Three runners A, B, and C race in four 100 m races with head starts. In the final race with no head starts, find the time difference (to 3 s.f.) between the winner and the third-place runner.
Find the basis and dimension of the subspace V⊂R4 given by the homogeneous system x1+2x2+x3+2x4=0,3x1+5x2+4x3+7x4=0. Then, find the homogeneous system of linear equations that define the subspace W⊂R4 spanned by the basis of V and the vector w=(1,0,0,0).
Airline operations manager wants to survey air passengers to estimate percentage preferring aisle seats. Find sample sizes to be 99% confident within 1.5% of true percentage, given (a) no prior information and (b) 38% prefer aisle seats. (a) n=7372
(b) n=600
Determine if log3(x+23)=2 has x=−14 as a solution. A) True, −14+23=32. B) False, log of negative is undefined. C) True, −14+23>0, log defined for positives. D) False, −14+23=23.
Asthma drug trial: 28 of 275 subjects had headaches. Test if headache rate is less than 12% at 1% significance level. z=−0.93, p-value =0.18. The test is right-tailed.
Find the original fraction where the denominator is 5 more than twice the numerator, and decreasing both numerator and denominator by 7 results in 61.
Estimate the true mean size of a university dance company with 99% confidence, assuming normal distribution. Data: {35,35,30,29,28,27,26,25,22,21,47,40,25,22,22,30,26,40}.
A popular author brings 8,428 copies of her new book on her book tour. She sells 85 books at each signing. Using estimates 8,400÷70=120 and 8,100÷90=90, how many signings are needed to sell all books?
Estimate the true proportion of adults who would like to travel to outer space with 93% confidence. Use a graphing calculator and round the answer to at least three decimal places.