Let f be a continuous function on the closed interval [0,1] with a range also contained in [0,1]. Prove that f that there exists an x in [0,1] such that f(x)=x. Is the same explanation still valid if f is not continuous?

5. Find a closed-form formula for the exponential generating function for the number of strings of length n with symbols a, b, c, where (number of a′s) + (number of b′s) ≥ 1; and, # c′s = even

Determine if the following requirements for a wet well control system, are consistent:

a) If the pump is on then the valve shall be open.

b) If the valve is closed then the water level is ≤ 10 meters.

c) If the water level is >10 meters then the pump is on.

A country’s government has been running a deficit for the past few years. Suppose this country decides to increase its government spending. Compare the impact of the increase in government spending in a closed economy and an open economy.

Describe how the Liskov Substitution Principle can influence the way that you might implement the Open Closed Principle in software. (Describe how it might help but also how it might constrain implementations of the OCP.)

the construction activity for the year-end 31 December 2020, are as follows:

Required:

1) Prepare a schedule by project, showing clearly the amount of gross profit (loss) of the project before deducting selling, general, and administrative expenses for the year ended 31 December 2020 using the percentage-of-completion method.(based on estimated costs.)

2)Based on the schedule, show the amount of gross profit ( or loss) before selling, general,and administrative expenses for the year ended 31 December 2020, which would be reported if the following method are used:

(I) the cost-recovery method.

(II) The percentage-of-completion method ( based on estimated costs)

3) Determine the construction in process balance that would appear in the statement of financial position of the company as at 31/12/2020 for the project AA, assuming that the precentage-of-completion method is used. show all the working.

The following information is from Alberta Ltd financial statements for the year ended Dec 31, 2020: - Net income for the year $ 460,000. - 8% Convertible bonds issued at par $1,000,000 ($1000 per bond), each bond convertible into 20 common shares $1,000,000 - 6% non-cumulative preferred shares $100 par value. $1,000,000 - Common shares 120,000 authorized, 60,000 issued and outstanding $ 600,000 - Stock options (call option granted in a prior year) to purchase 30,000 common shares at $10 per common share. - Average market price per common share during 2020 was $12, and the tax rate for 2020 is 35% - Alberta declare and pay $100,000 dividends during 2020 There were no changes during 2020 in the number of common shares, preferred shares, stock options or convertible bonds. Also for simplicity, ignore the requirement to book the convertible bonds’ equity portion separately. Instruction: A) Calculate the basic EPS for 2020 B) Calculate diluted EPS for 2020 (Show your calculation for each transaction/ affect)

The following information is from Alberta Ltd financial statements for the year ended Dec 31, 2020: - Net income for the year $ 460,000. - 8% Convertible bonds issued at par $1,000,000 ($1000 per bond), each bond convertible into 20 common shares $1,000,000 - 6% non-cumulative preferred shares $100 par value. $1,000,000 - Common shares 120,000 authorized, 60,000 issued and outstanding $ 600,000 - Stock options (call option granted in a prior year) to purchase 30,000 common shares at $10 per common share. - Average market price per common share during 2020 was $12, and the tax rate for 2020 is 35% - Alberta declare and pay $100,000 dividends during 2020 There were no changes during 2020 in the number of common shares, preferred shares, stock options or convertible bonds. Also for simplicity, ignore the requirement to book the convertible bonds’ equity portion separately. Instruction: A) Calculate the basic EPS for 2020 B) Calculate diluted EPS for 2020 (Show your calculation for each transaction/ affect)