1. Give an example of the 4 steps of the scientific method as applied to objects in motion

2.  A mass of 10 Kg is accelerating at 3 m/s². What is the applied net force?

2. A mass of 10 Kg is accelerating at 3 m/s². What is the applied net force?

(1 point) Is the point (−4,−5,3) visible from the point (4,5,0) if there is an opaque ball of radius 1 centred at the origin? Suppose that you stand at the point (4,5,0) and look in the direction of a point that is not visible because it is behind the ball. You will then be looking at a point on the sphere. If (−4,−5,3) is not visible from (4,5,0), find the point on the sphere at which you are looking if you look in the direction of (−4,−5,3). Otherwise, find the point on the sphere at which you look if you are looking in the direction of (−4,−5,2). Point (?,?,?)=

1. Consider a biased dice, where the probability of rolling a 3 is 4 9 . The dice is rolled 7 times. If X denotes the number of 3’s thrown, then find the binomial distribution for x = 0, 1, . . . 7 and complete the following table (reproducing it in your written solutions). Give your answers to three decimal places.

2. The Maths Students Society (AUMS) decides to conduct small lottery each week to raise money. A participant must pays $2 to enter and chooses three distinct numbers between 1 and 10 (the order does not matter). If their three chosen numbers match the three numbers drawn by AUMS they win a $70 jackpot offered each week, otherwise they recieve nothing. No two entries can use the same numbers.

(a) How many distinct entries can there be?

(b) Write out the probability distribution of returns for one random entry?

(c) A student enters 15 times in one week with different sets of numbers. Determine their probability of winning and the expected return.

(d) A different student enters once each week for 12 weeks. Determine their probability of winning at least once and the expected return.

(e) Suppose 20 entries are made every week for a year. By first calculating the expected amount raised each week, determine how much money AUMS expects to raise in a year?

31. Consider the function f(x) = 3x⁴ − 8x³ + 1.

(a) Find the derivative f 0 (x), and hence the critical points for the function (for this question give both x and y coordinates).

(b) Classify the critical points using the first derivative test to determine if they are local maximum or minimum or neither.

(c) Find any points of inflection for f(x) (give both x and y coordinates).

1. A company buys a machine for $72,000 that has an expected life of 4 years and no salvage value. The company anticipates a yearly net income of $3,450 after taxes of 30%, with the cash flows to be received evenly throughout each year. What is the accounting rate of return?

a. 6.71% b. 9.58% c. 4.79% d. 2.87% e. 19.17%

2. Park Co. is considering an investment that requires immediate payment of $35,000 and provides expected cash inflows of $12,000 annually for four years. What is the investment's payback period?

3. Project A requires a $425,000 initial investment for new machinery with a five-year life and a salvage value of $38,500. The company uses straight-line depreciation. Project A is expected to yield annual net income of $27,000 per year for the next five years.

Compute Project A’s accounting rate of return.

4. Consider the following regression:

Y_t = a + b₁X_t + b₂X_t-1 + u_t

a) Explain the difference between weak and strong dependency.

b) If dependency is weak, what can we do to address the issue of autocorrelation in this regression? What if dependency is strong?

c) Calculate the impact and long-term multipliers in this regression.

A Carnot cycle consists of a cycle of 4 processes, in the order:

1) isothermal expansion at T(hot)=90oC,

2) adiabatic expansion to T(cold)=30oC,

3) isothermal contraction at T(cold),

4) adiabatic contraction to the original state.

The gas in the system can be treated as a monotonic ideal gas

Part A. After one complete cycle, what is the change in thermal energy of the gas in the system?

Part B. After a complete cycle what is the change in entropy? (The answer to this part is 0 J)

Part C.In this cycle heat can be transferred during which parts of the cycle? (The answer to this part is leg 1 and 3 only)

Part D. What is Q3/Q1, the ratio of heat transferred in leg 3 divided by heat transferred in leg 1 of the cycle?

Part E. What is the Work in terms of Q1 and Q3? (Hint: The work does not depend on Q1 and Q3)

Part F. What is the efficiency of the cycle?

(LO 3, 4 ) (Accounting for an Operating Lease) On January 1, 2020, a machine was purchased for $900,000 by Young Co. The machine is expected to have an 8-year life with no salvage value. It is to be depreciated on a straight-line basis. The machine was leased to St. Leger Inc. for 3 years on January 1, 2020, with annual rent payments of $150,955 due at the beginning of each year, starting January 1, 2020. The machine is expected to have a residual value at the end of the lease term of $562,500, though this amount is unguaranteed. Instructions

A. How much should Young report as income before income tax on this lease for 2020?

B. Record the journal entries St. Leger would record for 2020 on this lease, assuming its incremental borrowing rate is 6% and the rate implicit in the lease is unknown.

C. Suppose the lease was only for one year (only one payment of the same amount at commencement of the lease), with a renewal option at market rates at the end of the lease, and St. Leger elects to use the short-term lease exception. Record the journal entries St. Leger would record for 2020 on this lease.

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

HoHo : pA=0.25pA=0.25;  pB=0.4pB=0.4;  pC=0.1pC=0.1;  pD=0.25pD=0.25

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

What is the chi-square test-statistic for this data? (2 decimal places)
χ2=( )
What is the P-Value? (3 decimal places)
P-Value = ( )
For significance level alpha 0.025,
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

2/ You are conducting a multinomial hypothesis test (αα = 0.05) for the claim that all 5 categories are equally likely to be selected. Complete the table.

Report all answers accurate to three decimal places. But retain unrounded numbers for future calculations.

What is the chi-square test-statistic for this data? (Report answer accurate to three decimal places, and remember to use the unrounded Pearson residuals in your calculations.)
χ2=χ2=

What are the degrees of freedom for this test?
d.f.=

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null
• accept the alternative

As such, the final conclusion is that...

• A/ There is sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
• B/ There is not sufficient evidence to warrant rejection of the claim that all 5 categories are equally likely to be selected.
• C/ The sample data support the claim that all 5 categories are equally likely to be selected.
• D/ There is not sufficient sample evidence to support the claim that all 5 categories are equally likely to be selected.

1. Consider the CAPM. The risk-free rate is 4%, and the expected return on the market is 18%. What is the expected return on a stock with a beta of 1.2?
A.
6%
B.
15.6%
C.
18%
D.
20.8%

2. The CAL provided by combinations of 1-month T-bills and a broad index of common stocks (i.e. market portfolio) is called the ______.
A.
SML
B.
CAPM
C.
CML
D.
total return line

Suppose that apples cost $1. A consumer feels that they are willing to give up 4 apples in order to consume a banana, as long as they are consuming 10 or less bananas. After the 10th banana their appreciation for them is not as high, so they are willing to trade 2 apples for an additional banana, as long as their banana consumption is less than or equal to 20. After the 20th banana they are fed up of bananas and would not give up a single apple for a banana.

Questions:

(1) What is the demand curve for bananas (a picture, fully lablled, is enough)

(2) Assume the supply curve for bananas is S(p)=5p. What is the equilibrium price and quantity in the market for bananas?

(3) Suppose that there is a natural disaster in apple growing countries, so now the price of apples is $2. Assume that the resources used in banana production are not suitable for apple production, so this change in the price of apples leaves supply of bananas unaffected. What is the new equilibrium price and quantity in the market for bananas?