The table shows the population of various cities, in thousands, and the average walking speed, in feet per second, of a person living in the city.

Chardonnay Felix
2020-12-28
Answered

The table shows the population of various cities, in thousands, and the average walking speed, in feet per second, of a person living in the city.

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toroztatG

Answered 2020-12-29
Author has **98** answers

Graph: Consider Walking speed as y-coordinates and population as x-coordinate and the table for this is given below:

Use these points to plot the scatter plot. Thus, the scatter plot for the data is: Interpretation: The data in the scatter plot increase rapidly at first and then begin to level off a bit, the shape suggests that the logarithmic function is good choice for modeling the data.

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Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. $(1,3),(2,6),(3,12),(4,24)$

Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.

Part B: Use a recursive formula to determine the time she will complete station 5.

Part C: Use an explicit formula to find the time she will complete the 9th station.

Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer.

Part B: Use a recursive formula to determine the time she will complete station 5.

Part C: Use an explicit formula to find the time she will complete the 9th station.

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Here's a problem I thought of that I don't know how to approach:

You have a fair coin that you keep on flipping. After every flip, you perform a hypothesis test based on all coin flips thus far, with significance level $\alpha $, where your null hypothesis is that the coin is fair and your alternative hypothesis is that the coin is not fair. In terms of $\alpha $, what is the expected number of flips before the first time that you reject the null hypothesis?

Edit based on comment below: For what values of α is the answer to the question above finite? For those values for which it is infinite, what is the probability that the null hypothesis will ever be rejected, in terms of $\alpha $?

Edit 2: My post was edited to say "You believe that you have a fair coin." The coin is in fact fair, and you know that. You do the hypothesis tests anyway. Otherwise the problem is unapproachable because you don't know the probability that any particular toss will come up a certain way.

You have a fair coin that you keep on flipping. After every flip, you perform a hypothesis test based on all coin flips thus far, with significance level $\alpha $, where your null hypothesis is that the coin is fair and your alternative hypothesis is that the coin is not fair. In terms of $\alpha $, what is the expected number of flips before the first time that you reject the null hypothesis?

Edit based on comment below: For what values of α is the answer to the question above finite? For those values for which it is infinite, what is the probability that the null hypothesis will ever be rejected, in terms of $\alpha $?

Edit 2: My post was edited to say "You believe that you have a fair coin." The coin is in fact fair, and you know that. You do the hypothesis tests anyway. Otherwise the problem is unapproachable because you don't know the probability that any particular toss will come up a certain way.