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Suppose the mean length of time between submission of a state tax return requesting a refund and the issuance of the refund is 47 days, with standard deviation 6 days. Find the probability that in a sample 50 of returns requesting a refund, the mean such time will be more than 50 days
Given that ๐บ = {๐ โ โ|๐ โ โ1} and ๐ โ ๐ = ๐ + ๐ + ๐๐, show that (๐บ, โ) is indeed a group.
When considering the set of all the natural numbers (โ), show whether the mathematical operations of addition, subtraction, multiplication and division are: (a) Associative (b) Commutative.
Define K-edge colouring and K-vertex colouring of a graph. Find the edge chromatic numbers to colour the edges of the complete graph with four and five vertices
If l, m be the portions of the axes of x and y intercepted by the tangent at any point ( x,y) on the curve (ย x/a )๏ปฟ^2/3+ย ย (ย ย y/b)๏ปฟ^2/3ย ย , show thatย ( l^2/a^2) +(m^2/b^2)=1
The drawing below shows a square with side a. A straight line intersects the square and encloses
an area A. The heights x and y on the left and right side (in a distance d from the square) of
the intersecting line can be varied. Assuming that x y and x; y a, nd an expression for
the enclosed area A(x; y) with respect to x and y.
It is claimed that the average time it takes high school seniors to complete a standardized
test is more than 30 minutes. A random sample of 24 high school seniors took an average
of 30 minutes to complete this test with a standard deviation of 3 minutes. Test the claim
at 1% level of significance.
State the Pigeonhole Principle. A chess player wants to prepare for a championship match by playing
some practice games in 77 days. She wants to play at least one game a day but no more than 132
games altogether. Prove that there is a period of consecutive days within which she plays exactly 21
games
State the Pigeonhole Principle. In a result sheet of a list of 60 students, each marked โPassโ or โFail
โ. There are 35 students pass. Show that there are at least two students pass in the list exactly nine
students apart. (for example students at numbered 2 and 11 or at numbered 50 and 59 satisfy the
condition).
Prices of basic commodities are often greatly affected by typhoons. During the aftermath of recent typhoon, the prices of bangus were reported to have been sold at P20 - P25 more
