Search & Filtering
Frequent checks on the spending patterns of tourists returning from countries in Asia were made and the average amount spent by all tourists was found to be R1010 per day. To determine whether there has been a change in the average amount spent, a sample of 70 travelers was selected and the mean was determined as R1090 per day with a standard deviation of R300. A researcher wants to test for evidence of a change in the expenditure amount changed, using 0.05 level of significance. What is the appropriate distribution to use? Motivate your answer
3. A certain report claims that less than 40% of BTS fans based on Southeast Asia come from
the Philippines.
H 0 : ___________________________________________________________
H a : ___________________________________________________________
1.Find the domain of the function π(π₯)=log4(π₯2+4π₯β5ππ₯β1).
Β
2. Construct the tangent line to the graph of the function π(π₯)=βπ₯+2π₯ which is perpendicular to the line π₯+3π¦β2=0.
Β
3. Find the maximal intervals of monotonicity of the function π(π₯)=arctg(π₯2β4π₯).
Β
4. Calculate the integral β«π₯2(π₯3+4)2 ππ₯2β1.
Β
5. Find the particular solution of the differential equation π¦β²=β(2π¦+1)β tg(π₯) which fulfills the initial condition π¦(π4)=12.
Β
6. Solve the matrix equation 2π³+π=3β¬βππ³ if π=(β4β332), β¬=(1β121).
Β
1. Solve the matrix equation 4π³ββ¬=π³β¬+2π if π=(β2141), β¬=(71β72).
Β
2. Calculate the inverse matrix to the matrix π=(001011111). Check whether the obtained inverse matrix is correct.
Β
3. Solve the system of linear equations: π₯β2π¦+π§=5,β2π₯+3π¦βπ§=β8,βπ₯βπ¦+2π§=2.
Β
Β
4. Calculate the area of the flat shape bounded by the curves: π¦=βπ₯β1,π¦=3βπ₯,π¦=0.
Β
5. Find all the extrema of the function π(π₯)=β16βπ₯2.
Β
6. Find the maximal intervals of convexity (concavity) of the function π(π₯)=2π₯+arctg(3π₯). Find the respective inflection points.
Β
1.Β Β Β Β Strong steel company operates two steel mills with different production capacities. Mill I can produces 1000 tons per day of AAA steel, 3000 tons per day of AA steel , 5000 tons of per day of A steel. Mill F can produce 2000 tons per day of each grade of steel. The company has made a contract with the construction firm to provide 24,000 tons of AAA steel, 32,000 tons of AA steel and 40,000 tons of A steel. The cost of running mill I is $1,400 per day and mill F is $ 1000 per day.Β (2 pt each)
a)Β Β Formulate linear programming model?
b)Β Β How many amount of mill I and F should be produced? Solve by using graphical method? & Simplex Solution Method
Find each of the following percentile points
under the normal curve.
1. P76
2. P85
3. P39
4. P51
5. P88
A nationwide survey of college seniors by the
University of Michigan revealed that almost 70% disapprove of daily pot smoking, according to a report in
Parade. If 12 seniors are selected at random and asked
their opinion, find the probability that the number who
disapprove of smoking pot daily is
(a) anywhere from 7 to 9;
(b) at most 5;
(c) not less than 8
The integrated curriculum mode, sometimes referred to as integrative teaching, is both a method of teaching and a way of organising the teaching programme so that many subject areas and skills provided in the curriculum can be linked to one another. Provide an example of how you, as the teacher, could use the content in Natural Sciences as a vehicle for mathematical skills development.
Adequate knowledge of the content, coupled with the knowledge of the learners,
enables the teacher to plan and modify his/her teaching. Do you agree with
statement? Motivate.
Let R be a reflexive relation on a set A. Show that R β R2.
