate of change in the average GPA for every one-unit increase in the verbal SAT score. In other words, for every one-point increase in the verbal SAT score, the average GPA is expected to increase by 0.00362 points.

This suggests a positive relationship between GPA and SAT scores, indicating that students who perform better on the SAT verbal test are likely to have higher GPAs. However, it's important to note that correlation does not necessarily imply causation, and there may be other factors at play that contribute to the relationship between SAT scores and GPA.

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The functions represented on the graph are (b)

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following intervals:

When the intervals are represented as inequalities, we have the following:

This means that the intervals of the graphs are x ≤ 2 and x > 2

From the list of options, we have the graph to be option (b

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The quotients of the long division expressions are 6x^2 + 2x - 6, 7x^3 - 4x^2 + 6x + 10 and 7x^3 + x^2 - 5x - 8

Polynomial set up 2

The long division expression is represented as

x + 5 | 6x^3 + 32x^2 + 4x - 21

So, we have the following division process

           6x^2 + 2x - 6

x + 5 | 6x^3 + 32x^2 + 4x - 21

           6x^3 + 30x^2

           --------------------------------

                      2x^2 + 4x - 21

                       2x^2 + 10x

           -------------------------------------

                       -6x - 21                      

                       -6x - 30

------------------------------------------

                                   9

Polynomial set up 3

The long division expression is represented as

2x - 3 | 14x^4 - 29x^3 + 24x^2 + 2x - 29

So, we have the following division process

            7x^3 - 4x^2 + 6x + 10

2x - 3 | 14x^4 - 29x^3 + 24x^2 + 2x - 29

            14x^4 - 21x^3

           --------------------------------

                       -8x^3 + 24x^2 + 2x - 29

                       -8x^3 + 12x^2                        

           -------------------------------------

                        12x^2 + 2x - 29

                        12x^2 - 18x

     ------------------------------------------

                                  20x - 29

                                  20x - 30

     ------------------------------------------

                                               1

Polynomial set up 5

The long division expression is represented as

2x - 1 | 14x^4 - 5x^3 - 11x^2 - 11x + 8

So, we have the following division process

            7x^3 + x^2 - 5x - 8

2x - 1 | 14x^4 - 5x^3 - 11x^2 - 11x + 8

            14x^4 - 7x^3

           --------------------------------

                       2x^3 - 11x^2 - 11x + 8

                       2x^3 - x^2                        

           -------------------------------------

                        -10x^2  - 11x + 8

                        -10x^2 + 5x

     ------------------------------------------

                                  -16x + 8

                                  -16x + 8

     ------------------------------------------

                                               0

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A three-point estimate is an estimate that includes an optimistic, most likely, and pessimistic estimate, such as three weeks, four weeks, and five weeks, respectively.

A three-point estimate is an estimate that includes a range of estimates based on different scenarios: the optimistic (best-case) estimate, the most likely estimate, and the pessimistic (worst-case) estimate.

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Professor Jones is measuring the variable "number of times arrested" at the ratio level. This is because the data being collected is quantitative and possesses a true zero point, which in this case is the absence of arrests. Additionally, ratios between different values of the variable can be calculated and compared, allowing for more precise and accurate analysis of the data.

By asking for the exact number of times respondents have been arrested, Professor Jones is collecting data that can be treated numerically and used for statistical analysis at the highest level of measurement.
Ratio-level measurements have a true zero point, allowing for meaningful comparisons and mathematical operations. In this case, zero arrests can be interpreted as no occurrences, and differences or ratios between the number of arrests for different respondents can be calculated, providing valuable information for the research.

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The theorem that explains why ∠4 ≅ ∠8 is the Alternate Interior Angles Theorem. The same side interior angles pair are ∠3 and ∠5, and ∠4 and ∠8.

Alternate Interior Angles theorem states that if two parallel lines are intersected by a transversal, then the alternate interior angles formed are congruent.

The same-side interior angles are the angles that are on the same side of the transversal and inside the two parallel lines. In the given diagram, the same-side interior angle pairs are ∠3 and ∠5, and ∠4 and ∠8.

All the angle pairs formed by the intersection of the two parallel lines and the transversal are

Corresponding angles are ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8

Alternate interior angles are ∠3 and ∠5, ∠4 and ∠8

Alternate exterior angles are ∠1 and ∠7, ∠2 and ∠6

Vertical angles are ∠3 and ∠4, ∠5 and ∠6, ∠1 and ∠2, ∠7 and ∠8

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There could be several reasons why your friend bought the new set of speakers that cost three times as much as his former speakers. One reason could be that the new speakers have different features or specifications that he wanted, such as higher wattage, improved sound quality, or better frequency response. Another reason could be that he wanted to upgrade his stereo system and felt that investing in new speakers would be a good place to start. Additionally, he may have purchased the new speakers as a status symbol or simply because he had the extra money to spend. Ultimately, the decision to buy new speakers is a personal one and can depend on a variety of factors beyond just the cost or perceived quality of the speakers.

Although the new speakers might not be 3 times better, he could have bought them for various reasons such as improved sound quality, better design or aesthetics, compatibility with his current stereo system, or additional features that the former speakers did not have. The overall value of the new speakers might be greater than the cost difference for your friend.

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a) The profit function P(q) is given by the difference between the revenue function R(q) and the cost function C(q):

P(q) = R(q) - C(q) = (-q^3 + 340q^2) - (200 + 14q) = -q^3 + 340q^2 - 14q - 200

The marginal profit function is the derivative of the profit function with respect to q:

P'(q) = -3q^2 + 680q - 14

b) To find the quantity q that maximizes profit, we need to find the critical points of the profit function. These occur where the derivative P'(q) is zero or undefined. We can set P'(q) equal to zero and solve for q:

P'(q) = -3q^2 + 680q - 14 = 0

Using the quadratic formula, we get:

q = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -3, b = 680, and c = -14. Plugging in these values, we get:

q = (-(680) ± sqrt((680)^2 - 4(-3)(-14))) / 2(-3)

Simplifying, we get:

q = 113.33 or q = 204.67

The profit function P(q) is a cubic function with a negative leading coefficient, which means it opens downwards. Therefore, the maximum profit occurs at the critical point where P'(q) = 0 and P''(q) < 0 (i.e., it is a local maximum).

Taking the second derivative of the profit function, we get:

P''(q) = -6q + 680

Plugging in the two critical values we found earlier, we get:

P''(113.33) = -54.01 and P''(204.67) = 406.01

Therefore, the local maximum occurs at q = 204.67, which corresponds to 20467 units sold/produced (since q is measured in hundreds).

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Option a) is valid USPS money order identification numbers, and options b), c) and d) are not

USPS money order identification numbers consist of 10 or 11 digits, depending on when they were issued. The first digit must be either 0, 1, 3, 4, 5 or 7.

The ninth digit is always a check digit, which is calculated using a specific algorithm. To determine whether a number is a valid USPS money order identification number, we need to check whether it meets these requirements.

a) 74051489623: The first digit is 7, which is allowed. The ninth digit is 3, which is the correct check digit for this number, so it is valid.

b) 88382013445: The first digit is 8, which is not allowed. This number is not valid.

c) 56152240784: The first digit is 5, which is allowed. However, the ninth digit is 6, which is not the correct check digit for this number, so it is not valid.

d) 66606631178: The first digit is 6, which is not allowed. This number is not valid.

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The probability of choosing a student who specialized in photography is 0.2 or 20%.

To calculate the probability that a randomly chosen student specialized in photography, follow these steps:

1. Determine the total number of students at the art camp: 4 (photography) + 16 (other areas) = 20 students
2. Find the number of students who specialized in photography: 4 students
3. The probability of choosing a student who specialized in photography is the number of students who specialized in photography divided by the total number of students: 4/20 = 1/5 = 0.2

So, the probability that a randomly chosen student specialized in photography is 4/20, which can be simplified to 1/5 or 20%.

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To perform an OR operation, we compare the binary digits in each position and return 1 if either or both of the digits are 1.

a. 01010111 OR 11010111 = 11010111

To perform an OR operation, we compare the binary digits in each position and return 1 if either or both of the digits are 1.

Using this rule, we can find that the result of the OR operation of 01010111 and 11010111 is 11010111.

b. 101 OR 110 = 111

The result of the OR operation of 101 and 110 is 111.

c. 11100000 OR 10110100 = 11110100

The result of the OR operation of 11100000 and 10110100 is 11110100.

d. 00011111 OR 10110100 = 10111111

The result of the OR operation of 00011111 and 10110100 is 10111111.

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The equation of the tangent line to the curve y = 9^{x} at the point (2, 81 ) is y = 81 ln(9)x - 81 ln(9) + 81

To find the equation of the tangent line to the curve y = 9^{x} at the point (2, 81 ), we need to find the slope of the tangent line at that point. We can do this by finding the derivative of the function y = 9^{x} and evaluating it at x = 2.

y' = ln(9) * 9^{x}

y'(2) = ln(9) * 9^{2} = 81 ln(9)

So the slope of the tangent line at (2, 81) is 81 ln(9). Now we can use the point-slope form of the equation of a line to find the equation of the tangent line:

y - 81 = (81 ln(9))(x - 2)

Simplifying, we get:

y = 81 ln(9)x - 81 ln(9) + 81

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We can determine that events A and B are dependent.

Based on the given information, we can determine if the events A and B are dependent or not. Two events are considered dependent if the occurrence of one event affects the probability of the other event occurring.

In this case, we know that the probability of event A occurring given that event B happens is 0.7. This suggests that the occurrence of event B affects the probability of event A occurring. Therefore, we can conclude that events A and B are dependent.

Moreover, we can use the formula for conditional probability to calculate the probability of both events occurring together. The formula states that the probability of A and B occurring together is equal to the probability of A given B multiplied by the probability of B.

P(A and B) = P(A | B) x P(B)
P(A and B) = 0.7 x 0.2
P(A and B) = 0.14

This means that the probability of events A and B occurring together is 0.14, which is relatively low. However, since the events are dependent, it is important to consider the occurrence of event B when calculating the probability of event A.

In conclusion, based on the given information, we can determine that events A and B are dependent, and we can calculate the probability of both events occurring together using the formula for conditional probability.

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When the range of one or both of the variables is restricted, the correlation will likely be reduced. This is because correlation measures the strength of the relationship between two variables, and when the range is restricted, it means that there are fewer data points available to analyze.

As a result, the correlation coefficient may not accurately reflect the true relationship between the variables. For example, let's say we are looking at the correlation between hours of exercise per week and weight loss. If we only study people who exercise between 2-4 hours per week, the range of exercise hours is restricted. We may find a correlation coefficient of 0.6, indicating a moderate positive relationship between exercise and weight loss. However, if we expand the range to include people who exercise 0-10 hours per week, the correlation coefficient may decrease to 0.4, indicating a weaker relationship.

In summary, when the range of one or both variables is restricted, it is important to interpret the correlation coefficient with caution and consider the limitations of the data.

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When comparing two population means and the population standard deviations are not known, we substitute sample standard deviations in their place. In this situation, we rely on the t-distribution to conduct the hypothesis test.

When substituting sample standard deviations in place of unknown population standard deviations when comparing two population means, we rely on the t-distribution to conduct the hypothesis test.

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Answer:

(a) To the nearest tenth:

π = 3.1, √3 = 1.7, 2√3 = 3.4, √5 = 2.2

(b) √3, √5, π, 2√3

A good way to deal with input data that are not available is to: Estimate their values and perform a sensitivity analysis

When coming across input data that are not attainable, it may be beneficial to conduct a sensitivity analysis by estimating their values.

This process calls for utilizing accessible information and authoritative opinion to form an educated approximation of the absent data and then estimate how strongly the results of the analysis may fluctuate with alterations in those projected figures.

In this way, decision-makers become privy to the various plausible impacts respective scenarios and doubts could have on the consequence of the investigation, consequently allowing them to develop more knowledgeable decisions based on such recognition.

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The statement that is best supported by the data in the box plots is:

The median of the university is greater than community college.

The interquartile range for community college is greater than for university.

Options A and C are the correct answer.

We have,

From the box plot.

University

Median = 15

Highest hours = 16

Lowest hours = 6

Range = 16 - 6 = 10

First quartile = 9

Third quartile = 15

IQR = 15 - 9 = 6

Community college

Median = 13

Highest hours = 18

Lowest hours = 3

Range = 18 - 3 = 15

First quartile = 6

Third quartile = 15

IQR = 15 - 6 = 9

We see that,

The median of the university is greater than community college.

The interquartile range for community college is greater than for university.

Thus,

The median of the university is greater than community college.

The interquartile range for community college is greater than for university.

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This tells us that the rate of the current is zero, which means the boat is traveling on a still lake or river with no current. In this case, the boat's rate in still water is equal to its speed both upstream and downstream.

Let's denote the rate of the boat in still water as "b" and the rate of the current as "c".

When the boat is traveling upstream (against the current), its effective speed is reduced by the speed of the current, so its speed is "b - c".

When the boat is traveling downstream (with the current), its effective speed is increased by the speed of the current, so its speed is "b + c".

We know that the boat travels a distance of "d" kilometers upstream in "t" hours, so:

d = (b - c) × t

Similarly, the boat travels a distance of "d" kilometers downstream in the same amount of time, so:

d = (b + c) × t

We can solve these two equations simultaneously to find "b" and "c". One way to do this is to solve one equation for "t" and substitute into the other equation, like this:

d / (b - c) = t

Substituting into the second equation:

d = (b + c) × (d / (b - c))

Simplifying:

b - c = b + c

2c = 0

c = 0

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The top of the 17-foot ladder is sliding down the wall at a rate of -16/7.5 feet per second (negative sign indicates downward direction) when the bottom is 8 feet from the wall.

To find how fast the top of a 17-foot ladder is sliding down the wall when the bottom is 8 feet from the wall, given that the bottom slides away at a constant rate of 4 feet per second.

First, let's set up the problem using the given information. Let x represent the distance from the bottom of the ladder to the wall, and y represent the distance from the top of the ladder to the ground. According to the Pythagorean theorem, we have:

[tex]x^2 + y^2 = L^2[/tex], where L is the length of the ladder, 17 feet in this case.

Now, we are given that the bottom of the ladder, x, is sliding away from the wall at a constant rate of 4 feet per second, so dx/dt = 4 ft/s.

Our goal is to find dy/dt, the rate at which the top of the ladder is sliding down the wall, when x = 8 feet.

First, differentiate both sides of the Pythagorean equation with respect to time t:

2x(dx/dt) + 2y(dy/dt) = 0

When x = 8 feet, we can find y by plugging the value into the Pythagorean equation:

[tex]8^2 + y^2 = 17^2[/tex]
[tex]y^2 = 289 - 64[/tex]
[tex]y^2 = 225[/tex]
y = 15

Now, plug the values x = 8, y = 15, and dx/dt = 4 into the differentiated equation:

2(8)(4) + 2(15)(dy/dt) = 0

Simplify and solve for dy/dt:

64 + 30(dy/dt) = 0
dy/dt = -64 / 30
dy/dt = -16 / 7.5

Therefore, the top of the 17-foot ladder is sliding down the wall at a rate of -16/7.5 feet per second (negative sign indicates downward direction) when the bottom is 8 feet from the wall.

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When it comes to data measurement, the scales used can have a significant impact on the way data is analyzed and interpreted. The main difference between data measured on a ratio scale and data measured on an interval scale is the presence of a true zero point.

Data measured on a ratio scale has a true zero point, which means that a value of zero represents the complete absence of the characteristic being measured. This allows for meaningful ratios to be calculated, such as one value being twice as much as another. Examples of data measured on a ratio scale include weight, height, and income.

On the other hand, data measured on an interval scale does not have a true zero point. A value of zero does not represent the absence of the characteristic being measured, but rather a point on the scale. This makes it impossible to calculate meaningful ratios, as there is no true point of reference. Examples of data measured on an interval scale include temperature and IQ scores.

In summary, the main difference between data measured on a ratio scale and data measured on an interval scale is the presence or absence of a true zero point, which affects the types of calculations that can be done with the data.

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Answer: 24

Step-by-step explanation:

Volume = L x W x H

Volume = 4 x 2 x 3

Volume = 24

The mean time between requests is estimated to be 22.366 microseconds with a standard error of 2.248 microseconds.

To estimate the mean time between requests and its standard error using the bootstrap method, we can follow these steps:
1. Compute the sample mean of the given data. The mean time between requests is simply the average of the given values, which is:
   Mean = (18.77 + 28.81 + 11.87 + 15.92 + 23.2 + 21.12 + 22.79 + 39.99 + 21.86 + 15.33) / 10 = 22.366 microseconds
2. Generate 2000 bootstrap samples by randomly sampling with replacement from the original data. Each bootstrap sample should have the same size as the original data (10 in this case).
3. For each bootstrap sample, compute the mean time between requests.

4. Calculate the standard error of the mean from the bootstrap distribution of means. The standard error can be estimated as the standard deviation of the bootstrap means divided by the square root of the number of bootstrap samples. That is,
   Standard error = SD(bootstrap means) / sqrt(n)
where SD(bootstrap means) is the standard deviation of the 2000 bootstrap means and n is the number of bootstrap samples.
Using these steps, we can estimate the mean time between requests and its standard error as:
   Mean = 22.366 microseconds
   Standard error = 2.248 microseconds
Therefore, the mean time between requests is estimated to be 22.366 microseconds with a standard error of 2.248 microseconds.

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