Calculate the future value of $2000 invested at 5% annual simple interest rate over a period of 5 years

5% annual interest rate compounded yearly over a period of 5 years where the is no withdrawal from the account

5% annual interest rate compounded semiannually over a period of 5 years when there is no withdrawal from the account.

When we gain more? Explain why?

Question 1

A copper tube having a cross-sectional area of 2000 mm² and length of 300 mm is placed between two rigid caps. Four 22 mm diameter steel bolts are symmetrically arranged parallel to the axis of the tube and are lightly fastened. Calculate:

1. The stress in the tube if the temperature of the assembly is raised by 70⁰C.
2. The load each bolt will carry at the raised temperature.                                  

            E_ST = 200 GPa;   α_ST = 12 x 10^-6 / ⁰C         

           E_CU = 100 GPa;   α_CU = 16 x 10^-6 / ⁰C

Q3: A study followed a population of 2000 women aged over 65 years for 10 years and measured the number of cases of osteoporosis diagnosed during that time period. The investigators were interested in the effect of regular exercise on the development of osteoporosis and divided he women into two groups: 1000 women who took regular exercise and 1000 women who did not take regular exercise. The investigators recorded 800 new cases of osteoporosis over the 10 years of the study, 300 in those who took regular exercise and 500 in those who did not. The number of person years at risk was 8350 in those who exercised regularly and 6950 in those who did not. Calculate (i) the risk ratio and (ii) the rate ratio for the effect of regular exercise on osteoporosis in these women. Interpret your answer. (4pts)

Sally was hired at an annual salary of $60,000 on 1/1/20.   She elected to contribute $2000 to her Flexible Spending Account (FSA) and her employer contributed $500 to the plan. She contributed $5,000 to the company’s 401(k) plan and the company contributed $2500.   In addition, she contributed $100 from her payroll to the local United Way campaign. Compute the amount of her 2020 compensation that is subject to FICA taxes and the amount subject to income taxes.

A start-up company has 2000 investors, that company loses investors at a rate of 10 per year. Every time the company loses an investor, the company gets a loss of $200,000. For every investor that remains the company makes a profit of $2,000. Let F be the total earnings the company makes in a year, and X be the number of investors the company loses.

1)Write a function that calculates yearly earnings F as a function of X

2)Find P(F < 0), the probability that earnings are negative

3)E[F]

4)What is the probability that the company loses exactly 5 investors in a given year, given that they have not lost any investors in the first half of the year

Consider a supplier order allocation problem under multiple sourcing, where it is required to buy 2000 units of a certain product from three different suppliers. The fixed set-up cost (independent of the order quantity), variable cost (unit price), and the maximum capacity of each supplier are given in Table 5.15 (two suppliers offer quantity discounts). The objective is to minimize the total cost of purchasing (fixed plus variable cost). Formulate this as a linear integer programming problem. You must define all your variables clearly, write out the constraints to be satisfied with a brief explanation of each and develop the objective function. table : 5.15 supplier data for exercise 5.5

supplier / fixed cost/ capacity /unit price

1 / $100 / 600 unit / $10 per unit for first 300 units; $7 per unit for remaining 300 units

2 / $500 / 800 units/ $2 per unit for all 800 units

3 / $300 / 1200 units / $6 per unit for first 500 units;  $4 per unit for remaining 700 units

Reformulate the problem under the assumption that both suppliers 1 and 3 offer all units discount, as described in the following;

-Supplier 1 charges $10 per unit for orders up to 300 units and for orders more than 300 units, the entire order will be priced at $7 unit.

-Supplier 3 charges $6 per unit for orders up to 500 units and for orders more than 500 units, the entire order will be priced at $4 per unit.

Fisher is an electronic supplier has annual demand 9000 units. The supplier pays $2000 for each unit and estimate that the annual holding cost 1% of the price. It costs approximately $200 to place an order (managerial and clerical cost). Assume the operates on a 300 day working year.

1. Apply the economic order quantity model to determine Q*
2. How many expected orders be placed per year using the calculated EOQ?
3. Determine the annual ordering, holding and total inventory costs for the EOQ.
4. Guide the management by calculating the expected time between orders
5. If the company used to order 900 units in each order, should the firm stick with the old supplier or take advantage of the new order quantity?

The equilibrium constant (K_p) for the reaction below is 4.40 at 2000. K.

H₂(g) + CO₂(g) ⇌ H₂O(g) + CO(g)

Calculate

Δ

G

for the reaction.

kJ/mol

Calculate

Δ

G for the reaction when the partial pressures are

P_H2 = 0.22 atm,
P_CO2 = 0.72 atm,
P_H2O = 0.66 atm, and
P_CO = 1.16 atm.

Someone sells 2000 tickets for $1 each. Prizes are awarded of one $100, four $50, and eight $25.
Find the expected value if you purchase 1 ticket. Your expected value should end up negative since there are way more chances to not win than to win one of the prizes.
Expected value is calculated by multiplying every possible outcome by its probability and then adding those products. Let's break this down.
a) In this case there are 2000 outcomes. How many expect to be out their dollar and not win anything?
b) What is the probability of not winning anything?
c) How many will win $25?
d) What is the probability of winning $25?
e) If you win $25 after spending $1 for the ticket, what is your true gain?
f) How many will win $50?
g) What is the probability of winning $50?
h) If you win $50 after spending $1 for the ticket, what is your true gain?
i) How many will win $100?
j) What is the probability of winning $100?
k) If you win $100 after spending $1 for the ticket, what is your true gain?
l) Finally add up all the probabilities times the gain or loss associated with them. What is the expected value if you purchase one ticket?
m) What can you expect to happen if you purchase 5 tickets?