In a location in outer space far from all other objects, a nucleus whose mass is 4.019480 × 10−25 kg and that is initially at rest undergoes spontaneous alpha decay. The original nucleus disappears, and two new particles appear: a He-4 nucleus of mass 6.640678 × 10−27 kg (an alpha particle consisting of two protons and two neutrons) and a new nucleus of mass 3.952926 × 10−25 kg. These new particles move far away from each other, because they repel each other electrically (both are positively charged). Because the calculations involve the small difference of (comparatively) large numbers, you need to keep seven significant figures in your calculations, and you need to use the more accurate value for the speed of light, 2.9979246e8 m/s. Choose all particles as the system. Initial state: Original nucleus, at rest. Final state: Alpha particle + new nucleus, far from each other.

Part 1 (a) What is the rest energy of the original nucleus? (Round your answer to seven significant figures.) J the tolerance is +/-2%

Part 2 (b) What is the sum of the rest energies of the alpha particle and the new nucleus? (Round your answer to seven significant figures.) J the tolerance is +/-2%

Part 3 (c) Did the portion of the total energy of the system contributed by rest energy increase or decrease? decrease The total rest energy is unchanged. increase

Part 4 (d) What is the sum of the kinetic energies of the alpha particle and the new nucleus?

Write a program in C that allows you to determine the endianness of your computer. Hint: use unsigned char* ptr.

Your task is to explain this code. Make sure that you are detailed in your explanation by explaining the significant lines. In particular, correct explanation of lines 12, 13, 15, 18, 21, 22, 24, 25, 26 and 27 will earn 1 point each. Additionally, explain the overall purpose of the logical operations in lines 24-27 for 2 points. Your explanation should not just reiterate the code. For example, don’t simply say that the for loop iterates 4 times, but rather, explain why and what doing so accomplishes. It would be beneficial to run the code and examine memory contents in gdb.

Here’s an example explanation for line #20: Line #20 prints out the hexadecimal value of x to the console. The %#010x format specifier specifies that the value is printed in hexadecimal (the ‘x’ flag). The # indicates to prepend “0x” to the number. The ‘0’ flag following it indicates that the number should be padded by 0s at the left. The number following it, in this case ‘10’ is the total width of the number we want to display, including the ‘0x’. For example, if the value of x is 1C, then 6 0s are padded to fill up the 10-character space.

1/*

2 * endian.c

3 * Determines endianess. If endianess cannot be determined

4 * from input value, defaults to "big endian"

5 * Bob Plantz - 22 June 2009

6 */

7

8#include

9

10 int main(void)

11{

12 unsigned char *ptr;

13 int x, i, bigEndian;

14

15 ptr = (unsigned char *)&x;

16

17 printf("Enter a non-zero integer: ");

18 scanf("%i", &x);

19

20 printf("You entered %#010x and it is stored\n", x);

21 for (i = 0; i < 4; i++)

22 printf(" %p: %02x\n", ptr + i, *(ptr + i));

23

24 bigEndian = (*ptr == (unsigned char)(0xff & (x >> 24))) &&

25 (*(ptr + 1) == (unsigned char)(0xff & (x >> 16))) &&

26 (*(ptr + 2) == (unsigned char)(0xff & (x >> 8))) &&

27 (*(ptr + 3) == (unsigned char)(0xff & x));

28 if (bigEndian)

29 printf("which is big endian.\n");

30 else

31 printf("which is little endian.\n");

32

33 return 0;

34}

Grunewald Industries sells on terms of 1/10, net 40. Gross sales last year were $4,416,500 and accounts receivable averaged $482,500. Half of Grunewald's customers paid on the 10th day and took discounts. What are the nominal and effective costs of trade credit to Grunewald's nondiscount customers? (Hint: Calculate daily sales based on a 365-day year, calculate the average receivables for discount customers, and then find the DSO for the nondiscount customers.) Do not round intermediate calculations. Round your answers to two decimal places!

A 155 gg mass attached to a horizontal spring oscillates at a frequency of 3.70 Hz . At t =0s, the mass is at x= 6.40 cmcm and has v =− 45.0 cm/s . Determine:

a)The maximum speed

b)The maximum acceleration.

c)The total energy.

d)The position at t= 4.80 s

A 145 g mass attached to a horizontal spring oscillates at a frequency of 5.50 Hz. At t = 0s, the mass is at x = 6.60 cm and has v_x =− 35.0 cm/s.

Determine:

a) The maximum speed.

b) The maximum acceleration.

c) The total energy.

d) The position at t = 3.20 s.

ASSUME THAT MUSTAFA OPERATES THE ONLY SIGHTEEING TOUR BUSINESS IN NEW YORK, AND HE MAKES A LOT OF MONEY. HE HAS ONLY ONE BUS WHICH CAN FIT 50 PEOPLE PER TOUR AND EACH TOUR LASTS 2 HOURS. HIS TOTAL COST OF OPERATING ONE TOUR IS FIXED AT $450. MUSTAFA'S COST IS NOT REDUCED IF HE RUNS A TOUR WITH A PARTIALLY FULL BUS. WHILE HIS COST IS THE SAME FOR ALL TOURS. MUSTAFA CHECKS IS'S AND CHARGES EACH PASSENGER THEIR WILLINGNESS TO PAY BASED ON THEIR AGE: ADULTS $18 PER TRIP, CHILDREN $10 PER TRIP, AND SENIOR CITIZENS $12 PER TRIP. AT THOSE RATES, ON A TYPICAL DAY MUSTAFA'S DEMAND IS:

ASSUME THAT MUSTAFA'S CUSTOMERS ARE ALWAYS AVAILABLE FOR THE TOUR; THEREFORE, HE CAN FILL HIS BUS FOR EACH TOUR AS LONG AS THERE IS SUFFICIENT TOTAL DEMAND FOR THE DAY.

A. WHAT IS THE MICROECONOMIC TERM(NAME) FOR MUSTAFA'S PRICING STRATEGY?

B. WHAT IS MUSTAFA'S TOTALCOST OF SERVING ALL PASSENGERS WANTING A TOUR ON A TYPICAL DAY?

C. WHAT IS MUSTAFA'S TOTAL PROFIT ON A TYPICAL DAY?

D. ANGELA TELLS MUSTAFA THAT HE WOULD MAKE MORE PROFITS IF HE CHARGED A SINGLE PRICE OF $18 PER TICKET. ASSUMING NO CHANGES IN CONSUMER DEMAND, WHAT WOULD MUSTAFA'S TOTAL PROFIT BE IF HE CHARGED EVERY CUSTOMER$18? DO YOU AGREE WITH ANGELA? EXPLAIN

E. EMILY TELLS MUSTAFA THAT HE WOULD MAKE MORE PROFITS IF HE CHARGED A SINGLE PRICE OF $12 PER TICKET. ASSUMING NO CHARGES IN CONSUMER DEMAND, WHAT WOULD MUSTAFA'S TOTAL PROFIT BE IF HE CHARGED EVERY CUSTOMER $12? DO YOU AGREE WITH EMILY? EXPLAIN

The general manager of Design Impression Company has proposed the purchase of one of two large six-colour presses designed for long, high-quality runs. The purchase of a new press would enable the firm to reduce its cost of labour and therefore the price to the clients, putting the firm in a more competitive position. The key financial characteristics of the existing press and the two prosed presses are summarised below. Old press: Originally purchased three years ago at an installed cost of $400,000, it is being depreciated using a straight-line method over a 10-year effective life. The old press has a remaining economic life of five years. It can be sold today to net $460,000 before taxes. If the old press is retained, it can be sold to net $150,000 before taxes at the end of five years. Press A: This highly automated press can be purchased for $830,000 plus $40,000 in installation costs. It will be depreciated using the straight-line method over a five-year effective life. At the end of the five years, the machine could be sold to net $400,000 before taxes. Press B: This press is not as sophisticated as press A. It costs $640,000 plus $20,000 in installation costs. It will be depreciated using the straight-line method over a five-year effective life. At the end of five years, it can be sold to net $330,000 before taxes. The firm estimates that its earnings before depreciation and taxes with the old press and with press A or press B for each of the five years will be as show in the table. Assume the firm is subject to a 30% tax rate on ordinary income and NZ tax rule applies on capital gain (capital gain is not taxed). The firm’s cost of capital applicable to the proposed replacement is 14%. Profit before depreciation and taxes for Design Impression Company’s presses Year Old press Press A Press B 1 $120,000 $250,000 $210,000 2 120,000 270,000 210,000 3 120,000 300,000 210,000 4 120,000 330,000 210,000 5 120,000 370,000 210,000 Recommend which, if either, of the presses the firm should acquire. You can write answer and reason directly on Excel spreadsheet.

A farmer focusing on the production of eco-friendly chicken eggs collects the following data about his output. In a sample of 50 eggs, the farmer finds the average egg to weigh 47 grams. The standard deviation of the egg weight is 2 grams and the distribution of weights resembles a normal distribution reasonably closely. The farmer can sell the eggs to a local distributor. However, they have to be in the interval between 44 grams and 50 grams (i.e., the lower specification limit is 44 grams and the upper specification limit is 50 grams). What is the capability score of the eco-friendly chicken egg operation? What percentage of the produced eggs fall within the specification limits provided by the local distributor? By how much would the farmer have to reduce the standard deviation of the operation if his goal were to obtain a capability score of Cp=2/3 (i.e., get 4.5% defects)?

The owner of a specialty coffee shop wants to study coffee purchasing habits of customers at her shop. She selects
a random sample of 60 customers during a certain week. Data are available in the worksheet labeled “Problem 2”
in the spreadsheet.

1. Construct a 90% confidence interval on the proportion of customers who say they “definitely will”
recommend the specialty coffee shop to family and friends.

Problem 2 Data Set

Note: Y is an indicator variable, i.e., if Y=1, then customer said they "definitely would" recommend specialty shop to family and friends, and Y=0 otherwise.