Prove that gcd(a,b,c)d is the smallest positive integer

Prove that gcd(a,b,c)=d is the smallest positive integer of the form ax+by+cz

Solution

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Let f(pq)1q if function pq is in lowest terms and f(x)0

Let f(p/q)=1/q if function p/q is in lowest terms and f(x)=0 for irrational x. Prove that f is continuous at x if and only if x is irrational or x=0

Solution

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Let a and b be integers. If a divides b, then for every

Let a and b be integers. If a divides b, then for every natural number k, a^k divides b^k.

Solution

Let a and b be integers. If a divides b, then for every natural number k, a^k divides b^k.

use mathematical induction

for k = 1

a divides b   is correct

let assume that a^k divides b^k

now we have to prove that this is true for n = k+1

now consider

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Having problems with this assignment. Argentina Partne

Having problems with this assignment.

Argentina Partners is concerned about the possible effects of inflation on its operations. Presently the company sells 60,000 units for $30 per unit. The variable production costs are $15, and fixed costs amount to $700,000. Production engineers have advised management that they expect unit labor costs to rise by 15 percent and unit materials cost to rise by 10 percent in the coming year. Of the $15 variable costs, 50 percent are from labor and 25 percent are from materials. Variable overhead costs are expected to increase by 20 percent. Sales prices cannot increase more than 10 percent. It is also expected that fixed costs will rise by 5 percent as a result of increased taxes and other miscellaneous fixed charges. The company wishes to maintain the same level of profit in real dollar terms. It is expected that to accomplish this objective profits must increase by 6 percent during the year.

Required:
A. Compute the volume in units and the dollar sales level necessary to maintain the present profit level, assuming that the maximum price increase is implemented.

B. compute the volume of sales and the dollar sales level necessary to provide the 6 percent increase in profits, assuming that the maximum price increase is implemented.

C. If the volume of sales were to remain at 60,000 units, what price increase would be required to attain the 6 percent increase in profits?

Solution

A. Compute the volume in units and the dollar sales level necessary to maintain the present profit level, assuming that the maximum price increase is implemented.

Existing Profit
Sales            60,000 x $30                              $1,800,000
Less : Variable costs
            Direct materials $15×0.25×60,000        $225,000                  
            Direct labor $15×0.50×60,000             $450,000                  
            Variable OH $15×0.25×60,000            $225,000
             Total Variable costs $15 x 60,000     $900,000                       
             Contribution Margin $15 x 60,000      $900,000
Less : Fixed costs                                             $700,000
Net profit                                                            $200,000

Revised Sale price per unit $30 x 1.1           $33.00
Revised Variable costs after increase
DM    $15 x 0.25 x 1.10          $4.125
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Question 22 Net sales divided by average accounts re

Question 22

Net sales divided by average accounts receivable is the:
Answer

Days\’ sales uncollected.

Average accounts receivable ratio.

Current ratio.

Profit margin.

Accounts receivable turnover ratio.
1 points
Question 23

Net income divided by net sales is the:
Answer

Return on total assets.

Profit margin.

Current ratio.

Total asset turnover.

Days\’ sales in inventory.
1 points
Question 24

Annual cash dividends per share divided by market price per share is the:
Answer

Price-earnings ratio

Price-dividends ratio.

Profit margin.

Dividend yield ratio.

Earnings per share.
1 points
Question 25

The average number of times a company\’s inventory is sold during an accounting period, calculated by dividing cost of goods sold by the average inventory balance, is the:
Answer

Accounts receivable turnover.

Inventory turnover.

Days\’ sales uncollected.

Current ratio.

Price earnings ratio.
1 points
Question 26

A company had a market price of $37.50 per share, earnings per share of $1.25, and dividends per share of $0.40. Its price-earnings ratio equals:
Answer

3.1.

30.0.

93.8.

32.0.

3.3.
1 points
Question 27

A company reports basic earnings per share of $3.50, cash dividends per share of $0.75, and a market price per share of $64.75. The company\’s dividend yield equals:
Answer

1.16%.

2.14%.

4.67%.

5.41%.

18.50%.

Solution

22) Accounts receivable turnover ratio
23) Profit margin
24) Dividend yield ratio
25) Inventory turnover ratio
26) Price-earnings ratio = Market price per share / Earning per share
                                    = $37.50 / $1.25
                                    = $█████
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The question is, Determine for each plan the earnings p

The question is, Determine for each plan the earnings per share of common stock, assuming that the income before bond interest and income tax is $30,000,000.
this is how far i got on the problem

Earnings per Share of Common Stock
Plan 1 Plan 2 Plan 3
Earnings before bond interest and income tax $ 30,000,000 $ 30,000,000 $ 30,000,000
Bond interest 0% 0%   
Income before income tax $ 30,000,000 $ 30,000,000   
Income tax     12,000,000     12,000,000   
Net income         
Dividends on preferred stock 0%      
Earnings available for common stock         
¸ Shares of common stock outstanding         
Earnings per share on common stock         

Solution

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1)What are at least four depreciation methods that are

1)What are at least four depreciation methods that are available to a company?
2)What are their similarities and differences?
3)Why does a company select one method over another?

Please answer seperately (no word count just explain in detail)

Solution

1) a) Straight-line depreciation Depreciates the asset in static increments until it hits scrap value. b)Declining-balance depreciation Depreciates the asset by a % of the book value (FMV rarely used) of the asset until it hits scrap value. c)Activity depreciation Depreciates the asset by how often it is used, and how often it is expected to run until it becomes inoperable. d)Sum-of-years-digits depreciation Depreciates the asset through an algorithm. (2n/(n+n^2) where n is how many years it is until the asset hits scrap value. 2)a,b,d are all time-based depreciation methods that assumes the asset is consumed on a regular basis. In addition, b & d assumes the asset is loses value immediately more so th█████ ███ █████████ █████████ ███████ █████ ███████ ██████████████ ██ ██████ ████████, ███████████████████ █████████████ ████████████, ██████ ███████████████ █████ ██████ ███████ █████ ██████████ ███████ █████████████ ███████████████ ███████ ████████ ██ █████ ██████████ ███ ███ ██████████████████████████ ███████ ███████████ ██████████ ███ ███████████████, ████ ███████ ████████ ████ █████████████████ █████████ █████████ ████████ ██████████████████ ██████████████ ██████████ ████ █████ ███████████ ██████ ████████ ███████████████ █████ ██ █████████████████████ ████████████ █████ ███████████████ ███████ ████████ ████████ ████ ████████ ██████████ ████ ██████████████ ██████████████████ ███)█████████████████████████ ████████████ ████████ ███ ███████████████ █████ ████████████████ ████████████ ███████████████████ █████████████████ ██████████████ ███████ ████████████ ███ ███████ ██████████\&#████████;███ ███████ █████ ██████████████ ██,██,█ █████ ████ ██████████ ██████████ ████████████ █████ ███████████████ █████████, █████ ████████████ █████████████████████ ████ ████████ ███████████████ █████████ ██ ██████████████████████████████ █████████████ █████████████████ ███████████ █ ██████████ ████ ██████ ████████████████████ ██████████, █████ █████████ ████████████████ █████ ███████████ ███████████ ████████ ██████████████████ ████████████████████████

Accounting for construction contract Construct Pty Ltd

Accounting for construction contract

Construct Pty Ltd uses the percentage of completion method of accounting for construction contracts. In 2011 Construct Pty Ltd entered into a contract to build a commercial building with a contract price of $4,200,000 for Kairns Ltd. The details relating to the contract are as follows:

2011 2012
$ $
Costs incurred during the year 300,000 2,750,000
Estimated costs to complete at 30 June 2,400,000 0
Billings during the year 720,000 3,480,000
Collections during the year 500,000 3,200,000
Required:

(a) Calculate the amount of profit to be recognised by Construct Pty Ltd for the two years.

(b) Prepare the general journal entries for both years, assuming the outcome of the contract can be reliably estimated.

Solution

a) $225,000 Year 1 and $1,225,000 Year 2 Year 1 Completion: 12.5% ($300,000/$2,700,000) Gross Profit: $1,800,000 ($4,200,000-$2,700,000) Year 1 Profit: $225,000 ($1,800,000 * 0.125) Year 2 Completion: 87.5% (100% – 12.5%) Gross Profit: $1,150,000 ($4,200,000-$3,050,000) Year 2 Profit: $925,000 ($1,150,000-$225,000) b) Year 1 Debit Construction in Process 300,000 Credit Accounts Payable 300,000 Debit Accounts Receivable 720,000 Credit Progre███ ███████████████ ██████,██████ ████████████ ███████████████████████████ █████ ███████████████████ █████,████████ ████████████ ████████████████████████ ████████████████ ██████,██████ ███████████████ ███████████████████████ ██████████████ ██████,████ ███████ ███ ███████████ ███████████████████████ █████ ████████████ ██,█████,██████ ██████████ ████████████████ ███████████████ ███,█████,██████ █████████ ██████████████████ ███████████████ ███,████████,██████ █████████████ ███████████ ██████████████ █,████████,███████ ████████ ███████████████████ ███ ██████████████ ████████,████ ███████████ ██████████████████ ██████████████ ██,█████,██████ ███████████████ ████████████████████████ ███████████████ █,█████,█████ █████████████ ███████████████ █████████████████████ ██,█████,████ ███████████ ███████████████████ ███ ████████████████ █,█████,███████