Given the following project:

1. Develop a time limited resource profile chart assuming unlimited resource availability. That is, determine the resource requirement on a weekly basis if the project is to be completed in the minimum time.
2. Develop a resource-constrained schedule using the sequential heuristic.

Assume the followings:

• The original relationships of the network cannot be violated.
• Scheduling priority for each activity is determined via the following rules

• least total slack
• early start time
• smallest duration
• maximum resource level

• once an activity is scheduled it continues without interruption

The available resource is three units

1.Find the equation of the tangent to x=t^2-t, y=t^2+t+1, at the point t=1

2.Find the length of the curve x=t*sint, y=t*cost, 0≤t≤1

a, The vectors v1 = < 0, 2, 1 >, v2 = < 1, 1, 1 > , v3 = < 1, 2, 3 > , v4 = < -2, -4, 2 > and v5 = < 3, -2, 2 > generate R^3 (you can assume this). Find a subset of {v1, v2, v3, v4, v5} that forms a basis for R^3.

b. v1 = < 1, 0, 0 > , v2 = < 1, 1, 0 > and v3 = < 1, 1, 1 > is a basis for R^3 (you can assume this.) Given an arbitrary vector w = < a, b, c > write w as a linear combination of v1, v2, v3.

c. Find the dimension of the space spanned by x, x-1, x^2 - 1 in P2 (R).

A researcher tested whether aerobics increased the fitness level of eight undergraduate students participating over a 4-month period. Students were measured at the end of each month using a 10-point fitness measure (10 being most fit). The data are shown here. Conduct an ANOVA to determine the effectiveness of the program, using alpha = .05. Use the Bonferroni method to detect exactly where the differences are among the time points (if they are different).

In the previous item, we used the Mann-Whitney test rather than an independent t-test. Why might we Mann-Whitney rather than the t-test?

Original question- A sample of nurses with affiliation to private hospitals (affiliation = 0) and to university hospitals (affiliation = 1) was asked to rate their confidence in making the right decisions based on their level of ongoing inservice professional development. Use a Mann-Whitney U-test to determine if the distribution of confidence in each group is the same. Be sure to always write the null and alternate hypotheses, so that the decision is made in the correct direction. Also, conduct all as two-tailed tests at α = 0.05.

On 15 September 2020 you plan to buy a 6% p.a. Treasury bond maturing on 15 September 2026.

a. How much would you pay to earn 7% p.a. on your transaction? Ignore taxation considerations.

b. How much would you pay to earn a net return of 7% p.a. on your transaction, allowing for tax on interest only of 30%? In this instance, assume tax on interest is paid immediately.

c. How much would you pay to earn a net return of 7% p.a. on your transaction, allowing for tax on interest and capital gains of 30%? In answering this question, you should assume that the tax on interest and capital gains is deferred by twelve months.

d. Allowing for tax on interest and capital gains of 30%, what would your net annual yield be if you paid $97.447 for the bond? Again, assume that the tax on interest and capital gains is deferred by twelve months.

that all the interest rates given in this question are j2 rates. Pls answer it on excel or spreadsheet with separate part for each questions

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1.Verify that the hypotheses of the Mean-Value Theorem are satisfied for the function ?(?) = (√(? − 1) + 1) on the interval [2,10], and find all values of ? in the given interval that satisfy the conclusion of the theorem.

2. Verify that the hypotheses of the Rolle’s Theorem are satisfied for the function ?(?) = (?^2−1)/(?−2) on the interval [−1,1], and find the value of ? in the given interval that satisfy the conclusion of the theorem.

3. Evaluate lim ?→ ∞ (√(4?+1)+√(4?−1) / (?) ) . Hint if divide by x or x^2 then please show to understand.

4. State the ...

a. Mean-Value Theorem

b. Rolle's Theorem

Only one answer is correct for each question

Q1:

Lactobacillus acidophilus is responsible for

Question 1:

Sequence the jobs shown below by using a Gantt chart. Assume that the move time between machines is one hour. Sequence the jobs in priority order 1, 2, 3, 4.

1. Using finite capacity scheduling, draw a Gantt chart for the schedule (Marks 0.5)
2. What is the make span? (Marks 0.5)
3. How much machine idle time is there? (Marks 0.5)
4. How much idle time (waiting time) is there for each job? (Marks 0.5)
5. When is each job delivered? (Marks 0.5)
6. Which department is the bottleneck? (Marks 0.5)
7. Calculate the machine utilization? (Marks 0.5)