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Question: Dominoes. Can you arrange the 28 dominoes of an ordinary set in a closed loop, so that each matches with its neighbor in the usual way? Can you do so if all dominoes with a 6 on them are removed? Can you state a general theorem about dominoes with numbers 0,1 , .. . , n on them? (Hint: consider each domino as an edge of a graph with vertices labeled 0, 1, . . . ,n.)
The points (4, 1, 7) and (10,9,7) are endpoints of a diameter of a sphere. How to find the center and radius of the sphere?
Establish a bijection between regions of AG and acylic orientations of G, and conclude that the number of acyclic orientations of G is |PG(-1)|
In multiple regression analysis, even when there is no linear relationship between any of the independent variables and the dependent variable
Determine the interval(s) at which f(x) is concave down given that f " (x) = 3x2 + 3x - 18. Give a formula for f (x) given that f is continuous and 2 x4 + x3 + 2 = 0∫x[f(t)/(t+4)] dt.
At a certain instant each edge of a cube is 5 inches long and its surface area is increasing at a rate of 2in2/min . How fast is the volume of the cube increasing?
A flagpole is n feet tall. On this flag pole we display flags of the following types: red flags that are 1 foot tall, blue flags that are 2 feet tall and green flags that are 2 feet tall.
Find the slope of a line normal to the curve of y = cscv(2x + 1) where x = 0.45 Verify the result by using the numerical derivative feature of a calculator.
A diamond dealer finds that the demand for flawless diamonds is governed by p = -x2 + 4x where x is in carats and p is in thousands of dollars.
What is an example of a subset of the set of all rational numbers that is neither open or closed? Also, what is an example of a compact, nonempty subset of the set of all rational numbers?
A semicircle with radius 6 m is submerged vertically in water so that the top is 3 m above the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Give your answer correct to the nearest whole numb..
Let v(t)=3t^2-12t be the velocity of a particle moving along the x-axis for time t, t>(less than or equal to)0 When t=0 the particle is at x=-6.
how many weeks does the rate of revenue exceed the rate of cost?
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