Prove that each argument is valid by replacing each proposition with a variable to obtain the form of the argument. then use the rules of inference to prove that the form is valid. (a) if i drive on the freeway, i will see the fire. i will drive on the freeway or take surface streets (or both). i am not going to take surface streets. : i will see the fire. (b) if i work out hard, then i am sore. if i am sore, i take an aspirin. i did not take an aspirin. : : i did not work out hard.

There are 10 chicks on ginger's farm .she has 2 chicks in one outdoor pen and 5 chicks in another. the rest of the chicks are in the barn.what is the fraction of total chicks in outdoor pens?

Order the equations from least to greatest based on the number of solutions to each equation.-4^x -1 = 3^(-x) – 2 -3x + 6 = 2^x+13^x – 3 = 2x - 2

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.