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a. Determine the number of sets of all possible random samples that can be drawn from the given population by using formula,nCn,where N is the population size and n is the sample size.write your solutions in the box below.
Find the 90th percentile of the normal curve
Find the 99th percentile of a normal curve
The results of the nationwide aptitude test in mathematics are normally distributed with mean=63 and standard deviation =5 . What is the 97.5th percentile?
Let a_{k} = 3^{k} + k - 2 for all k \geq 0.
Write down the values of a_{1}, a_{2} and a_{3}.
Write down the values of A(1), A(2) and A(3) defined by the recurrence relation: A(0) = -1, A(k) = 3A(k - 1) - 2k + 7, k \geq 1
Show that A(k) = a_{k} is a solution of the recurrence relation for all values of k \geq 1.
When heating a 15 cm long square metal plate, its size increases by 0.05 cm.
Actions to be performed:
Answer: approximately how much did its area increase?
Determine how much its volume increases if it were a cubic plate.
If the plate is cooled and its side decreases by 0.05, how much did its area decrease?
If it is a cubic plate determined and it is cooled by decreasing its side by 0.05, determine how much its volume decreased?
Write down all derangements of the set \left\{ a,b,c,d \right\} and show that the number of derangements is the same as predicted by the recurrence D(n) = (n - 1)(D(n - 2) + D(n - 1)) with initial values D(1) = 0 and D(2) = 1. Hint: a derangement is a permutation of an ordered set where no element is in the same place as before. Example: \left\{ b,a,d,c \right\} is a derangement of \left\{ a,b,c,d \right\} because all of the letters positions have changed.
. A bed mart company is in the business of manufacturing beds and pillows. The company has 40 hours for assembly and 32 hours for finishing work per day. Manufacturing of a bed requires 4 hours for assembly and 2 hours for finishing. Similarly a pillow requires 2 hours for assembly and 4 hours for finishing. Profitability analysis indicates that every bed would contribute Birr 80, while a pillow contribution is Birr 55 respectively. Find out the daily production of the company to maximise the contribution (profit). Solve the problem by graphical method.
In a certain Algebra 2 class of 30 students, 7 of them play basketball and 15 of them play baseball. There are 10 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?
A bed mart company is in the business of manufacturing beds and
pillows. The company has 40 hours for assembly and 32 hours for
finishing work per day. Manufacturing of a bed requires 4 hours for
assembly and 2 hours for finishing. Similarly a pillow requires 2 hours
for assembly and 4 hours for finishing. Profitability analysis indicates
that every bed would contribute Birr 80, while a pillow contribution is
Birr 55 respectively. Find out the daily production of the company to
maximise the contribution (profit). Solve the problem by graphical
method.
