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Let n be your special number. Let p be the smallest prime divisor of n. Consider the complete bipartite graph Kp,n. (a) Does Kp,n have a Hamilton circuit? If so, describe it. If not, explain why not. (b) Does Kp,n have a non-cyclic Hamilton path? If so, describe it. If not, explain why not. (c) Does Kp,n have an Euler cycle? Explain your answer. (d) Does Kp,n have a non-cyclic Euler path? Explain your answer.
A division wide aptitude test in mathematics was conducted to 1000 pupils. The mean of the test is 58 and the standard deviation is 12. The scores also approximate the normal distribution. What is the minimum score to belong the upper 20% of the group?
- Directions: Determine each of the following areas and show these graphically. Use probability notation in your final answer. NOTE: Use graphing paper to graph.
1. To the left of z = 1.96 5. Below z = -1.96 9. 1.27≥z≥-2.1
2. At most z = 2.58 6. z≥1 10. z=-0.58
3. At least z = 1.96 7. z≤-1.5
4. To the right of z = 0.33 8. -0.92≤z≤1.75
For a two-tailed test with variance unknown, n=19, and a=0.05, what is the critical value?
The value that separates a rejection region from an acceptance region is called a
In a right-trailed test with a = 0.01. the critical value of z is
If the power series {summation} an xn converges uniformly in ] α ,β [ then so does {summation} an (-x)n . true or false ? Justify
Check whether the series {Summation} n2x5/(n4+x3) , x belongs to [0, a] is uniformly convergent or not ,where a belongs to R
Find 𝑝̂𝑎𝑛𝑑 𝑞̂, given X and n.
1. X = 56, n = 80
B. Find the finite population correction factor given the following: 1. 𝑁=150 𝑛=15 2. 𝑁=600 𝑛=35
