Suppose that Serena has a .7 probability of defeating Venus in a set of tennis, independently from set to set. For questions 1 – 3, suppose that they play a best-of-three-set match, meaning that the first player to win two sets wins the match.

1. Determine the probability that Serena wins the match by winning the first two sets.

2. Determine the probability that the match requires three sets to be played (meaning that each player wins one of the first two sets).

3. Determine the probability that Serena wins the best-of-three-set match.

For questions 4 – 5, suppose that they play a total of three sets, regardless of who wins the sets.

4. Determine the probability that Venus wins at least one of the three sets.

5. Determine the probability that Serena wins at least two of the three sets.

Two soccer players, Mary and Jane, begin running from nearly the same point at the same time. Mary runs in an easterly direction at 4.34 m/s, while Jane takes off in a direction 60.9^o north of east at 5.71 m/s. How long is it before they are 26.7 m apart?

What is the velocity of Jane relative to Mary? Enter first the x-component and then the y-component.

How far apart are they after 3.96 s?

Suppose Elizabeth Warren has a 66% chance of becoming the Democratic Party candidate for President, and Kamala Harris has a 34% chance of becoming the Democratic Party candidate in 2020. If Donald Trump runs against Elizabeth Warren, he has a 40% chance of winning the election. If Donald Trump runs against Kamala Harris, he has a 35% chance of winning the election. If Trump loses the election, what is the probability that he ran against Elizabeth Warren?

The family planning wing of the health department of a certain state wishes to conduct a survey at a university campus for estimating the average time gap between the births of children in families having two children. The frame available, of course, lists all the 400 families of the campus. As the prior identification of the families in the population, who have just two children was difficult, the investigator selected a WOR random sample of 50 families. In the sampled families, 20 families were found having two children. These 20 families were interviewed, and the information collected was:

Estimate the average gap between the births of two children, and obtain confidence limits for it.

**New code needed! Please do not reference code that has already been answered for this question as that code contains errors***

Write a C++ program to simulate a service desk. This service desk should be able to service customers that can have one of three different priorities (high, medium, and low). The duration for any customer is a random number (between 5 minutes and 8 minutes). You need to write a program that will do the following:

1. Generate random 100 service requests.
2. Each service request can be either high, medium, or low priority. (Your program should randomly allocate this priority to each service.)
3. Each service request may need any time to be serviced between 5 and 8 minutes. (Your program should randomly allocate this time to each service.)
4. Your program should simulate the case when you have one service station for all customers.
5. Your program should simulate the case when you have two service stations for these 100 customers.
6. For each case, output the following statistics:
   1. The number of requests for each priority along with the service time for each request
   2. The waiting time for each service request
   3. The average waiting time for service requests within each priority

You should submit your C++ source code along with screen shots of sample runs that showed successful runs for the above steps.

A scientist believes that the frequency of cricket chirping is a good predictor of the ambient temperature. A random sample produced the following data where x is the number of cricket chirps in one minute and y is the ambient temperature in Fahrenheit.

1. (a) Find an equation of the least squares regression line. Round the slope and y-intercept value to two decimal places.
2. (b) Based on the equation from part (a), what is the predicted temperature when a cricket chirps 170 times in one minute?
3. (c) Based on the equation from part (a), what is the predicted temperature when a cricket chirps 320 times in one minute?
4. (d) Which predicted temperature that you calculated for (b) and (c) do you think is closer to the true temperature and why?

prepare the following journal entries:

1) The company sold (5) payroll service packages, covering 6 months of fully automated payroll service for $6,000 each. The regular price was $6,500 each, but the customers received a discount for paying for the service up front. Each company will receive 2 payroll runs per month. One on the 15th and one on the 30th of each month.

2) The company provided $5,600 of tax consulting services to clients on account.

3) The company ran its first payroll service for two of the companies. The other three companies were not yet ready to begin running payroll.

4) The company paid $2,100 cash for two weeks salary earned by two employees.

5) The company purchased $950 for October advertising on account.

6) The company provided $8,200 of tax services to clients and received payment.

7) The company paid a $687 electic bill for October utilities.

8) The company collected $2,000 from clients that were provided service on account on the 13th.

9) The company paid 1/2 of the bill for paper and supplies that was purchased on the 8th.

10) The company paid $2,100 cash for two weeks salary earned by two employees.

11) The company ran payroll service for all five companies that purchased service in October. 30 The company paid dividends of $700.

12) An employee and received a $300 advance for November travel for the company.

For two sets ? and ?, their Jaccard similarity, denoted ?(?,?), is defined as

?(?,?) =
|? ∩ ?| |? ∪ ?|


where |?| is the size of set ?; ? ∩ ? is the intersection of ? and ?, that is the elements in both of ? and ?; and ? ∪ ? is the union of ? and ?, that is the elements in at least one of ? and ?. For example, if ? = {1,2,3,4} and ? = {2,4,6,8}, then ? ∩ ? = {2,4} and ? ∪ ? = {1,2,3,4,6,8} so

?(?,?) =
|? ∩ ?| |? ∪ ?|
=
|{2,4}| |{1,2,3,4,6,8}|
=
2 6
=
1 3


Write a method, jaccard, that given two sets represented as HashSets, returns their Jaccard similarity. The skeleton for the method is provided in the file Jaccard.java.

The following are a few sample runs:

Input : ? = [1, 2, 3, 4], ? = [2, 4, 6, 8] Return: 0.333333⋯

Input : ? = ["???ℎ???", "?ℎ??", "????", "??????", "????ℎ"] ? = ["?ℎ??", "?????", "????", "??????", "????ℎ", "??????"] Return: 0.375

import java.util.*;

public class Jaccard<T> {
   /**
   * Computes the Jaccard similarity of two sets represented as HashSets.
   *
   * Time Complexity: O(n) where n is the smaller of the sizes of the two input sets.
   *
   * @param A HashSet representation of one of the two input sets
   * @param B HashSet representation of the other of the two input sets
   * @return the Jaccard similarity of A and B
   */
   public double jaccard(HashSet<T> A, HashSet<T> B) {
      
       //Replace this line with your return statement
       return -1;
   }
}

public static java.lang.String mergeWithRuns​(java.lang.String t, java.lang.String s)

Merges two strings together, using alternating characters from each, except that runs of the same character are kept together. For example,

• mergeWithRuns("abcde", "xyz") returns "axbyczde"
• mergeWithRuns("abbbbcde", "xyzzz") returns "axbbbbyczzzde"

Either or both of the strings may be empty. If the first string is nonempty, its first character will be first in the returned string.

Parameters:

t - first string

s - second string

Returns:

string obtained by merging characters from t and s, preserving runs