Which expression, when simplified, is equal to 7p
1 answer:
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a. Use the mean value theorem. 16 falls between 12 and 20, so
(Don't forget your units - 5 m/min^2)
b. gives the Johanna's velocity at time
. The magnitude of her velocity, or speed, is
. Integrating this would tell us the total distance she has traveled whilst jogging.
The Riemann sum approximates the integral as
If you're not sure how this is derived: we're given 5 sample points, so we can cut the interval [0, 40] into 4 subintervals. The lengths of each subinterval are 12, 8, 4, and 16 (the distances between each sample point), and the height of the rectangle approximating the area under the plot of is determined by the value of
at each sample point, 200, 240, |-220| = 220, and 150.
c. Bob's velocity is given by , so his acceleration is given by
. We have
and at his acceleration is
m/min^2.
d. Bob's average velocity over [0, 10] is given by the difference quotient,
m/min
Find the z-scores for the two scores in the given interval.
For the score x =391,
.
For the score x = 486,
Now you want the area (proportion of data) under the normal distribution from z = -1 to z = 0. The Empirical Rule says that 68% of the data falls between z = -1 to z = 1. But the curve is symmetrical around the vertical axis at z = 0, so the answer you want is HALF of 68%.
For the score x =391,
For the score x = 486,
Now you want the area (proportion of data) under the normal distribution from z = -1 to z = 0. The Empirical Rule says that 68% of the data falls between z = -1 to z = 1. But the curve is symmetrical around the vertical axis at z = 0, so the answer you want is HALF of 68%.