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- 18. Lfe ]- 19.4(t + 2}]- -3t,if ln(a) = 2, ln(b) = 3, and ln(c) = 5, evaluate the following: Cat (₁) = [ (a) In (b) In √b-³c²a-¹ (c) In(a-4b-³) In((bc)¹) = = 4 a (d) (in_c²¹) (¹n_²/) ¹ = ln -1Suppose it is estimated that t months after January 30, 2020 (first COVID-19 case in the Philippines), the population of COVID patients for the country will be P(t) thousand people where P(t) = Ae^0.03t - Be^0.005t for certain constants A an B. The population of COVID cases for March is 1,546 and 78,000 after four months. a. Use the given information to find A and B b. What was the population for May? c. What will be the population of COVID cases in November?
- Suppose that P(A)=0.3, P(B)=0.2, and P(C)=0.1. Further, P(AUB)=0.44, P(A^cC)=0.07, P(BC)=0.02, and P(AUBUC)=0.496. Decide whether A, B, and C are mutually independent.Express the following in terms of x without logs or natural logs 1) log100x 2) 1000logx 3) log0.001x 4) ln e2x 5) eln (3x+2) 6) ln (1/e5x) 7) ln √exFind y(0) and y(inf) for the following: a.) Y(s) = 1/(s*(s+2)) b.) Y(s) = (s+1)/(s+2) c.) Y(s) = (s+2)/(s^2+2s+10)