The accompanying data table show the percentage of tax returns filed electronically in a city from 2000 to 2009. Complete parts a through e below.

Year   Percentage
2000   25
2001   33
2002   37
2003   38
2004   48
2005   50
2006   55
2007   59
2008   62
2009   64

a) Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with alpha= 0.1.

​b) Calculate the MAD for the forecast in part a.

c) Forecast the percentage of tax returns that will be electronically filed for 2010 using exponential smoothing with trend adjustment. Set alpha= 0.3 and beta= 0.4.

​d) Calculate the MAD for the forecast in part c.

Cherub purchased a financial asset on 1 October 2019, which it measured at fair value through other comprehensive income, in accordance with its business model. The asset had a nominal value of $12 million, a coupon rate of 3% payable in arrears and was purchased on market for $10 million. The effective rate of interest is 6% and the fair value of the asset at the reporting date of 30 September 2020 was $9 million. At the reporting date, the financial asset’s credit risk was low, with twelve-month expected credit losses of $0.3 million and lifetime expected credit losses of $0.8 million.

Required:

Discuss how this financial asset is recognised and measured in the year ended 30 September 2020, with calculations.         

Given the monthly returns that follow, find the R2, alpha, and beta of the portfolio. Compute the average return differential with and without sign. Do not round intermediate calculations. Round your answers to two decimal places. Month Portfolio Return S&P 500 Return January 5.3 % 5.5 % February -2.4 -2.9 March -1.8 -1.1 April 2.5 2.0 May 0.9 0.5 June -1.1 -0.5 July 0.2 0.4 August 1.3 1.7 September -0.8 -0.1 October -3.2 -3.8 November 2.8 2.3 December 0.8 0.3

R2:

Alpha: %

Beta:

Average return difference (with signs): %

Average return difference (without signs) %

Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard. Suppose thatP(A) = 0.7and P(B) = 0.3.

(a)Could it be the case thatP(A ∩ B) = 0.5?

Why or why not?

(b) From now on, suppose thatP(A ∩ B) = 0.2.

What is the probability that the selected student has at least one of these two types of cards?

(c)What is the probability that the selected student has neither type of card?

(d)Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard.

Calculate the probability of this event.

(e) Calculate the probability that the selected student has exactly one of the two types of cards.

You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:

HoHo : pA=0.1pA=0.1;  pB=0.4pB=0.4;  pC=0.3pC=0.3;  pD=0.2pD=0.2

Complete the table. Report all answers accurate to three decimal places.

What is the chi-square test-statistic for this data?
χ2=χ2=

What is the P-Value?
P-Value =  


For significance level alpha 0.005,

What would be the conclusion of this hypothesis test?

• Reject the Null Hypothesis
• Fail to reject the Null Hypothesis

Report all answers accurate to three decimal places.

A 6 meter tall concrete column 40 cm square is supporting a 4 MN compressive load. The concrete has an elastic modulus of 30 GPa, compressive strength of 28 MPa, tensile strength of 3.5 MPa and Poisson’s Ratio 0.3. The concrete is reinforced by 16 #8 W40 axial rebar (200 GPa elastic modulus, 275 MPa compressive strength), spaced 8 cm apart on each side, 8 cm from the surface of the column.

What is the compressive stress on the column?

What is the axial modulus of the reinforced concrete column?

What is the axial deflection (change in length) of the column?

What is the transverse change in dimension (change in width)?

Will this column fail? Why?

Calculate ?(? < 8) if: (i) ? is the number of distinctions reported in a year by 20 Colleges. Each College produces distinctions at the rate of 0.2 per year independently of the other Colleges. (ii) ? is the number of claims examined up to and including the fourth claim that exceeds K20,000. The probability that any claim received exceeds K20,000 is 0.3 independently of any other claim. (iii) ? is the number of deaths amongst a group of 500 TB patients. Each patient has a 0.01 probability of dying independently of any other patient. (iv) ? is the number of phone calls made before an agent makes the first sale. The probability that any phone call leads to a sale is 0.01 independently of any other call.

A CSTR activated sludge system is being designed for the Fulton Fish Processing Plant. The flow is relatively small (0.25 mgd), but the wastewater is strong due to all of the fish waste (BOD5 = 4500 mg/L). Primary settling removes 20% of the BOD5. In order to discharge to the town sewer the BOD5 must be reduced to a concentration that is 95% of the influent. What is the Dimensions of the basin assuming a 3:1 L:W ratio. Also, what is the sludge production rate?

Design Parameters

θc = 10 days

X = 2100 mg VSS/L

MLVSS is 75% of MLSS

Aeration Basin = 20 ft deep

Yobs = 0.3 mg MLSS/mg BOD5

Recycle Ratio = 50%

a)An object of mass ?m rests on a horizontal frictionless surface. A constant horizontal force of magnitude ?F is applied to the object. This force produces an acceleration:

• always
• only if ?F is larger than the weight of the object
• only while the object suddenly changes from rest to motion
• only if ?F is increasing

choice A

b)Now let there be friction between the surface and the object. If the object has a mass of 10 kg, and ??μs = 0.4, and ??=0.3μk=0.3, how much force would be required to cause the object to move?

c)If this force is then applied continuously, how far will the object be displaced after 4.8 seconds?

d)How fast will it be going after pulling with the same force above for 4.8 seconds?