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Let F be a field and b != 0 an element of F. Define the mapping varphi:F[x]->F[x] by varphi(f(x)) = f(bx) for every f(x) in F[x]. Prove that varphi is an automorphism of F[x] such that varphi(a) = a for every a in F.
Let E be a metric space, S a subset of E, and let f:E-R be the function which takes the value 1 at each point of S and 0 at each point of the complement of S. Prove that the set of points of E at which f is not continuous is precisely the boundary..
Assume that the average annual salary for a worker in the United States is $27,500 and that the annual salaries for Americans are normally distributed with a standard deviation equal to $6,250. Find the following:
$18,700 is invested, part at 13% and the rest at 8%. If the interest earned from the amount invested at 13% exceeds the interest earned from the amount invested at 8% by $690.94, how much is invested at each rate?
two trucks leave the warehouse at the same time. 3 hours later, they are 429 miles apart. If one truck was driving 15 MPH slower than the other, how many miles did each drive?
Find an 85 percent confidence interval
What is the line of symmetry? Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x - h)2 + k.
How do you solve for the conditional probability of a false positive for a cancer test?, An experimental test to detect a particular type of cancer indicates the presence of cancer in 90% of individuals known to have this type of cancer, and in 15..
a trough is 12 ft long, 2ft high and 2ft wide at the top and has isosceles triangular ends. if water is put in at the rate of 1ft^3 per minuter, how fast is the depth increasing when it is 1.5 ft deep?
Explain A developer can buy a piece of property that will produce a profit of $16,000 with probability
The cost of fuel for running a train is proportional to the square of the speed it generates in Km. per hour. It costs Rs. 750 per hour, at a speed of 60 km, per hour.
explore if X and Y are independent and find the conditional pmf of Y given that 3 eggs among the six selected are cracked. What is the probability that X 1?
Kira owes $6125 and agrees to pay $175 a month until paid. Let A represent the amount owed (in dollars) and let N represent the number of payments made.
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