22. Suppose that (ab, p)- 1 and that p> 2. Show that the number of solutions (x, y) of the congruence ax2 + by 1 (mod p) is -ab 22. Suppose that (ab, p)- 1 and that p> 2. Show that the number of solutions (x, y) of the congruence ax2 + by 1 (mod p) is -ab
5. If P(AB)-1, show that P(B (i) P(A n B n C) (ii) P(C|A B)-P(CB); and n C) for any event C (iii) P(A n CB) P(CB).
3. Let A and B be events. Show that P(ABl(AUB)) P(AB|A). When does equality hold?
3. Let A and B be events. Show that P(AB(AUB)) P(ABA). When does equality hold?
For reaction A-->P the intergrated rate is In [A]t = -Kt + In[A]0 (a) What is the order of the reaction? (b) Draw the graph of In[A]t vs t and show the intercept and slope (c) Calculate the half life
Problem 2. [25 pts) Side AB of the square ABCD is extended to P, A - B - P, so that BP 2 AB. With M the midpoint of DC, BM is drawn meeting AC at Q. PQ meets BC at R. Using Menelaus' theorem find the ratio R. P C M Problem 2. [25 pts) Side AB of the square ABCD is extended to P, A - B - P, so that BP 2 AB. With M the midpoint...
2) Suppose A and B are independent events, then) is incorrect. A P(AB) P(A) ( PCA n B) = P(A)P(B) P(AIB) = P(A) ⓑ P(A u B)-P(A) + P(8)
(h) What is P(AB) if P(AB) - 0.1? (2 pts) () What is P(AB) if P(AB) - 0.7? (3 pts) (2) A certain disease is prevalent in 10% of a given population. Scientists have developed a test for the disease. In the laboratory, the test correctly identifies samples known to have the disease 98% of he time. Also, the test is positive incorrectly 7% of the time when testing samples known not to have e disease. A doctor uses this...
2 P(A) = = ,P(B) = 1,P(A1B) ,P(AB) + P(BA) Find P( AUB 3
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