Prove that, if m | (a-b) then (a % m) = (b % m)
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- Suppose that start companies in chemistry have the probability 0.2 of profitability and that those in engineering have probability 0.15 of becoming profitable. A venture capitalist invests in one firm of each type. Assume the companies function independently: a). What is the probability that both companies become profitable? b). What is the probability that neither become profitable? c). What is the probability that at least one of the two become profitable?A bicycle safety organization claims that fatal bicycle accidents are uniformly distributed throughout the week. The table on the right shows the day of the week for which 777 randomly selected fatal bicycle accidents occurred. At. α=0.10, can you reject the claim that the distribution isuniform? Complete parts a through d below.assume that Pr[A] = 0.45, Pr[B] = 0.35, and Pr[A n B] = 0.25. Compute the following conditional probabilities: (1) Pr[A|B] = (2) Pr[B|A] =
- 12y 3p A) For the joint probability p(A.B)-5p 13p P(B/A), if y is three times larger than p. 4y. Find P(A). P(B). P(A/B), and 7plAssume that M= N(h)+k, h² + k, h* + ... Use the following data to find N,(). N,(h)=2.451, N,G)=2.896, N,)=3.285, N,(- = 3.786, N,()= 4.422 16 O a. 4.634 O b. 4.287 O c. 3.044 O d. 3.4146 O e. 3.953 O f. 5.058 Og. 3.674Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…
- The duration, x, of a monthly faculty meeting is uniformly distributed between 30 and 80 minutes. Which of the following statements is true (check all that apply)? a. Prob (x>80) = 0 b. Prob (x<85) = 1 c. Prob (x>35) = 1 d. Prob (x<30) < 0A container contains 30 green tokens, 10 blue tokens, and 3 red tokens. Two tokens are randomly selected without replacement. Compute P(F|E). E−you select a green token first F−the second token is non−green ... Question content area right Part 1 P(F|E)=enter your response here (Simplify your answer. Type an integer or a fraction.)TEST YOURSELF rinom Instruction: Compute for ! and F on a separate sheet and place your answers on the space providee m the table. 1. TEOV 609 a. P1 000 10% 3 years b. P2 000 2%/ month 2 years ertinom AS 6 months C. P3 000 12% d. P2 550 8% 2 quarters J2ST 9 monthshsup 1e E t bni e. P850 3%/ quarter heup 1ohsup 1eq boeesige1iw eeps ol ctetisup oi nevno :A naitul 21/1sup 8 = 2. If Lilia paid P980.00 in interest at 14% for 2 years, how much money did she borrow? (8)(PE) +0081S= AS+00S N- 88A 19= rUw motno of munne 1eg ol hevnoS nolulo