A badminton team of 4 men and 4 women is to be selected from 9 men and 6 women. (i) Find the total number of ways in which the team can be selected if there are no restrictions on the
selection.

Two of the men are twins.
(ii) Find the number of ways in which the team can be selected if exactly one of the twins is in the
team.

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If the value of cos330°is√3/2 then find cos 165°.

(b) suppose that consolidated power decides to use a level of significance of α = .05, and suppose a random sample of 100 temperature readings is obtained. if the sample mean of the 100 temperature readings is x⎯⎯ = 60.990, test h0 versus ha and determine whether the power plant should be shut down and the cooling system repaired. perform the hypothesis test by using a critical value and a p-value. assume σ = 5. (round your z to 2 decimal places and p-value to 4 decimal places.)