Yes, it can be concluded that this year's average time for women to finish the SF Marathon is statistically significantly different from the past year's average time based on the sample data and statistical analysis.
To determine if the difference is statistically significant, we can perform a hypothesis test. We will set up the null hypothesis ([tex]H_0[/tex]) as the average time for this year's marathon being equal to the past year's average time, and the alternative hypothesis ([tex]H_a[/tex]) as the average time being different.
We can use a t-test to compare the means. With a sample size of 3845 and a known population standard deviation of 1.11 hours, we can calculate the test statistic using the formula:
t = (sample mean - population mean) / (standard deviation / √sample size)
Substituting the values, we can calculate the test statistic. By comparing it to the critical value from the t-distribution, we can determine if the difference is statistically significant.
If the test statistic falls in the rejection region (outside the critical value), we reject the null hypothesis and conclude that there is a statistically significant difference between the average times. However, if the test statistic falls within the acceptance region, we fail to reject the null hypothesis, indicating no significant difference.
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In "Saving Tobe", why does Serafin risk his life to help Tobe when he is in danger of drowning in the river?
Question 8 options:
His wife and children are watching, and he knows they expect him to act.
He is the first person to arrive at the river and feels responsible to act.
His brother drowned and he cannot bear to watch it happen to someone else.
He is the person who is most qualified to attempt to save Tobe
Serafin risks his life to help Tobe when he is in danger of drowning in the river in "Saving Tobe" because he is the person who is most qualified to attempt to save Tobe.
In the story "Saving Tobe," Serafin risks his life to save Tobe because he is a great swimmer and knows how to swim in that river. He is aware of the fact that if he doesn't do anything about it, Tobe will die. Furthermore, he understands that if Tobe dies, the community will be shaken because Tobe is an integral part of the community. Serafin also realizes that he is the only one capable of saving Tobe and that if he doesn't act quickly, Tobe will perish.In addition, Serafin's actions are motivated by the fact that he sees himself in Tobe. Tobe reminds him of his younger self. Serafin also remembers how hard it was for him when he lost his brother to the river. He believes that he could have done something about it but was powerless at that time. Serafin now has the opportunity to do something about it, and he takes the chance.
In conclusion, Serafin risks his life to save Tobe because he understands the gravity of the situation, is the most qualified to perform the rescue, and sees himself in Tobe. Serafin is motivated by the prospect of saving Tobe's life and preventing the community from being shattered. He is also motivated by the opportunity to make amends for his previous failure to save his brother.
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Find any domain restrictions on the given rational equation:
2/3x^2+x/2=x+5/x
The domain restrictions for the given rational equation are x ≠ 0 and x ≠ -10.
To identify the domain restrictions of the rational equation, we need to consider values of x that would result in undefined expressions or division by zero.
Looking at the equation: 2/3x^2 + x/2 = (x + 5)/x
x ≠ 0: The expression involves division by x, so x = 0 would result in division by zero, which is undefined. Therefore, x ≠ 0 is a domain restriction.
x ≠ -10: If x = -10, the equation would have a denominator of 0 on the right-hand side, resulting in division by zero, which is undefined. Hence, x ≠ -10 is a domain restriction.
In summary, the domain restrictions for the given rational equation are x ≠ 0 and x ≠ -10. These restrictions ensure that the equation remains defined and avoids division by zero.
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Help me please with this angle
The measure of the missing angle of the geometric system is equal to 55°.
How to determine the measure of a missing angle
In this problem we find a geometric system formed three supplementary angles, that is, three angles whose measures sum a total of 180°. We need to determine the measure of the missing angle. The equation that describes the situation is:
α + 90° + 35° = 180°
Then, the angle is found by algebra properties:
α + 125° = 180°
α = 55°
The missing angles has a measure of 55°.
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The average age of CEO's is 54 years. Assume the variable is normally distributed. If the standard deviation is 3 years, find the probability that the age of a randomly selected CEO will be at least 61 years. Round answers to 4 decimal places.
The probability of selecting a CEO with an age of at least 61 years is approximately 0.0099 or 0.99%.
To find the probability that the age of a randomly selected CEO will be at least 61 years, we need to use the properties of the standard normal distribution.
Given that the average age of CEOs is 54 years and the standard deviation is 3 years, we can assume that the variable follows a normal distribution. The normal distribution is a bell-shaped curve that is symmetric around the mean.
To calculate the probability, we first need to standardize the value of 61 using the z-score formula. The z-score measures the number of standard deviations a given value is from the mean.
The z-score formula is given by:
z = (x - μ) / σ
Where:
x is the value we want to standardize (61 in this case),
μ is the mean of the distribution (54 in this case),
and σ is the standard deviation of the distribution (3 in this case).
By substituting the values into the formula, we get:
z = (61 - 54) / 3
z = 7 / 3
z ≈ 2.3333
The resulting z-score is approximately 2.3333.
Now, we need to find the probability to the right of this z-score in the standard normal distribution. This represents the probability of selecting a CEO whose age is at least 61 years.
Using a standard normal distribution table or a calculator, we can look up the area to the right of the z-score of 2.3333. The probability to the right of 2.3333 is approximately 0.0099.
Rounding to 4 decimal places, we find that the probability that the age of a randomly selected CEO will be at least 61 years is 0.0099.
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