Let C(x, y) mean that student x is enrolled in class y, where the domain for x consists of all students in your school and the domain for y consists of all classes being given at your school. Express each of these statements by a simple English sentence. a) C(Randy Goldberg, CS 252) b) ∃xC(x, Math 695) c) ∃yC(Carol Sitea, y) d) ∃x(C(x, Math 222) ∧ C(x, CS 252)) e) ∃x∃y∀z((x ≠ y) ∧ (C(x, z) → C(y, z)))f) ∃x∃y∀z((x ≠ y) ∧ (C(x, z) ↔ C(y, z))

Fredrick designed an experiment in which he spun a spinner 20 times and recorded the results of each spin

Which is a true statement comparing the graphs of x^2/6^2-y^2/8^2 = 1 and x^2/8^2-y^2/6^2 the foci of both graphs are the same points. the lengths of both transverse axes are the same. the directrices of = 1 are horizontal while the directrices of = 1 are vertical. the vertices of = 1 are on the y-axis while the vertices of = 1 are on the x-axis.

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) what is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips, inclusive? (b) what is the probability that a randomly selected bag contains fewer than 1125 chocolate chips? (c) what proportion of bags contains more than 1225 chocolate chips? (d) what is the percentile rank of a bag that contains 1425 chocolate chips?