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Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry).
Five years ago, an alumnus of a small university donated $50,000 to establish a permanent endowment for scholarships.
Let m be a sigma-algebra, M_1 and M_2 are measures on m. a). Is M = M_1 + M_2 a measure?
Prove that the following function is Borel-measurable function. Provide complete and step by step solution.
A 100 uL (microLiter) sample of a 7.0 millimolar protein is diluted to 500.0mL. If the error in measurement of the molarity(M) is ±0.02 mM.
Show that circles on the sphere map to circles on the plane but if the circle on the sphere passes through the point N, it maps onto a line.
Find the relation between the parameters a, b, and c that will ensure that the curve has only one turning point.
The manager is considering raising the prices but knows that for every 50 cent the price is raised, 20 fewer people go to the movies.
Draw a graph of the area function including an appropriate domain and find at what value of x is the area a maximum.
A field is to be marked off in the shape of a rectangle, with one side formed by a straight river.
Suppose wheat and sugar are two basic ingredients necessary to bake two items: a loaf of bread and a muffin.
Locate the absolute extrema of the function on the closed interval. g(t) = t^2/t^+ 3 [-1,1] Answer Min (0,0) Max (-1, 1/4) (1, 1/4)
How many days before 17th August is it, if 50 days ago, it was four times as many days since March 30th?
Express the amount A of material that is needed to make such a box as a function of the length x of a side of the square base.
The length of a rectangle is 2 ft longer then the width. If the area is 16 ft^2, then what are the length and width?
At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 19 knots.
The Employee Credit Union at Directional State University is planning the allocation of funds for the coming year.
Let F be an extension field of K. If u is an element of F is transcendental over K, then show that every element of K(u) that is not in K.
Construct an orthonormal basis with a1 and then a2 and then a3. Next, expand the given vector b in terms of those vectors.
If a manufacturer of lighting fixtures has a daily production cost of (x)=800-10x+0.25x^2 where c is the total cost in dollars and x is the number of units.
Suppose now Boeing is the Stackelberg leader. What are the optimal outputs for the two firms and the market price under this assumption?
"I'm thinking of a polynomial f(x) with non-negative integer coefficients. Can you tell which one?"
Let F be an extension field of K of degree 2, then F is the splitting field over K for some polynomial.
A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes in three sizes for each sex.
Show the Galois group of (x^2-2)(x^2+2) over Q (rationals) is isomorphic to Z_2xZ_2 (Direct product group of integers modulo 2).