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
Answer is -5.
Explanation- Since t equals 0. You put 0 in place of every t.
0(2)- 2(0)- 5 =
0-0-5= -5
There are two black queens in a standard deck, so the probability is 2/52 or 1/26.
If instead you know you pulled a black card from the deck and you’re wondering what the probably is that it’s a queen, then it’s 2/26, since there are still 2 black queens, but only 26 black cards.
C=10pi
C=2(r)pi so r=5
A=pi(r)^2
so A=pi(5)^2
A=25pi
