The displacement (in centimeters) of a particle moving back and forth along a straight line is given by the equation of motion s = 5 sin(πt) + 3 cos(πt), where t is measured in seconds. (Round your answers to two decimal places.) (a) Find the average velocity during each time period. (i) [1, 2] 6 cm/s (ii) [1, 1.1] -13.98 cm/s (iii) [1, 1.01] -15.56 cm/s (iv) [1, 1.001] -15.69 cm/s (b) Estimate the instantaneous velocity of the particle when t = 1.

Elena and her husband marc both drive to work. elena's car has a current mileage (total distance driven) of 15,000 and she drives 23,000 miles more each year. marc's car has a current mileage of 46,000 and he drives 9,000 miles more each year. will the mileages for the two cars ever be equal? explain.

Me max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

In priyas math class there are 10 boys and 15 girls. what is the ratio of boys to girls in priyas math class? express your answer as a decimal