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Q: 4. Find the area of the region bounded by the curves y = sin x, y = cos x, x = 0 and x = π/2.
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Q: Solve y' = + 8 ln x + 10 with y(1) = −2 Provide an exact answer (i.e. no decimal approximations)
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A: Given initial value problemy'=tanx, yπ4=3
Find the Laplace transform of the given function
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- We now need to attempt to find an exact value for n such that P(r ≥ 1) = 0.99. Clearly, if the bank has any chance of detecting a burglar they will need to have at least one alarm installed. So, we know that, minimally, n must be at least 1.Since n must be at least 1, suppose we start by trying n = 2, where there will be two alarms. When there are two alarms, r ≥ 1 means either one or both alarms could detect the burglar. If neither alarm detects the burglar it is considered a failure. Therefore, P(r ≥ 1) can be calculated using either of the following formulas. P(r ≥ 1) = P(1) + P(2) P(r ≥ 1) = 1 − P ( ___ ) fill in the blankwhats the mumber of injections f from S={1,2,3,4,5} to T={a,b,c,d,e,f} such that f(1)!=a and f(2)=!b ? i came to the conclusion 5^2 x 4^2 x 3 because: f(1) has 5 ways (when we exclude a and b) (2) has 4 (excluding a,b, f(1)) f(3) is back to 5 ( excluding f(1), f(2), but putting back a and b) f(4) has 4 f(5) has 3 is this correct?4. The lifetime, in years, of a type of small electric motor operating under adverse conditions is T ~Γ(6, 3.6). Whenever the motor fails, it is replaced with another of the same type. Find theprobability that fewer than 6 motors fail within one year.
- Figures obtained from a city's police department seem to indicate that of all motor vehicles reported as stolen, 63% were stolen by professionals (P), whereas 37% were stolen by amateurs (primarily for joy rides) (A). Of the vehicles presumed stolen by professionals, 25% were recovered within 48 hours (R<48), 23% were recovered after 48 hours (R>48), and 52% were never recovered (N). Of the vehicles presumed stolen by amateurs, 33% were recovered within 48 hours, 63% were recovered after 48 hours, and 4% were never recovered. (b) What is the probability that a vehicle stolen by a professional in this city will be recovered within 48 hours?(c) What is the probability that a vehicle stolen in this city will never be recovered? (Round your answer to four decimal places.)(!) In the morning section of a calculus course, 2 of the 9 women and 2 of the 10 men receive the grade of A. In the afternoon section, 6 of the 9 women and 9 of the 14 men receive A. Verify that, in each section, a higher proportion of women than of men receive A, but that, in the combined course, a lower proportion of women than of men receive A. Explain!In a recent study, 50males used a new weight-loss supplement, and 38 of them experienced weight loss after two weeks. In the same study, 20 females used the same supplement, and 16of them experienced weight loss after two weeks.Fill in t he blanks below to make the most reasonable statement possible. The new weight-loss supplement was less effective on ▼(Choose one: males/females) in the study. That is because only ____% of them lost weight after two weeks, whereas ____% of the ▼(Choose one:males/females) lost weight after two weeks.
- Suppose that you interview 100 exiting voters about who they voted for governor. Of the 100 voters, 55 reported that they voted for the democratic candidate. Is there sufficient evidence to suggest that the democratic candidate will win the election (gets at least 50% of votes) at the .01 level? Select one: a. T=1, there is evidence that the candidate will win. b. Z=1, there is evidence that the candidate will win. c. Z=1, there is no evidence that the candidate will win. d. T=1, there is no evidence that the candidate will win.5. For f(x) = 1 –x2on [−2, 1], do the hypotheses and conclusion of Rolle’s Theorem hold?If H1: μ1 – μ0 < 0, then zobs = -1 has a lower p-value than zobs =1. True or false?
