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A train travels 120 km in the same time that a plane covers 420 km. If the speed of the plane is 40 km per hr less than 4 times the speed of the train, find both speeds.
Let A be a real n x n matrix. Show that a linear subspace E of R^n is A-invariant if and only if E is e^{tA} -invariant for all t in R, where e^{tA} is the exponential matrix associated to A.
Let X be a subset of R, let E be a subset of X, let x_0 be an adherent point of E, and let f: X-->R, g: X-->R, h: X-->R be functions such that f(x)
Population growth rate
A random variable defined on all real numbers has a probability density proportional to: c/ X2 + 1. What is c? What is the probability that the random variable lies between 0 and 1?
Circle O and circle P are externally tangent circles. Circle O is tangent to circle P at T, OT = 12, TP = 6. AB is a common external tangent line to both circles. Find AB.
Suppose that at a certain instant the volume is 540 cubic centimeters and the pressure is 83 kPa and is decreasing at a rate of 11 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?
Write as a system of 2 equations in 2 unknowns. Solve each system by substitution and show each step. Perimeter of a rectangle : the length of a rectangular swimming pool is 15 feet longer than the width.
Identify and sketch the graph of the conic described by the quadratic equation x^2 + 4xy + y^2 - 12 = 0. Do this by writing this equation in matrix form
Ace Industries has current assets equal to $3 million. The company's current ratio is 1.5, and its quick ratio is 1.0. What is the firm's level of current liabilities? What is the firm's level of inventories?
A student team examined parked cars in four different suburban shopping malls. One hundred vehicles were examined in each location. Research question: At α = .05, does vehicle type vary by mall location?
Out of 32 students in a finite math class, 20 are male, 20 are business majors, 22 are first-year students, 13 are male business students, 16 are male first-year students, 14 are first-year students who are business majors, and 10 are male first-y..
Jerry has a total of 23 marbles. The marbles are either blue or green. He has three more blue marbles than green marbles. How many green marbles does he have?
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