A pendulum's first swing has an arc of 36 inches. As the pendulum swings back and forth, the arc length for each successive swing is 1/4 of the previous swing. If this pattern continues, at which swing of the pendulum will the length of the arc be less than 1/2 inch? At swing number the pendulum's arc length will be less than 1/2 inch.

[10 points, algebra 2]according to my answer key the restrictions are -1 and 4. but why not positive 1?

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.

How many liters of peroxide should be added to 12 liters of an 8% peroxide solution so that the resulting solution contains 16% peroxide?   original added new amount of peroxide 0.96 liters x 0.96 + x amount of solution 12 liters x 12 + x 0.18 liter 1.14 liters 1.92 liters 2.10 liters