The State of DeNile built a new toll road 3 years ago for $900 million. The state can charge tolls on the road for the next 20 years and expects to spend $3 million per year on maintenance and toll collection. Toll revenue is expected to be $80 million per year. The state has recently received an offer from the Otto Corporation to lease the road for 20 years. The company will pay DeNile $1 billion and will receive exclusive rights to collect and keep the tolls. Otto Corp will also be responsible for all maintenance and other expenses. The state can invest its money at 6% annual return. Should the state take this offer? Why or why not?

A sump pump (used to drain water from the basement of houses built below the water table) is draining a flooded basement at the rate of 0.55 L/s, with an output pressure of 2.95 × 105 N/m2.

A. The water enters a hose with a 2.8 cm inside diameter and rises 2.2 m above the pump. What is its pressure at this point N/m2? You may neglect frictional losses.

B. The hose goes over the foundation wall, losing 0.65 m in height, and widens to 4.6 cm in diameter. What is the pressure now in N/m2? You may neglect frictional losses.

1.If an inverting voltage amplifier with a large gain were built to amplify a small sinusoidal
signal and the output waveform was observed to be sinusoidal but with a much lower
amplitude than predicted by a theoretical analysis assuming an ideal operational amplifier,
what non ideal property of the operational amplifier would be likely contributing to this
degradation in performance?
40

warpbreaks is a built-in R dataset which gives This data set gives the number of warp breaks per loom, where a loom corresponds to a fixed length of yarn. We are interested in some descriptive statistics related to the warpbreaks dataset. We can access this data directly and convert the time series into a vector by using the assignment x <- warpbreaks$breaks. (In R, use ? warpbreaks for info on this dataset.) The values of x if assigned as above are:


[1] 26 30 54 25 70 52 51 26 67 18 21 29 17 12 18 35 30 36 36 21 24 18 10 43 28 15
[27] 26 27 14 29 19 29 31 41 20 44 42 26 19 16 39 28 21 39 29 20 21 24 17 13 15 15
[53] 16 28

You should get these values from the R assignment rather than manually copying.

h. What proportion of the x values are within 1 sample standard deviations away from the sample mean
i. Calculate the range of x. (one number)
j. How many times does the minimum value of x appear?
k. How many of the elements of x are smaller than the sample mean of x?

1. Luci and Sherry have decided to lease some newly built premises for the purpose of opening a seafood outlet. They intend to provide a wide range of different products, including a variety of seafood for sale and take-away fish and chips.

Discuss the types of economic decisions that they will be required to make, and the information that they will need to make those decisions. Distinguish non-economic and economic information, identify non-economic decisions that they will also be required to make. Discuss why Luci and Sherry may require the services of an accountant.

A high-rise tower built by a developer contains 200 condominium units. The QA department of the developer has to approve the tower before turning it over to sales. The QA department will select a random sample of 8 units and inspect them. If more than three major defects are found in any unit, they will reject the unit as defective. If more than 2 of the 8 inspected units are defective, the entire tower will be rejected. If 10 of the 200 units are known to have more than three major defects, what is the probability that the tower will be rejected?

A business built a simple linear regression model from a sample of 20 units. The resulting linear model equation is y' = 7.53 + 0.225x.

The correlation coefficient is 0.55. What is the value of the t critical value used to make the rejection region for the test "Is the correlation coefficient significantly different from zero?"  α= 0.01

A multivariate logistic regression model has been built to predict the propensity of

shoppers to perform a repeat purchase of a free gift that they are given. The

descriptive features used by the model are the age of the customer, the

socio-economic band to which the customer belongs (a, b, or c), the average amount

of money the customer spends on each visit to the shop, and the average number of

visits the customer makes to the shop per week. This model is being used by the

marketing department to determine who should be given the free gift. The weights in

the trained model are shown in the table below:

Feature Weight

Intercept -3.82398

Age -0.02990

Socio Economic Band B -0.09089

Socio Economic Band C -0.19558

Shop Value 0.02999

Shop Frequency 0.74572

Using this model to make predication for each of the following query instances:

ID Age Socio Economic Band Shop Frequency Shop Value

1 56 B 1.60 109.32

2 21 C 4.92 11.28

3 48 B 1.21 161.19

4 37 C    0.72 170.65

5   32 A 1.08 165.39