Provide an appropriate response.The standard normal probability density function is defined by f(x) = 
e- x2/2. (a) Use the fact that 
dx = 1 to show that 
dx =
.(b) Use the result in part (a) to show that the standard normal probability density function has variance 1.
What will be an ideal response?
(a) Since 
dx = 1 and f(x) is an even function, 
dx = 
. Then 
dx = 
dx = 
= 
dx = 
.
(b) The variance of the distribution is equal to 
dx = 
dx + 
dx = 
+ 
= 1.
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Solve the problem.The orbit of Vanguard 1 had a semimajor axis of a = 8872 km. Calculate the period of the satellite. 
and 
A. 138.6 min B. 78.2 min C. 12 hr D. 1.98 hr
Rewrite the given expression using an appropriate variable. Use the first letter of the given word as the variable.(Width) + 8
A. W- 8 B. W? 8 C. W+ 8 D. W÷ 8
Solve the problem.Wind speed varies in the first twenty meters above the ground. For a particular day, let 
compute the wind speed Win meters per second x meters above the ground. At what height is the wind speed 11 meters per second? Round results to the nearest hundredth.
A. 0.31 B. 3.22 C. 0.83 D. 1.17
Find absolute maximum and minimum values of the function, if they exist, over the indicated interval. Where no interval is specified, use the real line. List your answers in terms of ordered pairs.
f (x) = sec2 x + tan2 x; (??/ 2, ?/ 2)