Suppose that a and b are integers, a ≡ 11 (mod 19), and b ≡ 3 (mod 19). find the integer c with 0 ≤ c ≤ 18 such that
a. c ≡ 13a (mod 19).
b. c ≡ 8b (mod 19).
c. c ≡ a − b (mod 19).
d. c ≡ 7a + 3b (mod 19).
e. c ≡ 2a2 + 3b2 (mod 19). f ) c ≡ a3 + 4b3 (mod 19).

Scott harris can invest $7,000 in a 1-year cd that earns interest at an annual rate of 4 percent compounded monthly. the amount per $1.00 is 1.040742. he can also invest $7,000 in a 1-year cd at annual rate of 4 percent compounded quarterly. the amount per $1.00 is 1.040604. what is the difference in the amount of interest earned for each investment? a) $0.96 b) $0.81 c) $0.87 d) $0.88

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 – 10x +2?

Arestaurant chef made 1 1/2 jars of pasta sauce. each serving of pasta requires 1/2 of a jar of sauce. how many servings of pasta will the chef be bale to prepare using the sauce?