Brady is a figure skater. He finds a few of the jumps he does to
be difficult, but the rest are easy for him. He must include four
jumps in his routine. He always makes the first jump a difficult
one. After a difficult jump, there is a 0.4 probability that he'll
do another difficult jump, and otherwise he'll do an easy one.
After an easy jump, there is a 0.2 probability that he'll do
another easy one, and otherwise he'll do a hard
one.
What is the probability that the final (fourth) jump of his routine
will be an easy one?
What is the probability that all four jumps of his routine will be
difficult ones?
Enter your answers as whole numbers or decimals.
In: Advanced Math
In: Advanced Math
Let X = {1, 2, 3, 4}, Y = {a, b, c}.
(1) Give an example for f : X → Y so that ∀y ∈ Y, ∃x ∈ X, f(x) = y. 1 2
(2) Give an example for f : X → Y so that ∃y ∈ Y, ∀x ∈ X, f(x) = y.
(3) Give an example for f : X → Y and g : Y → X so that f ◦ g = IY
In: Advanced Math
Let Z2 [x] be the ring of all polynomials with coefficients in Z2. List the elements of the field Z2 [x]/〈x2+x+1〉, and make an addition and multiplication table for the field. For simplicity, denote the coset f(x)+〈x2+x+1〉 by (f(x)) ̅.
In: Advanced Math
QualSupport Corporation manufactures seats for automobiles, vans, trucks, and various recreational vehicles. The company has a number of plants around the world, including the Denver Cover Plant, which makes seat covers.
Ted Vosilo is the plant manager of the Denver Cover Plant but also serves as the regional production manager for the company. His budget as the regional manager is charged to the Denver Cover Plant.
Vosilo has just heard that QualSupport has received a bid from an outside vendor to supply the equivalent of the entire annual output of the Denver Cover Plant for $35 million. Vosilo was astonished at the low outside bid because the budget for the Denver Cover Plant’s operating costs for the upcoming year was set at $52 million. If this bid is accepted, the Denver Cover Plant will be closed down.
The budget for Denver Cover’s operating costs for the coming year is presented below.
|
Denver Cover Plant |
||
| Materials | $ 14,000,000 | |
| Labor: | ||
| Direct | $13,100,000 | |
| Supervision | 900,000 | |
| Indirect plant | 4,000,000 | 18,000,000 |
| Overhead: | ||
| Depreciation—equipment | 3,200,000 | |
| Depreciation—building | 7,000,000 | |
| Pension expense | 5,000,000 | |
| Plant manager and staff | 800,000 | |
| Corporate expenses* | 4,000,000 | 20,000,000 |
| Total budgeted costs | $52,000,000 | |
*Fixed corporate expenses allocated to plants and other operating units based on total budgeted wage and salary costs. |
||
Additional facts regarding the plant’s operations are as follows:
Due to Denver Cover’s commitment to use high-quality fabrics in all of its products, the Purchasing Department was instructed to place blanket purchase orders with major suppliers to ensure the receipt of sufficient materials for the coming year. If these orders are canceled as a consequence of the plant closing, termination charges would amount to 20% of the cost of direct materials.
Approximately 400 plant employees will lose their jobs if the plant is closed. This includes all of the direct laborers and supervisors as well as the plumbers, electricians, and other skilled workers classified as indirect plant workers. Some would be able to find new jobs while many others would have difficulty. All employees would have difficulty matching Denver Cover’s base pay of $18.80 per hour, which is the highest in the area. A clause in Denver Cover’s contract with the union may help some employees; the company must provide employment assistance to its former employees for 12 months after a plant closing. The estimated cost to administer this service would be $1.5 million for the year.
Some employees would probably choose early retirement because QualSupport has an excellent pension plan. In fact, $3 million of the annual pension expense would continue whether Denver Cover is open or not.
Vosilo and his staff would not be affected by the closing of Denver Cover. They would still be responsible for administering three other area plants.
If the Denver Cover Plant were closed, the company would realize about $3.2 million salvage value for the equipment and building. If the plant remains open, there are no plans to make any significant investments in new equipment or buildings. The old equipment is adequate and should last indefinitely.
Without regard to costs, identify the advantages to QualSupport Corporation of continuing to obtain covers from its own Denver Cover Plant.
QualSupport Corporation plans to prepare a financial analysis that will be used in deciding whether or not to close the Denver Cover Plant. Management has asked you to identify:
The annual budgeted costs that are relevant to the decision regarding closing the plant (show the dollar amounts).
The annual budgeted costs that are irrelevant to the decision regarding closing the plant and explain why they are irrelevant (again show the dollar amounts).
Any nonrecurring costs that would arise due to the closing of the plant, and explain how they would affect the decision (again show any dollar amounts).
Looking at the data you have prepared in (2) above, what is the financial advantage (disadvantage) of closing the plant? Show computations and explain your answer.
Identify any revenues or costs not specifically mentioned in the problem that QualSupport should consider before making a decision.
In: Advanced Math
Find a particular solution to the differential equation: y'' - 1y' - 20y = -400t^3
In: Advanced Math
An amount of $200,000 is borrowed for 5 years at a rate of 12%. Make an amortization schedule showing the quarterly payment, the quarterly interest on the outstanding balance, the portion of the payment going toward reducing the debt, and the balance.
In: Advanced Math
can someone explain the stokes theorem using an example other than flux or work?
In: Advanced Math
Solve by using eigen value of matrices. Provide a solution family of real functions.
x'=4x-10y
y'=5x-6y
In: Advanced Math
Find a primitive root for: (a) n = 18, (b) n = 50 (c) n = 27, (d) n = 625.
In: Advanced Math
In: Advanced Math
Using only membership tables (i.e., without Venn diagrams or set identities), prove or disprove that (? − ?) ∪ (? − ?) and ((? − ?̅) − ?) ∪ (? ∩ ?̅) ∪ (? − (? ∪ ?)) are equivalent. Ensure that you fill the table completely, even if you are disproving this equivalence, and do not skip any columns.
In: Advanced Math
Show that every cauchy sequence of reals is convergent
In: Advanced Math
The following has been received as a result of bids.
17. An RFP was issued for business training in an office environment. As a result, seven proposals were received. The subsequent rated and price evaluations for the firms are below.
Firm Rated Evaluation Financial Bid
A 90 $150.000
B 85 $140,000
C 80 $120,000
D 75 $110,000
E 70 $120,000
F 65 $119,000
G 60 $100,000
The evaluated pass mark for this requirement was 70
1. Which firm would be recommended to be awarded the contract if the method of evaluation is the lowest priced responsive (technically compliant) proposal?
2. Which firm would be recommended to be awarded the contract if the method of evaluation is the lowest priced responsive (technically compliant) proposal and there was a stipulated maximum financial budget of $139,000?
3. Which firm would be recommended to be awarded the contract if the method of evaluation is lowest price per point?
4. Which firm would be recommended to be awarded the contract if the method of evaluation is highest combined rating with price at 50% and rated evaluation 50% of the total?
5. Which firm would be recommended to be awarded the contract if the method of evaluation is highest combined rating with price at 25% and rated evaluation 75% of the total?
Note: you MUST show any calculations.
In: Advanced Math
Suppose you are on a game show and are shown three doors. Behind two are goats, and behind the third is a shiny new car. You are asked to pick a door, and will win whatever is behind it. Let's say you pick door 1. Before the door is opened, however, the host, who knows what's behind the doors, opens one of the other two doors, revealing a goat, and asks you if you wish to change your selection to the third door (i.e., the door that neither you nor he opened). What should you do?
In: Advanced Math