Emerson is making a punch that contains 60% grape juice and the rest lemon-lime soda. the punch has 2 liters of lemon-lime soda. part a: write an equation using one variable that can be used to find the total number of liters of grape juice and lemon-lime soda in the punch. define the variable used in the equation. (5 points) part b: how many liters of grape juice are present in the punch? show your work. (5 points)

Elizabeth claims that the fourth root of 2 can be expressed as 2^m since (2^m)^n = 2. find the values of m and n for the case where elizabeth's claim is true.

Varies inversely with x. if y=8.5 when x=-1 find x when y=-1

Atechnician compares repair costs for two types of microwave ovens (type i and type ii). he believes that the repair cost for type i ovens is greater than the repair cost for type ii ovens. a sample of 6767 type i ovens has a mean repair cost of $79.79$⁢79.79. the population standard deviation for the repair of type i ovens is known to be $19.18$⁢19.18. a sample of 5555 type ii ovens has a mean repair cost of $75.24$⁢75.24. the population standard deviation for the repair of type ii ovens is known to be $21.40$⁢21.40. conduct a hypothesis test of the technician's claim at the 0.050.05 level of significance. let μ1μ1 be the true mean repair cost for type i ovens and μ2μ2 be the true mean repair cost for type ii ovens. step 2 of 4 : compute the value of the test statistic. round your answer to two decimal places.