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Given the functions 𝑔(đ‘Ĩ) = đ‘Ĩ − 5 and 𝑓(đ‘Ĩ) = 𝑒

đ‘Ĩ

Determine (𝑓 ∘ 𝑔)(5)


Suppose the mean number of days to germination of a variety of seeds is 34, with a standard deviation of 4.3 days. What is the probability that the mean germination time of a sample of 250 seeds will be within 0.5 days of the population mean?



for h(x) = 2/3 x -5 find the value of x for which h(x) = -7


An electronic company in Laguna manufactures resistors that have a mean resistance of 120 ohms and a standard deviation of 13 ohms. Find the probability that a random sample of 40 resistors will have an average resistance greater than 114 ohms. 


Evaluate:



a) âˆĢâˆĢD (e^(y^2) + 1) dA where D is the triangle with vertices (0,0), (-2,4) and (8,4).



b) âˆĢâˆĢD x^(5)sin(y^4) dA where D is the region in the 2nd quadrant bounded by y =3x^2, y = 12 and the y-axis.

Determine the volume of the region that is between the xy plane and f(x, y) = 1 + y^(5) +√(x^(4)+1 and is above the region in the xy plane that is bounded by y = √x, x = 2 and



the x-axis.

The velocity of a particle moving on the x-axis is given by v(t) = t^(3) − 6t^(2) for the time interval 0 ≤ t ≤ 10.


a) When is the particle farthest to the left?


b) When is the velocity of the particle increasing the fastest?

Evaluate âˆĢâˆĢâˆĢE 6z^2dV where E is the region below 4x + 2y + 2z = 10 in the first octant.


Find favg for the functions given on the interval and determine the value of c in the given

interval for which f(c) = favg.

a) f(x) = 9 − 2e^(4x+1) on [2,6]

b) 8 − cos (x/4) on [0 4Ī€]


Normally in real life situations we use alpha =5% or lesser. If alpha =5% it means we are allowing an error of 5%. Equivalently, we are saying if we do the experiments 100 times we only expects to make errors 5 times. In practice, we want or expect the error to be small.

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