Let ƒ(n) and g(n) be asymptotically positive functions. prove or disprove each of the following conjectures.
a ƒ(n)∈o(g(n)) implies g(n)∈o(ƒ(
b ƒ(n)+ g(n)∈θ(min(ƒ(n),g(
c ƒ(n)∈o(g(n)) implies lg(ƒ(n))∈o(lg(g( where lg(g(n))≥1 and ƒ(n)≥1 for all sufficiently large n.
d ƒ(n)∈o(g(n)) implies 2^(ƒ(n))∈o(2g(
e ƒ(n)∈o((ƒ(n))^2).
f ƒ(n)∈o(g(n)) implies g(n)∈ω(ƒ(
g ƒ(n)∈θ(ƒ(n/
h ƒ(n)+ o(ƒ(n))∈θ(ƒ(

The jurassic zoo charges $14 for each adult admission and $5 for each child. the total bill for 77 people from a school trip was $565. how many adults and how many children went to the zoo? i

Dakota earned $7.50 in interest in account a and $18.75 in interest in account b after 15 months. if the simple interest rate is 4% for account a and 5% for account b, which account has the greater principal? explain. to make it a little easier, there is an image. good luck!

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.