If a is congruent to b (mod3n) prove that a^3 is congruent to b^3 (mod.docx

•Download as DOCX, PDF•

0 likes•5 views

If a is congruent to b (mod3n) prove that a^3 is congruent to b^3 (mod9n) Solution a is congruent to b mod(3n) So, 3n divides (b-a) To Prove: a 3 is congruent to b 3 mod(9n) So, we need to prove 9n divides (b 3 - a 3 ) Now, (b 3 - a 3 ) = (b - a)( b 2 + ab + a 2 ) ------------(1) since in R.H.S 3n divides (b-a), So we only need to show that 3 divides ( b 2 + ab + a 2 ) We can write (b-a) = 3nq , for some integer q or b = 3nq + a So, ( b 2 + ab + a 2 ) = [ (3nq+a) 2 + a(3nq+a) + a 2 ] = 9n 2 q 2 + 6nq + 3nq 2 + 3a 2 = 3 (3n 2 q 2 + 2nq + nq 2 + a 2 ) So, 3 divides ( b 2 + ab + a 2 ) Hence proved :) .

Education

If a is congruent to b (mod3n) prove that a^3 is congruent to b^3 (mod.docx

More from edwardk6

If the Android platform you are developing for does not support fragments, how would you go about providing fragment-like processing in you Android Application ? Hints: Would you have multiply activities? Which UI elements (controls/widgets) would you use? Solution A Fragment represents a behavior or a portion of user interface in an Activity.. One big reason to stick with the SupportFragment for a while is that you do not have access to the ChildFragmentManager until API17. Instead of creating fragments we can use by custom views for mutliple display. Letâ€™s implementation of fragments in views. First, weâ€™ll have the notion of a Container, which can show an item and also handle back presses. The activity assumes thereâ€™s always a container and merely delegates the work to it. The list is also quite trivial. Now, the meat of the work: loading different XML layouts based on resource qualifiers. Using custom views works great, but we would like to isolate business logic into dedicated controllers. we call those parameters. This makes the code much more readable and facilitates testing. MyDetailView could look something like this Make your fragments shells of themselves. Pull view code up into custom view classes, and push business logic down into a presenter that knows how to interact with the custom views. Then, your fragment is nearly empty, just inflating custom views that connect themselves with presenters: At that point you can eliminate the fragment .

If the Android platform you are developing for does not support fragme.docx

edwardk6

E13-7 On January 1, 2010, the stockholders\' equity section of Nunez Corporation shows: Common stock ($5 par value) $1,500,000; paid-in capital in excess of par value $1,000,000; and re tained earnings $1,200,000. During the year, the following treasury stock transactions occurred. Mar. 1 Purchased 50,000 shares for cash at $15 per share. July 1 Sold 10,000 treasury shares for cash at $17 per share. Sept. I Sold 8,000 treasury shares for cash at $14 per share. Instructions (a) Journalize the treasury stock transactions. Solution Journalize the treasury stock transactions. (For multiple debit/credit entries, list amounts from largest to smallest eg 10, 5, 3, 2.) Date Account/Description Mar.1 Dr Treasury stock 750,000 (50,000 x $15) Cr Cash 750,000 July 1 Dr Cash 170,000 Cr Treasury stock 150,000 (10,000 at COST of $15) Cr Paid-in cap. from treasury stock 20,000 At this point your Paid-in cap. from treasury stock stands at $20,000 (credit). Sept. 1 Dr Cash 112,000 (8,000 x $14) Dr Paid-in cap. from treasury stock 8,000 Cr Treasury stock 120,000 (8,000 at COST of $15) .

E13-7 On January 1- 2010- the stockholders-' equity section of Nunez C.docx

edwardk6

E 4. Elijah Samuels and Tony Winslow agreed to form a partnership. Samuels contributed $200,000 in cash, and Winslow contributed assets with a fair market value of $400,000. The partnership, in its initial year, reported net income of $120,000. Calculate the distribution of the first year\'s income to the partners under each of the following conditions: 1. Samuels and Winslow failed to include stated ratios in the partnership agreement. 2. Samuels and Winslow agreed to share income and losses in a 3:2 ratio. 3. Samuels and Winslow agreed to share income and losses in the ratio of their original investments. 4. Samuels and Winslow agreed to share income and losses by allowing 10 percent interest on original investments and sharing any remainder equally. Solution 1. When there is no stated ratio then profit distributed equally Share of Samuels = 120000x1/2= 60000 Share of winslow= 120000x1/2 = 60000 2. Share of Samuels=Â Â 120000x 3/5 = 72000 Share of winslow= 120000x2/5 = 48000 3. Value of investments= Samuels (200000) + Winslow (400000)= 600000 Share of samuels = 120000x200000/600000 = 40000 Share of winslow = 120000x 400000/600000= 80000 4. Income after interest on investments = 120000- 600000x10%= 60000 Share of samuels = 60000x1/2 = 30000 Share of winslow = 60000x1/2 =30000 .

E 4- Elijah Samuels and Tony Winslow agreed to form a partnership- Sam.docx

edwardk6

During October, Wichita Light Company experiences the following transactions in establishing a petty cash fund. Journalize the entries in October that pertain to the petty cash fund. (Credit account titles are automatically indented when amount is entered. Do not indent manually.) Date Account Titles and Explanation Debit Credit Oct. 1 Oct. 31 During October, Wichita Light Company experiences the following transactions in establishing a petty cash fund.Journalize the entries in October that pertain to the petty cash fund. (Credit account titles are automatically indented when amount is entered. Do not indent manually.) Solution Petty Cash Fund Business generally keeps small amounts of cash to meet small obligations such as emergency supplies, small delivery charges etc. This is called petty cash fund. The person who is responsible for maintaining the petty cash fund, documentation of disbursements made, and reconciling the petty cash is called .

During October- Wichita Light Company experiences the following transa.docx

edwardk6

During a total lunar eclipse, in which the moon passes entirely into the shadow of the earth as cast by the sun, the moon is not completely dark, but is often a deep red in color. The shade of red varies widely from one total eclipse to the other. Why? 1. During the sunset, the Sun transfers some red light to the moon. 2. The earth acts like a giant water drop because of its oceans, and the moon winds up 3. None of the worldâ€™s sacred holy books discuss this situation, so it must be forever a total mystery. 4. Low frequencies pass more easily through the long grazing path through the Earthâ€™s atmosphere to be refracted finally onto the moon. 5. High frequencies pass more easily through the long grazing path through the Earthâ€™s atmosphere to be refracted finally onto the moon. Solution 4) Some light from the sun passes through Earth\'s atmosphere and is bent toward the moon. Low frequencies (red is having low frequency and highest wavelength) pass more easily through the long grazing path through the Earthâ€™s atmosphere to be refracted finally onto the moon. .

During a total lunar eclipse- in which the moon passes entirely into t.docx

edwardk6

During 2011, Arthur Corportation reported a net income of $3,059,000. On January 1, Arthur had 2,800,000 shares of common stock outstanding. The company issued an additional 1,680,000 shares of common stock on October 1. In 2011, the company had a simple capital structure. During 2012, there were no transactions involving common stock, and the company reported net income of $4,032,000. 1. Determine the weighted-average number of common shares outstanding each year. 2. Compute earnings per shre for each year. Solution Answer : 1. weighted-average number of common shares outstanding each year. Note : = (3/4 * 2,800,000) +(1/4 *1,680,000) = 2,100,000 + 420,000 = 2,520,000 In year 2012 new shares are not purchased hence (Opening balance * 1) = 4,480,000 2. earnings per shre for each year Note : earnings per share = Net Income / Weighted Average No of outstanding shares .

During 2011- Arthur Corportation reported a net income of $3-059-000-.docx

edwardk6

Driving School has 4 learning centres. The network of each learning centre is a LAN of its own. Network Cheap is contracted to install network connections between the learning centres. Network Cheap proposed to use RIP version 2. As the CEO of Driving School, will you accept this proposal? If you do not accept the proposal, what would you use for the routing protocol? Give your reasons. Solution IGRPâ€”Interior Gateway Routing Protocol , EIGRPâ€”Enhanced Interior Gateway Routing Protocol or OSPF V2â€”Open Shortest Path First came to a mind but RIP V2â€”Routing Information Protocol is a good choice The characteristics of RIPv2 follow: Distance-vector protocol. Uses UDP port 520. Classless protocol (support for CIDR). Supports VLSMs. Metric is router hop count. Maximum hop count is 15; infinite (unreachable) routes have a metric of 16. Periodic route updates sent every 30 seconds to multicast address 224.0.0.9. 25 routes per RIP message (24 if you use authentication). Supports authentication. Implements split horizon with poison reverse. Implements triggered updates. Subnet mask included in route entry. Administrative distance for RIPv2 is 120. Used in small, flat networks or at the edge of larger networks. IGRP Converges slowly infact slower than RIP and for IGRP , OSPF or EIGRP all routers must be from Cisco Systems ( big constraint) .

Driving School has 4 learning centres- The network of each learning ce.docx

edwardk6

Donnie Hilfiger has two classes of stock authorized: S1 par preferred and S0.01 par value common. As of the beginning of 2015, 200 shares of preferred stock and 3,900 shares of common stock have been issued. The following transactions affect stockholders\' equity during 2015: March 1 Issues 1,000 shares of common stock for $41 per share. May 15 Repurchases 600 shares of treasury stock for S34 per share. July 10 Reissues 100 shares of treasury stock purchased on May 15 for $39 per share. October 15 Issues 100 shares of preferred stock for $44 per share. December 1 Declares a cash dividend on both common and preferred stock of SO.55 per share to all stockholders of record on December 15. (Hint Dividends are not paid on treasury stock.) December 31 Pays the cash dividends declared on December 1. Donnie Hilfiger has the following beginning balances in its stockholders\' equity accounts on January 1, 2015: Preferred Stock, S200; Common Stock, S39; Additional Paid-in Capital, $75,000; and Retained Earnings, $30,000. Net income for the year ended December 31, 2015, is $10,700. Taking into consideration all the transactions during 2015, respond to the following for Donnie Hilfiger: 4 .56 points Prepare the statement of stockholders\' equity for the year ended December 31, 2015. (Amounts to be deducted should be indicated by a minus sign.) Solution Par Value = 1000*0.01 = 10 Additional Paid in Capital = 40990 Par Value = 100 Additional Paid in Capital = 4300 .

Donnie Hilfiger has two classes of stock authorized- S1 par preferred.docx

edwardk6

Doris Washington recently assumed her new position as HR Director at the XYZ Company, a software development firm with approximately 350 employees. Her staff includes a seasoned generalist as well as a benefits clerk. During her first 90 days on the job, Doris has noted the following issues that seem to be embedded in XYZ\'s culture: 1) managers create their own interview questions; 2) for some employees, their compensation is simply determined by managers, not based on training, experience, geographic region, and so on; and, 3) the company seems to draw new employees from only two sources, one is the university from which the President of the company graduated. While Doris has been contemplating these trends, the CEO has asked her to attend a strategic planning meeting about opening the company\'s first location on in Toronto, Canada in approximately nine months. She needs to provide a recommendation to the CEO that can be used appropriately. Instructions: Solution 1. Four potential issues faced by Doris as a HR director are listed below: 2. Key issue: The Company does not follow a standard process for hiring the employees as managers of the company uses their own set of interview questions. This would be one of the most difficult problems for the company, because uneven hiring process might result in hiring of incompetent employees. In future, such employees would not be able to contribute towards the company .

Doris Washington recently assumed her new position as HR Director at t.docx

edwardk6

Doppler Effect: True or False John is listening to a horn. He knows the frequency of the horn is 300 Hz when both he and the horn are at rest. If he hears a pitch of 330 Hz, there are clearly several possibilities. For each of the following statements, indicate whether it is correct or incorrect. Both can be moving and have different speeds, Both can be moving and have the same speed John and the horn are both moving in the same direction but John is behind and moving faster than the horn. Both can be moving, in opposite directions. John is moving towards the horn at rest. The distance between John and the horn is increasing with time. Submit Answer Tries 0/10 Solution QUESTION: A) John is moving towards the horn at rest. B) Both can be moving and have the same speed. C) Both can be moving and have different speeds. D) Both can be moving, in opposite directions. E) The distance between John and the horn is increasing with time. F) Both cannot be moving in the same direction. ANSWER: A) True, when John moves towards the horn, it is the same as if he stood still and the horn moved towards him. B) True, if they are moving toward each other at the right speed, John would hear more waves per unit time, thus a higher frequency. C) True, the horn could be getting closer to John. D) True, same as B, they can approach each other to achieve this effect. E) False, it must be decreasing to hear a higher frequency. F) False, they could be. If both are moving and the horn is catching up to John, this effect could be achieved. .

Doppler Effect- True or False John is listening to a horn- He knows th.docx

edwardk6

DQ #4 Explain the US Government Thrift Savings Plans. Solution The US Government Thrift Savings Plans is a defined-contribution plan designed to give federal employees the same retirement savings related benefits which will be equal to that of workers in the private sector enjoy with 401(k) plans. Contributions to these plans are automatically deducted from each paycheck of federal employees. The thrift savings plan offers six different funds (government security fund, fixed-income fund, common stock fund, small cap stock fund, international stock fund and a life cycle fund) in which federal employees can invest. Because the thrift savings plan is based on tax-deferred contributions, any contributions made into it will not be taxed until the money is withdrawn, which can be deferred until retirement. Other Benefits of these US Government Thrift Savings Plans includes 1) agency matching contributions 2) agency automatic contributions 3) catch up contributions and 4) low expense ratios. .

DQ #4 Explain the US Government Thrift Savings Plans-SolutionThe US Go.docx

edwardk6

More from edwardk6 (11)