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A box contains 2 plain pencils and 2 pens. A second box contains 5 color pencils and 7 crayons. One item from each box is chosen at random. What is the probability that a pen from the first box and a crayon from the second box are selected? Write your answer as a fraction in simplest form.
The motion of a spring that is subject to a frictional force or a damping force is often modeled by the product of an exponential function and a sine or cosine function. Find the velocity of the point after t seconds.
the entries in the 3 x 3 array are all the digits from 1 to 9 arranged so that the entries in every row and every
Find the surface area that portion of the surface y2 + z2 = a2 that lies inside the surface x2 + y2 = a2
The sales representative here tells you they also have two floor plans available, but they only have 15 homes available. The representative tells you that floor plan #1 sells for $110,000 and floor plan #2 sells for $135,000.
find four consecutive odd integers where the product of the two smaller numbers is 64 less than the product of two larger numbers.
we are going to estimate the average number of acres on a farm to within 30 acres with 95 confidence. if the population
Find the unit vectors in the directions of the steepest descent and the steepest ascent at (2, 4). Mark these directions on the graph in (b). Verify that the gradient at (2, 4) is orthogonal to the level curve through this point.
How many solution sets do systems of linear inequalities have? Must solutions to systems of linear inequalities satisfy both inequalities?
Of the registered voters in a certain town, 64% are Democrats, 59% favor a school loan, and 49% are Democrats who favor a school loan. Suppose that a registered voter is selected at random from the town.
Consider the helix with arc-length parametrization r(s) = αcos(αs)i + αsin(αs)j + αbsk, α - (a2 + b2)-1/2. Show that the unit binormal vector makes a constant angle with the axis of the cylinder on which the helix lies.
Show that radG ≤ diamG ≤ 2radG for every graph G.Prove the weakening of Theorem 1.3.4 obtained by replacing average with minimum degree. Deduce that | G | ≥ n0(d/2, g) for every graph G as given in the theorem.
Perform the operation and make the result in standard form
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