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Some believe that Captain America can run the fastest mile of any person alive. In order to test this theory, Captain America decided to run the mile multiple times and record how long it took him (in seconds) to run each one. He decided to attempt running the mile 40 times and determine his average mile time. Let’s assume his true mean mile time was 138 seconds with a standard deviation of 16 seconds. Use this information to find the following probability.  What is the probability that his average mile time would be less than 137 seconds?   Make sure to round your final answer to 3 decimal places. For example, if you thought the answer was 0.123456 then you would type in 0.123.

Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle’s path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion.x = 3 cos t, y = 3 sin t, π ≤ t ≤ 2π

Replace the polar equation with an equivalent Cartesian equation. 8r cos θ + 5r sin θ = 1

Find the slope of the polar curve at the indicated point.r = 7 cos 3θ, θ = 

A recursion formula and the initial term(s) of a sequence are given. Write out the first five terms of the sequence.a1 = 1, an+1 = 4an

Find the area of the specified region.Inside one leaf of the four-leaved rose r = 3 sin 2θ

Find the slope of the polar curve at the indicated point.r = 5 cos 3θ, θ = 

Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle’s path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion.x = 4 cos t, y = 4 sin t, π ≤ t ≤ 2π

Replace the polar equation with an equivalent Cartesian equation. 3r cos θ + 5r sin θ = 1

Express the number as the ratio of two integers.0.77777 . . .