Given the activity network below with ini- tial activity A and final activity F, what is the minimum time that the entire project will be completed? B -3- D 2 10 5 15 35 A 3 6 7 -3- E 5 4 F
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- MELC182 Activity 1: Classify the following as discrete or continuous. 1. The number of senators present in the meeting. 2. the weight of newborn babies for the month of June. 3. The number of ball pens in the box 4. The amount of salt needed to bake a loaf 5. The capacity of an auditorium. of bread. 6. The number of households with television. 7. The height of mango trees in a farm. 8. The area of lots in a subdivision. 9. The number of students who joined the field trip. 10. The time it takes a student to finish his test in a particular subject MELC3 Activity 2: Determine the values of the random variable in each of the following situations. 11. Two coins are tossed. Let T be the number of tails that occur. Determine the values of the random variable T. 12. Three coins are tossed. Let T be the number of tails that occur. Determine the values of the random variable T. 13. A meeting of consuls was attended by 4 Americans and 2 Germans. If three consuls were selected at random one…find the mximum possible order of S5The game commissionintroduces 100 deer into newly acquired state gamelands. The population N of the herd is modeled byN = 20(5 + 3t)/1 + 0.04t, t ≥ 0where t is the time in years.(a) Use a graphing utility to graph this model.(b) Find the populations when t = 5, t = 10, andt = 25.(c) What is the limiting size of the herd as timeincreases?
- Construct index number of price from the following data byapplying: 1)Fisher’s Ideal method 2016 2016 2017 2017 Commodity Price Quantty Price QuanttyA 2 8 4 6B 5 10 6 5C 4 14 5 10D 2 19 2 13The manager of a market can hire either Mary or Alice. Mary, who gives you service at an exponential rate 20 customers per hour, can be hired at a rate of $3 per hour. Alice, who gives service at an exponential rate of 30 customers per hour, can hired at a rate of $C per hour. The manager estimates that, on the average, each customer’s time is worth $1 per hour and should be accounted for in the model. Assume customers arrive at a Poisson rate of 10 per hour. a) What is the average cost per hour if Mary is hired? If Alice is hired? b) Find C if the average cost per hour is the same for Mary and Alice.An efficiency study of the first shift (from 8:00 A.M. to 5:00 P.M.) at a certain factory indicates that an average worker who arrives on the job at 8:00 A.M. will have assembled Q(t) = -2t3 + 8t2 + 10t MPEG Players t hours later. How many hours after the start of the shift is the worker performing most efficiently?
- A researcher designs an experiment using two drugs, she prepares 15 independent flasks of yeast growth medium and yeast cells. She adds tunicamycin (T) or caffeine (C) to 5 flasks each. Remaining 5 flasks get no drugs (ND). Doubling time of the yeast cells are measured in each flask, data is provided below: Flask T Flask C Flask ND 1 8.2 6 5.2 11 6 2 6.8 7 6.1 12 5.1 3 8 8 6.2 13 5.6 4 7.6 9 5.7 14 5.2 5 7.9 10 6.3 15 6.1 a. Test if mean doubling time is different in Caffeine (C ) when compared to no drug (ND) using an ANOVA method, report an approximate p-value for the level of significance. b. If a drug decreases the doubling time of yeast cells, what could be the purpose of using this drug?Environment-friendly agricultural practice includes the application of pesticides when it is really necessary, e.g., at the beginning of a pest emergence. Such practice, depending on the field conditions, and the reaction of growers, for the same level of “alert”, inspired this question.Assume that in the middle of the growing season in a given area, there is one pest emergence every two weeks on average. There is a generalized emergence of pests in a given area. At this stage of the emergence, not all growers decide to apply pesticides, hoping that the emergence will be brief or without implication for their field. Accordingly, assume 75% of the growers in that area at that time decide to apply pesticides. a) What is the probability that among five growers randomly sampled, two decide not to apply pesticides? b) What is the probability that among 10 randomly sampled growers, more than nine decide to apply pesticides?A researcher designs an experiment using two drugs, she prepares 15 independent flasksof yeast growth medium and yeast cells. She adds tunicamycin (T) or caffeine (C) to 5 flasks each. Remaining 5 flasks get no drugs (ND). Doubling time of the yeast cells are measured in each flask, data is provided below: Flask T Flask C Flask ND 1 8.2 6 5.2 11 6 2 6.8 7 6.1 12 5.1 3 8 8 6.2 13 5.6 4 7.6 9 5.7 14 5.2 5 7.9 10 6.3 15 6.1 Test if mean doubling time is different than others in at least one growth condition (ND, T or C), using a non-parametric method and report an approximate p-value for the level of significance. What is the hypotheses and the assumptions of this test?
- Consider the following list of activities with time (in months) Activity A B C D E F G H Immediate Predecessor ----- ----- A A,B A,B C D,F E,G Activity Optimistic Most Probable Pessimistic A 3.5 4.0 4.5 B 2.0 3.0 7.0 C 6.5 7.5 10.0 D 5.0 5.5 6.0 E 5.0 6.5 8.0 F 8.0 9.5 11 G 6.0 7.0 9.5 H 4.0 5.0 6.0 c) What is the variance of the project completion time? d) What is the probability of completing in 32 months?We want to make a time study on a worker-machine cycle. To do that, we observe times via the snapback method. This cycle comprises threeelements: x, y, and z. Elements x and y are worker-controlled and performance rated at 100%. Element z is machine-controlled. Besides, it is giventhat elements y and z are performed at the same time. The PFD allowance = 17% and the machine allowance = 10%. At each cycle, the systemproduces one work piece. Q: Find (a) the normal time and (b) standard time for the cycle. a) a: 2,25; b: 3,6155b) a: 3,15; b: 3,7855c) a: 2,25; b: 2,5625d) a: 3,15; b: 2,5625e) a: 3,15; b:3,6155In each of the following populations, per capita production changes over time according to a fixed pattern (rather than a random pattern). For each population, find the population during the first 6 years and sketch a graph. Do you think it will grow or shrink in the long run? Find the average per capita production in each case. Does an average greater than 1.0 always mean that the population is growing? A population starts at size 1000 and grows with per capita production rt that alternates between 0.6 and 1.5.