1. (2 marks) (Covering part 1 of the lecture slides) Consider the subset A of natural...

1. (Covering part 1 of the lecture slides)

Consider the subset A of natural numbers, defined by A={ all natural numbers n : n is congruent to 1 (mod 3) }

First consider G: N -------> {0,1} to be the characteristic function of A.

a) Determine G(23) and G(25)

b) determine which sequence of 0,1 is this set associated with. (Write about 9 terms of it, or describe it with a formula.)

c) Which real number in the interval (0,1) in base 2 is associated with this set?

Expert Solution

Colby Messinger answered 1 year ago

Consider a project of the Pearson Company (as in an example from Lecture 3 slides). The...

Consider a project of the Pearson Company (as in an example from Lecture 3 slides). The timing and size of the incremental after-tax cash flows for an equity-financed project are: Year 0 1 2 3 4 CF -1,000 325 250 375 500 The firm is financing the project with $600 debt which carries 8% interest rate. The firm currently has no leverage, faces 40% tax rate and has 10% cost of capital. Value the project using flow to Equity...

Question 3.3 (Total: 45 marks; part 1: 24 marks; part 2: 15 marks; part 3:...

Question 3.3 (Total: 45 marks; part 1: 24 marks; part 2: 15 marks; part 3: 6 marks) Star Finder Inc. has provided the following information for the year ended December 31, 2021: Sales revenue $1,300,000 Loss on inventory due to decline in net realizable value $80,000 Unrealized gain on FV-OCI equity investments 42,000 Loss on disposal of equipment 35,000 Interest income 7,000 Depreciation expense related to buildings omitted by mistake in 2020 55,000 Cost of goods sold 780,000 Retained...

Question 3.3 (Total: 45 marks; part 1: 24 marks; part 2: 15 marks; part 3: 6...

Question 3.3 (Total: 45 marks; part 1: 24 marks; part 2: 15 marks; part 3: 6 marks) Star Finder Inc. has provided the following information for the year ended December 31, 2021: Sales revenue $1,300,000 Loss on inventory due to decline in net realizable value $80,000 Unrealized gain on FV-OCI equity investments 42,000 Loss on disposal of equipment 35,000 Interest income 7,000 Depreciation expense related to buildings omitted by mistake in 2020 55,000 Cost of goods sold 780,000 Retained earnings...

Pick a subset of {1, 2, · · · , 10} so that any subset is...

Pick a subset of {1, 2, · · · , 10} so that any subset is equally likely to be picked. What is the probability that a. the subset contains the element one, given it is of size three? b. the subset has no even numbers given that it is of size 4? c. the maximum element of the subset is 8, given that the minimum element in it is 3?

Question #5. (13 marks) Lecture Week 6, Lectures 1 and 2 Supposedly high-fiber diets reduce serum...

Question #5. Lecture Week 6, Lectures 1 and 2 Supposedly high-fiber diets reduce serum cholesterol levels. The results of two of these diets (the “Nut” diet and the “Oat” diet) were compared. Thirty-two men with high serum cholesterol were randomly allocated to either receive the Nut diet or the Oat diet for a period of six months. The results are shown in the following table. Decrease in Cholesterol Level (mg/dl) Diet n Mean SD Nut 16 82 25 Oat 25...

Assignment Choice #1: Consolidated Financial Statements Scenario The first part is a scenario covering the topic...

Assignment Choice #1: Consolidated Financial Statements Scenario The first part is a scenario covering the topic of consolidated financial statements. The second part is the preparation of a consolidated financial statement. You will submit both parts separately. Part 1: Scenario - Written A new employee has been given responsibility for preparing the consolidated financial statements of Sample Company. After attempting to work alone for some time, the employee seeks assistance in gaining a better overall understanding of the way in...

(1) (26 pts) In lecture we talked about how demographic forces and natural selection can affect...

(1) (26 pts) In lecture we talked about how demographic forces and natural selection can affect patterns of polymorphism (i.e. genetic variation within species). (a) Describe 2 patterns in genetic variation data (e.g. polymorphism data) that can be caused by balancing selection. (b) List three ways a bottleneck can affect genetic variation. (c) Describe 2 approaches one can use to distinguish bottlenecks from selection scenarios at generating the pattern in the data.

There are two unrelated parts to this question. Part 1 is worth 9 marks and Part...

There are two unrelated parts to this question. Part 1 is worth 9 marks and Part 2 is worth 11 marks. On 1 January 2018, Walli Ltd purchased equipment for a total cost of $55,016 paying cash. The estimated useful life of the equipment was 8 years, with an estimated residual value of $5,000. The entity’s reporting period ends on 30 June, and it uses straight-line depreciation. On 1 July 2018, Walli Ltd revalued the equipment upwards to reflect the...

This is a multi-part question. Part 1: Citric acid is a natural tri-protic organic acid that...

This is a multi-part question. Part 1: Citric acid is a natural tri-protic organic acid that has the generic formula of H3Cit, with the following Ka's: Ka1=8.4*10^-4, Ka2=1.8*10^-5, and Ka3=4.0*10^-6. If you start with a 0.2424 M solution of Na2HCit, write all of applicable chemical equations and the math equations, including all equilibria and mass and charge balance, that would be necessary to solve this? Part 2: For the same citric acid problem above, what is the pH of the...

(a) Show that B {[2, 3, 0,1],[1, 1, 1,1]} is a maximal linearly independent subset of...

(a) Show that B {[2, 3, 0,1],[1, 1, 1,1]} is a maximal linearly independent subset of S {[1, 4, 1,2],[1, 1, 1,1],[3, 2,1, 0],[2, 3, 0,1]}. (b) Calculate dim(span(S)). (c) Does span(S) R4? Why or why not?

Question