For groups g_1 and g_2 a function f: g_1 -rightarrow g_2 is a homomorphism if f (g*1 h) = f(g) *2/(h) for every g, h e g1. let k = {g e g1 {(g) = e_2} where e_2 is the identity of g_2. show that k is a subgroup of g1. show that if f is one-to-one then k = {e1} and conversely that if k = {e1} then f must be one-to-one.

For which of the following counts would a binomial probability model not be reasonable? a)the number of people in a classroom born in januaryb) the number of people in a classroom with red hair c) the number of people admitted to a hospital in a day with a particular disease d) the number of heart beats in a one-minute perio.

Each month, a shopkeeper spends 5x + 14 dollars on rent and electricity. if he spends 3x−5 dollars on rent, how much does he spend on electricity? for which value(s) of x is the amount the shopkeeper spends on electricity less than $100? explain how you found the value(s).

Jamie went to home depot. she bought 25 bags of soil that cost $9 per bag. she bought 15 pots at $8 each, and she bought 23 bags of pebbles at $15 each. she used a coupon that gave her $5 off for every 100 dollars she spent. how much did jame pay at the end?