Let p and q be the propositions p: I bought a lottery ticket this week. q :I won the million dollar jackpot. Express each of these propositions as an English sentence.
a)¬p
b) p∨q
c) p → q
d) p∧q
e) p ↔ q
f) ¬p →¬ q
g) ¬p∧¬q
h) ¬p∨(p∧ q)

Sketch the region enclosed by the given curves. decide whether to integrate with respect to x or y. draw a typical approximating rectangle and label its height and width. y= 5x, y=7x^2then find the area s of the region.

Ibeg you to me 20. a reaction produces 4.93 l of oxygen, but was supposed to produce 1 mol of oxygen. what is the percent yield?

Aaron invested a total of $4,100, some in an account earning 8% simple interest, and the rest in an account earning 5% simple interest. how much did he invest in each account if after one year he earned $211 in interest? select one: a. $200 at 8%, $3,900 at 5% b. $3,200 at 8%, $900 at 5% c. $900 at 8%, $3,200 at 5% d. $3,900 at 8%, $200 at 5%