PK Ltd manufactures four types of mobile phones which all use “goggles”, a component made in only one factory. Each goggle costs $50 to purchase. Due to a prolonged strike in the goggle factory, PK Ltd will only be able to purchase 20,000 goggles this year. The following information relates to each type of mobile manufactured by PK Ltd: Mobile A Mobile B Mobile C Mobile D Maximum demand(units) 11000 3000 3500 700 Cost per mobile: $ $ $ $ Goggle 50 100 200 350 Other direct materials 30 80 98 300 Direct Labour 30 40 30 55 Fixed Costs 60 80 40 70 Profit per mobile 50 70 52 490 Selling Price per mobile 220 370 420 1265 (a) Calculate the numbers of each type of mobile to be produced and sold that would maximize the profit of PK Ltd. (b) Prepare a Marginal Income Statement showing the profit for the year. PK Ltd has been approached by an outside supplier who can supply any of the four mobile phones at a cost of 80% of PK Ltd’s selling price. (c) Calculate the overall profitability if PK Ltd wants to supply all the four types of mobile phones at normal capacity. 3 (d) Identify and explain two issues which PK Ltd should take into account when buying ready-made mobiles from an outside supplier. (e) PK Ltd has a normal credit period of 55 days. The new policy of company is to allow a discount of 3% for payment within 12 days. The company operates a bank overdraft at 16.5% per annum. You are required to calculate the cost of the discount for Rs100 sales and advise if any

6.Geometry John is playing around with probabilities and thinking about rolling a die until he gets a 6. He computes that (5/6)4 is equal to 0.4823, and concludes, “Cool, I’ve got a better than 50% chance of seeing my first six by my fourth roll.” Then Geometry John wonders, “if I roll a die until I roll two sixes, do I have a better than 50% chance of seeing my second six by my eighth roll?” What is the answer to Geometry John’s question? Compute the probability.

7. Suppose you have a shipment of 100 drills, and four of them are defective. If you randomly select ten of the 100 drills and inspect them closely, what is the probability that you will find (at least) one of the defective ones in your sample of ten?

9. If you call a randomly selected person, there is a 1/10 chance that they are left-handed. If you sequentially call randomly selected people until you speak to your third left-handed person, what is the probability that it this takes exactly 10 calls?

please help me to solve this questions

The National Longitudinal Study of Adolescent Health interviewed several thousand teens (grades 7 to 12). One question asked was “What do you think are the chances you will be married in the next 10 years?” Here is a two-way table of the responses by gender:

1. How many individuals are described in this table?
2. How many females were among the respondents?
   
   
3. The percent of females among the respondents was about %.
   
4. Your percent from the previous exercise is part of
   • the marginal distribution of sex.
   • the marginal distribution of opinion about marriage.
   • the conditional distribution of sex among adolescents with a given opinion.
   
   
5. What percent of females thought that they were almost certain to be married in the next 10 years?
   %
   
6. Your percent from the previous exercise is part of
   • the conditional distribution of sex among those who thought they were almost certain to be married.
   • the marginal distribution of opinion about marriage.
   • the conditional distribution of opinion about marriage among women.

A)In a certain state's lottery, 40 balls numbered 1 through 40 are placed in a machine and eight of them are drawn at random. If the eight numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. In this lottery, the order in which the numbers are drawn does not matter.

Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket. Write your answer as a reduced fraction.

1. PP(win) =    

A single lottery ticket costs $2. Compute the Expected Value, to the state, if 10,000 lottery tickets are sold. Round your answer to the nearest dollar.

1. Answer: $

A single lottery ticket costs $2. Compute the Expected Value, to you, if you purchase 10,000 lottery tickets. Round your answer to the nearest dollar.

1. Answer: $

B)There are nine female board members and twenty-one male board members.

i.How many ways are there to make a committee of eight board members?

ii.How many ways are there to make a committee of eight board members if exactly three must be female?

iii.Determine the probability of selecting a committee of eight board members where exactly three of the members were female. Write your answer as a decimal, rounded to the nearest thousandth.

C)Suppose a jar contains 8 red marbles and 38 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Write your answer as a reduced fraction.

Answer:

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ou have just begun work at XYZ Manufacturing Company. Among its benefits offerings is a generous qualified 401(k) plan with an employer match. In 2015, your annual salary is $45,000 and you are age 55. You’ve decided to contribute 10 percent of your annual salary to your 401(k) plan even though the Internal Revenue Service allows you to contribute up to $24,000 in 2015 ($18,000 plus a $6,000 catch up contribution for employees age 50 or more). The annual addition is $53,000.

   1   How much more money would you need to contribute to meet the allowable maximum contribution?

   2   In 2015, the company offers a $0.75 match for each dollar that you contribute between 3 percent and 6 percent of your annual salary. How much is the company match based on your 10 percent contribution?

   3   Based on the sum of your answers to questions 9-9 and 9-10, what is the difference between the IRS maximum annual addition for 2015 and the total contribution to your 401(k) plan?

Relevant cash flows long dash—No terminal value  

 Central Laundry and Cleaners is considering replacing an existing piece of machinery with a more sophisticated machine. The old machine was purchased 3 years ago at a cost of

$47,500​,

and this amount was being depreciated under MACRS using a​ 5-year recovery period. The machine has 5 years of usable life remaining. The new machine that is being considered costs

$75,700 and requires $4,000 in installation costs. The new machine would be depreciated under MACRS using a​ 5-year recovery period. The firm can currently sell the old machine for

$55,600 without incurring any removal or cleanup costs. The firm is subject to a tax rate of 40%.

The revenues and expenses​ (excluding depreciation and​ interest) associated with the new and the old machines for the next 5 years are

given in the table

. ​(Table)

contains the applicable MACRS depreciation​ percentages.) Note: The new machine will have no terminal value at the end of 5 years.

a. Calculate the initial investment associated with replacement of the old machine by the new one.

b. Determine the incremental operating cash inflows associated with the proposed replacement.​ (Note: Be sure to consider the depreciation in year​ 6.)

c. Depict on a time line the relevant cash flows found in parts

​(a​) and ​(b​) associated with the proposed replacement decision.

The local library if they get more patrons visiting by shifting some early morning hours to evening. They take a sample of days with morning hours included (8-5) compared to 12-9. Data below.

8am-5pm hours: 50, 40, 60, 60, 70, 35, 40 12-9 PM hours : 40, 80, 70, 60, 85, 90, 70

a) Provide null and alternative hypotheses in formal terms and layperson's terms for the t test for independent samples

b) Do the math and reject/accept at a=.05

c) Explain the results in layperson's terms

d) Calculate and explain a 95% confidence interval in layperson's terms if appropriate. If not, you must explain why not.

Use the heights from the SCC data to answer the following questions. Men are to use the male data, and women are to use the female data (only answer the questions for ONE set of data, not both).

2. State the following for the SCC sample male heights.

a. Sample size (n)

b. Sample mean (?̅)

c. Sample standard deviation (s

male Student # Gender Height Shoe Age Hand

1 M 67 10 19 R

2 M 74 12 17 R

3 M 72 11.5 19 R

4 M 69 10 35 R

5 M 66 9 18 R

6 M 71 10.5 17 R

7 M 72 10.5 17 R

8 M 66 10 20 R

9 M 67 10 18 R

10 M 71 10.5 24 R

11 M 66 10 21 R

12 M 71 10.5 18 R

13 M 69 10 22 R

14 M 66 9.5 18 L

15 M 76 14 18 R

16 M 69 11 22 R

17 M 68 9 19 R

18 M 70 12 30 R

19 M 67 10 24 R

20 M 70 11 21 R

21 M 70 10 52 R

22 M 63 9 27 R

23 M 69 11 22 R

24 M 72 10 22 R

25 M 76 11.5 20 L

26 M 75 11 17 R

27 M 72 11 50 L

28 M 69 11 20 R

29 M 70 12 20 R

30 M 69 11.5 23 R

31 M 70 11 18 R

32 M 67 10 21 R

33 M 68 11 44 R

34 M 76 13 48 R

35 M 62 8 23 L

36 M 69 9 19 R

37 M 72 10 60 R

38 M 73 11.5 41 R

39 M 70 9.5 39 R

40 M 78 15 24 R

41 M 65 8.5 23 R

42 M 68 9.5 20 R

You measure 44 watermelons' weights, and find they have an average weight of 54 grams. Assume the population standard deviation is 4.8 grams. Based on this, what is the margin of error associated with a 99% confidence interval for the true population mean watermelon weight. The sample size is sufficiently large that the normal distribution value can be used in deriving the margin of error. Give your answer as a decimal, to two places

Owen’s Electronics has nine operating plants in seven southwestern states. Sales for last year were $100 million, and the balance sheet at year-end is similar in percentage of sales to that of previous years (and this will continue in the future). All assets (including fixed assets) and current liabilities will vary directly with sales. The firm is working at full capacity.

Owen’s has an aftertax profit margin of 9 percent and a dividend payout ratio of 30 percent.

If sales grow by 25 percent next year, determine how many dollars of new funds are needed to finance the growth. (Do not round intermediate calculations. Enter your answer in dollars, not millions, (e.g., $1,234,567).)