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One of four coins may be counterfeit. If it is counterfeit, it may be lighter or heavier than the others. How many weighings are needed, using a balance scale, to determine whether there is a counterfeit coin, and if there is, whether it is lighter or heavier than the others? Describe an algorithm to find the counterfeit coin and determine whether it is lighter or heavier using this number of weighings.
find the median and the upper and lower quartiles.
exp(integral from 0 to t fo A(x) ds) is not a matrix solution of the system x' = A(t)x. However, show that the given exponential formula is a solution in the scalar case (A(t) in R), and dene when it is a solution in the matrix valued case (A(t) in R..
Consider the function f(x,y,z)= e^xy cos(x+z). What is the directional derivative for f at the point P(0, -pie/6, pie/3) in the direction u parallel to i - j + 2k
james buys a share at $53.41 on Monday, which gaines $1.35 on tuesday, loese $2.10 on Wednesday, and gains $4.65 on Thursday. What is James man daily profit or loss?
Plot different members of the families y1=x2+C1 and y2=-x2+C2. Constuct a piece wise defined function- not a member of the previous two- which is also a solution of the same DE.
There are two lines through the point (2,-3) that are tangent to y=x²+x. Find the x-coordinates of the points where these lines touch the parabola.
multiple choice question from probability and set language.choose the one alternative that best completes the statement
Carl wants to construct three rectangular dog-trainig arenas side-by-side, as shown, using a total of 340 feet of fencing. What should the overall length and width be in order to maximize the area of the three combined arenas?
a carpenter is building a rectangular room with a fixed perimeter of 328 ft. what dimensions would yield the maximum area? what is the maximum area?
Mr. Smith feels that each day his dog should have at least 8 units of protein, 5 units of carbohydrates, and 16 units of fat. How many cans of each dog food should he give to his dog each day to provide the minimum requirements at the least cost?
the cost of the fencing parallel to the stream is $15 per foot installed , and installed . Find the dimensions of the maximum enclosed area
In a box there are 7 red spheres and 12 blue spheres. 2 spheres are taken without return. If the third sphere is red, what is the probability that 2 first spheres are blue ?
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