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For the functions:
f(x)=4-x^2
g(x)=e^(-x)
a. Sketch both graphs. Find and label the intersection points.
b. Find the area between the graphs using integration. Give the full integral, including limits, in proper notation.
Determine the probability distribution, and the cumulative probability distribution of car arrivals. Simulate 20 hours of car arrivals at Joe Kelly's oil change and tune-up place.
How many different 4-card hands are possible? How many different 4-card hands contain a number less than 7?
What is the probability it would be a student, a faculty member, an admin staff member, a faculty or admin staff member and anyone except an admin staff member?
Suppose you have 50 American coins totaling exactly $1. This includes at least one quarter, and may contain nickels, dimes, and/or pennies.
The following linear trend equation was developed for annual sales from 1984 to 1990 with 1984 the base or zero year. Y1 = 500 + 60X (in $ thousands). What are the estimated sales for 1984?
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 35 liters per minute. There are 500 liters in the pond to start.
Show that the curve with parametric equations x=sin(t), y=cos(t), and z=sin^2(t) is the curve of the surfaces z=x^2 and x^2 + y^2=1. Use this fact to help sketch the curve.
Problems on probability
Probability and combination based questions. A golf ball is selected at random from a golf bag. If the golf bag contains 9 Titleist's, 8 Maxflis, and 3 Top Flites, find the probability of each event.
A company is constructing an open-top, square-based, rectangular metal tank that will have a volume of 46.5ft^3. What dimensions yield the minimum surface area? Round to the nearest tenth, if necessary.
Relationship between the variables
Assuming that the total cost per day, C(x), is linearly related to the total output per day, x, write an equation for the cost function.
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