The Yum and Yee food truck near the business school serves customers during lunch hour by taking orders and making fresh batches of stir fry. Customers have only one choice during the lunch hour, since the objective is to maximize the number of customers served. Assume that each customer places just one lunch order, and all lunch orders are the same size –one unit of stir-fry. The stir fry cooking works in this manner. First, a batch of orders is cooked in a wok by one person. The cooking depends upon the number of orders in the batch. The time to cook just one order is 3 minutes. For each additional order in the batch, it takes 0.5 minutes more to cook. Thus, cooking two orders in a batch takes 3.5 minutes, cooking three orders takes 4 minutes, and so on. The other activity is bagging and accepting payments (done by a separate person), which takes 0.80 minutes per order.

If Yum and Yee operates with batch sizes of 9 units, what is their process capacity (in orders per miute)?

Reba Dixon is a fifth-grade school teacher who earned a salary of $38,400 in 2018. She is 45 years old and has been divorced for four years. She receives $1,235 of alimony payments each month from her former husband (divorced in 2016). Reba also rents out a small apartment building. This year Reba received $50,400 of rental payments from tenants and she incurred $19,656 of expenses associated with the rental.

Reba and her daughter Heather (20 years old at the end of the year) moved to Georgia in January of this year. Reba provides more than one-half of Heather’s support. They had been living in Colorado for the past 15 years, but ever since her divorce, Reba has been wanting to move back to Georgia to be closer to her family. Luckily, last December, a teaching position opened up and Reba and Heather decided to make the move. Reba paid a moving company $2,080 to move their personal belongings, and she and Heather spent two days driving the 1,440 miles to Georgia.

Reba rented a home in Georgia. Heather decided to continue living at home with her mom, but she started attending school full-time in January at a nearby university. She was awarded a $3,070 partial tuition scholarship this year, and Reba helped out by paying the remaining $570 tuition cost. If possible, Reba thought it would be best to claim the education credit for these expenses.

Reba wasn't sure if she would have enough items to help her benefit from itemizing on her tax return. However, she kept track of several expenses this year that she thought might qualify if she was able to itemize. Reba paid $5,870 in state income taxes and $12,570 in charitable contributions during the year. She also paid the following medical-related expenses for herself and Heather:

Insurance premiums $ 5,865

Medical care expenses $ 1,170

Prescription medicine $ 350

Nonprescription medicine $ 170

New contact lenses for Heather $ 270

Shortly after the move, Reba got distracted while driving and she ran into a street sign. The accident caused $970 in damage to the car and gave her whiplash. Because the repairs were less than her insurance deductible, she paid the entire cost of the repairs. Reba wasn’t able to work for two months after the accident. Fortunately, she received $2,070 from her disability insurance. Her employer, the Central Georgia School District, paid 60% of the premiums on the policy as a nontaxable fringe benefit and Reba paid the remaining 40% portion.

A few years ago, Reba acquired several investments with her portion of the divorce settlement. This year she reported the following income from her investments: $2,270 of interest income from corporate bonds and $1,570 interest income from the City of Denver municipal bonds. Overall, Reba’s stock portfolio appreciated by $12,070 but she did not sell any of her stocks.

Heather reported $6,340 of interest income from corporate bonds she received as gifts from her father over the last several years. This was Heather’s only source of income for the year.

Reba had $10,000 of federal income taxes withheld by her employer. Heather made $1,000 of estimated tax payments during the year. Reba did not make any estimated payments. Reba had qualifying insurance for purposes of the Affordable Care Act (ACA).

Is Reba allowed to file as a head of household or single?

b Determine the amount of FICA taxes Reba was required to pay on her salary. (Round your final answer to the nearest whole dollar amount.)

c Determine Heather’s federal income taxes due or payable. Use Tax Rate Schedule, Dividends and Capital Gains Tax Rates, Estates and Trusts for reference. (Round your intermediate

d computations and final answer to the nearest whole dollar amount.)

Kate deposits P5,000 to her bank account every year when she was in high school for four years to prepare for her college degree. She took an engineering course and since then, she stopped depositing to her bank account. Right after graduation (she graduated on time), she got a job that pays P250,000 a year. If she continues to deposit to the same bank account P50,000 every year for 10 years, calculate the future worth after 30 years if the deposits are made at the end of each year and the bank pays 2% interest per year

Austin Clemens is writing a report for his high school environmental science class about the city’s climate. To impress his teacher, Austin would like to show evidence that the population mean daily low temperature during the five-year period from 1998–2002 is less than the population mean daily low temperature during the five-year period from 2013–2017. He researches the claim using a website that records all of the weather data observed at a local airport. After conducting the research, Austin assumes that the population standard deviation is 10.48∘F for 1998–2002 and 11.29∘F for 2013–2017. Due to the large amount of data in each five-year period, Austin randomly selects the daily low temperatures for each group. The sample statistics are shown in the table below. Let μ1 be the population mean daily low temperature during the five-year period from 1998–2002 and μ2 be the population mean daily low temperature during the five-year period from 2013–2017. The p-value rounded to three decimal places is 0.192, the significance level is α=0.10, the null hypothesis is H0:μ1−μ2=0, and the alternative hypothesis is Ha:μ1−μ2<0.

1998–2002 2013–2017 x

x=44.31∘F x2=46.02

n=59 n=63

Which of the following statements are accurate for this hypothesis test to evaluate the claim that the difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is less than zero? Select all that apply:

A)Reject the null hypothesis that the true difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is equal to zero.

B)Fail to reject the null hypothesis that the true difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is equal to zero.

C)Based on the results of the hypothesis test, there is not enough evidence at the α=0.10 level of significance to suggest that the true difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is less than zero.

D)Based on the results of the hypothesis test, there is enough evidence at the α=0.10 level of significance to suggest that the true difference between the population mean daily low temperature during the five-year period from 1998–2002 and the population mean daily low temperature during the five-year period from 2013-2017 is less than zero.

High school graduates: Approximately 78% of freshmen entering public high schools in the United States in 2005 graduated with their class in 2009. A random sample of 128 freshmen is chosen.

(a)Find the mean μp

.(b)Find the standard deviation σp

.

(c)Find the probability that less than 91% of freshmen in the sample graduated.

(d)Find the probability that between 68%and 83% of freshmen in the sample graduated.

(e)Find the probability that more than 68%of freshmen in the sample graduated.Cumulative Normal Distribution Table as needed. Round your answers to at least four decimal places if necessary.

An education minister would like to know whether students at Gedrassi high school on average perform better at English or at Mathematics. Denoting by μ₁ the mean score for all Gedrassi students in a standardized English exam and μ₂ the mean score for all Gedrassi students in a standardized Mathematics exam, the minister would like to get a 95% confidence interval estimate for the difference between the means: μ₁ - μ₂.

A study was conducted where many students were given a standardized English exam and a standardized Mathematics exam and their pairs of scores were recorded. Unfortunately, most of the data has been misplaced and the minister only has access to scores for 4 students.

The populations of test scores are assumed to be normally distributed. The minister decides to construct the confidence interval with these 4 pairs of data points. This Student's t distribution table may assist you in answering the following questions.

a)Calculate the lower bound for the confidence interval. Give your answer to 3 decimal places.

Lower bound =

b)Calculate the upper bound for the confidence interval. Give your answer to 3 decimal places.

Upper bound =

An assistant claims that there is no difference between the average English score and the average Math score for a student at Gedrassi high school.

c)Based on the confidence interval the minister constructs, the claim by the assistant

be ruled out.

In a survey of

184184

females who recently completed high​ school,

7575​%

were enrolled in college. In a survey of

175175

males who recently completed high​ school,

7272​%

were enrolled in college. At

alpha equals 0.06α=0.06​,

can you reject the claim that there is no difference in the proportion of college enrollees between the two​ groups? Assume the random samples are independent. Complete parts​ (a) through​ (e).

​(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

The claim is​ "the proportion of female college enrollees is

▼

less than

the same as

greater than

different than

the proportion of male college​ enrollees."Let

p 1p1

represent the population proportion for female college enrollees and

p 2p2

represent the population proportion for male college enrollees. State

Upper H 0H0

and

Upper H Subscript aHa.

Choose the correct answer below.

A.

Upper H 0H0​:

p 1p1less than or equals≤p 2p2

Upper H Subscript aHa​:

p 1p1greater than>p 2p2

B.

Upper H 0H0​:

p 1p1not equals≠p 2p2

Upper H Subscript aHa​:

p 1p1equals=p 2p2

C.

Upper H 0H0​:

p 1p1equals=p 2p2

Upper H Subscript aHa​:

p 1p1not equals≠p 2p2

D.

Upper H 0H0​:

p 1p1greater than or equals≥p 2p2

Upper H Subscript aHa​:

p 1p1less than<p 2p2

E.

Upper H 0H0​:

p 1p1greater than>p 2p2

Upper H Subscript aHa​:

p 1p1less than or equals≤p 2p2

F.

Upper H 0H0​:

p 1p1less than<p 2p2

Upper H Subscript aHa​:

p 1p1greater than or equals≥p 2

(b) Find the critical​ value(s) and identify the rejection​ region(s).

The critical​ value(s) is(are)

nothing.

​(Use a comma to separate answers as needed. Type an integer or a decimal. Round to two decimal places as​ needed.)

Identify the rejection​ region(s). Select the correct choice below and fill in the answer​ box(es) within your choice. ​(Round to two decimal places as​ needed.)

A.

nothingless than<zless than<nothing

B.

zgreater than>nothing

C.

zless than<nothing

and

zgreater than>nothing

D.

zless than<nothing

​(c) Find the standardized test statistic.

zequals=nothing

​(Round to two decimal places as​ needed.)

​(d) Decide whether to reject or fail to reject the null hypothesis.

Choose the correct answer below.

Fail to rejectFail to reject

Upper H 0H0

because the test statistic

is notis not

in the rejection region.

Fail to rejectFail to reject

Upper H 0H0

because the test statistic

isis

in the rejection region.

RejectReject

Upper H 0H0

because the test statistic

is notis not

in the rejection region.

RejectReject

Upper H 0H0

because the test statistic

isis

in the rejection region.

​(e) Interpret the decision in the context of the original claim.

Choose the correct answer below.

A.At the

66​%

significance​ level, there is

sufficientsufficient

evidence to support the claim.

B.At the

66​%

significance​ level, there is

sufficientsufficient

evidence to reject the claim.

C.At the

66​%

significance​ level, there is

insufficientinsufficient

evidence to support the claim.

D.At the

66​%

significance​ level, there is

insufficientinsufficient

evidence to reject the claim.

High school graduates: Approximately

78%

of freshmen entering public high schools in the United States in

2005

graduated with their class in

2009

. A random sample of

128

freshmen is chosen. Use

(a)Find the mean

μp

.(b)Find the standard deviation

σp

.

(c)Find the probability that less than

91%

of freshmen in the sample graduated.

(d)Find the probability that between

68%

and

83%

of freshmen in the sample graduated.

(e)Find the probability that more than

68%

of freshmen in the sample graduated.

Cumulative Normal Distribution Table as needed. Round your answers to at least four decimal places if necessary.

High school graduates: Approximately

74%

of freshmen entering public high schools in the United States in

2005

graduated with their class in

2009

. A random sample of

175

freshmen is chosen. Use Cumulative Normal Distribution Table as needed. Round your answers to at least four decimal places if necessary.

(a)Find the mean

μp

.

Part 2 of 6

(b)Find the standard deviation

σp

.

Part 3 of 6

(c)Find the probability that less than

75%

of freshmen in the sample graduated.

Part 4 of 6

(d)Find the probability that between

64%

and

78%

of freshmen in the sample graduated.

Part 5 of 6

(e)Find the probability that more than

64%

of freshmen in the sample graduated.

Part 6 of 6

(f)Would it be unusual if the sample proportion of freshmen in the sample graduated was more than

83%

?