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Explain that odd positive integer to be a perfect square, Show that for odd...

Show that for odd positive integer to be a perfect square, it should be of the form 8k +1. Let a=2m+1 Ans: Squaring both sides we get a2 = 4m (m +1) + 1 ∴ product of two

Upper limit of normal , Frequently, tests that yield abnormal results are r...

Frequently, tests that yield abnormal results are repeated for confirmation.  What is the probability that for a usual person a test will be at least 1.5 times as high as the upper

Farmer counting grasshoppers in his fields, Farmer counting grasshoppers in...

Farmer counting grasshoppers in his fields, probably not normally distributed due to growing conditions. After various rows the mean number of grasshoppers is 57 SD 12. What will b

Rationalize the denominator, Rationalize the denominator for following.  Su...

Rationalize the denominator for following.  Suppose that x is positive. Solution We'll have to start this one off along with first using the third property of radica

Find out height of the box which will give maximum volume, We contain a pie...

We contain a piece of cardboard i.e. 14 inches by 10 inches & we're going to cut out the corners as illustrates below and fold up the sides to form a box, also illustrated below. F

Analysis and optimization, 1. In an in finite horizon capital/consumption m...

1. In an in finite horizon capital/consumption model, if kt and ct are the capital stock and consumption at time t, we have f(kt) = ct+kt+1 for t ≥ 0 where f is a given production

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