Let x be the size of a certain population of predators and y the size of the population of prey upon which they feed. As function of time t, x = t 2 + 4 and
y = 2t 2 − 3t . Let u be the number of prey to each predator. Find the rate of change of u .
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The following data were obtained in a study of the relationship between the resistance (ohms) and the failure time (minutes) of certain overloaded resistors.
| Resistance | 48 28 33 40 36 39 46 40 30 42 44 48 39 34 47 |
| Failure time | 45 25 39 45 36 35 36 45 34 39 51 41 38 32 45 |
Vectors a and b are given by a = 3i − 2j + k and b = −2i + 2j + 4k . Find
i) magniture of a and b and the angle between them.
ii) projection of the vector (a +1/ 2b) onto a .
iii) which of the following vectors are perpendicular to a ?
c = −i − 4j + 2k, d = −3i + k, e = 2i + 2j − 2k .
The probability that a person over 60 years of age in a certain community drinks alcohol 2/5 is
and the probability that a person over 60 years of age has heart disease is 2/15 . The
probability that a person over 60 years of age drinks alcohol and has heart disease is 1/16 . Are
‘drinking alcohol’ and ‘heart disease’ independent events?
A training director wishes to find out whether a particular training programme increases the efficiency of the employees. He plans to take a random sample of employees and record their efficiency rating before the training starts. After the completion of the programme, the efficiency of the same sample of employees is recorded as given in the table below. At 0.05 level of significance do you reject or accept the null hypothesis
H 0 : µd = 0 against H1 : µd > 0
where µd = 0 is the mean of the difference?Four groups of students were subjected to different teaching techniques and tested at the end of a specified period of time. As a result of dropouts from the experimental groups the number of students varied from group to group. Do the data shown below present sufficient
evidence to indicate a difference in the mean achievement for the four teaching techniques at 0.01 level of significance? What is the conclusion if you fix the level of significance at 0.05?
| Group 1 | Group 2 | Group 3 | Group 4 |
| 65 | 75 | 59 | 94 |
| 87 | 69 | 78 | 89 |
| 73 | 83 | 67 | 80 |
| 79 | 81 | 62 | 88 |
| 81 | 72 | 83 |
|
| 69 | 79 | 76 |
|
|
| 90 |
|
|
The following distribution gives the top speeds (in kilometers per hour)
at which thirty races were clocked in auto race.
| Top speed | 145 | 150 | 160 | 170 |
| No. of racers | 9 | 8 | 11 | 2 |
A continuous random variable X has the p.d.f.
Calculate the mean and standard deviation of X . Construct the distribution function F ( x) and hence evaluate P( X > 1/4) .