6 plates and 5 cups cost 25.70 dollars. 7 plates and 6 cups cost 30.20 dollars. Each plate costs the same amount as the other plates, and each cup costs the same amount as the other cups. What is the cost of 1 plate? What is the cost of 1 cup?

(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.)