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250 members of a certain society have voted to elect a new chairman. Each member may
vote for either one or two candidates. The candidate elected is the one who polls most votes.
Three candidates x, y z stood for election and when the votes were counted, it was found that:
- 59 voted for y only, 37 voted for z only
- 12 voted for x and y, 14 voted for x and z
- 147 voted for either x or y or both x and y but not for z
- 102 voted for y or z or both but not for x
Required
i. Present the information in a Venn diagram. (6 Marks)
ii. How many voters did not vote? (4 Marks)
iii. How many voters voted for x only? (2 Marks)
iv. Who won the elections? (2 Marks)
A 70 lb bag of rice is being pulled by a person by applying a force F at an angle θ as shown. The force required to drag the bag is given by: F(θ)=70μ/μsinθ+cosθ where μ=0.35 is the friction coefficient. (a) Determine F(θ) for θ= 5°, 10°, 15°, 20°, 25°, 30°, 35° (b) Determine the angle θ where F is minimum. Do it by creating a vector θ with elements ranging from 5°to 35°and spacing of 0.01. CalculateF for each value of θ and then find the maximum F and associated θ with MATLAB's built-in function max
Suppose that each firm currently catches $100 worth of fish per year, and there is $200 worth of fish left in the lake. In the following spreadsheet, enter the amount that each firm would earn in each of the next 10 years if the two firms continue to fish.
Four coins are tossed.Let Z be the random variable representing the number of heads that occur.Find the values of the random variable Z
According to USA Today (March 18, 1997), of 4 million workers in the general workforce, 5.8% tested positive for drugs. Of those testing positive, 22.5% were cocaine users and 54.4% marijuana users. (a) What is the probability that of 10 workers testing positive, 2 are cocaine users, 5 are marijuana users, and 3 are users of other drugs? (b) What is the probability that of 10 workers testing positive, all are marijuana users?
(c) What is the probability that of 10 workers testing positive, none is a cocaine user?
Two balls are picked in succesion without replacement -4 white balls and 5 green balls. Let Y be the random variable representing the number of green balls
find the inverse of f(x) = 5/2 − x, x < 2 ;
1/x, x ≥ 2
the result of a particular examination are given in the table below
passed with distinction 10%
passed without distinction 60%
failed 30%
it is known that a candidate fails in the examination if he obtains less than 40 marks while he must obtain at least 75%marks in order to pass with distinction . determine the mean and standard deviation of distribution of marks .assuming these is to be nominal
An investigator thinks that people under the age of forty have vocabularies that are different than those of
people over sixty years of age. The investigator administers a vocabulary test to a group of 31 younger
subjects and to a group of 31 older subjects. Higher scores reflect better performance. The mean score for
younger subjects was 14.0 and the standard deviation of younger subject's scores was 5.0. The mean score
for older subjects was 20.0 and the standard deviation of older subject's scores was 6.0. Does this
experiment provide evidence for the investigator's theory?
Random sample of 400 men and 200 women is locality were whether they would like to have bus stop near their residence 200 men and 40 women are favor of proposal the test is there any significance diff b/w men and women at 5%.
