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(Requires calculus) a) Let n be a positive integer.
a) Show that the relation R on the set of all polynomials with real-valued coefficients consisting of all pairs (ƒ, g) such that ƒ (n)(x) = g(n)(x) is an equivalence relation. [Here ƒ (n)(x) is the nth derivative of f (x).]
b) Which functions are in the same equivalence class as the function ƒ (x) = x4, where n = 3?
1. In the 2000 U.S. Census, a small city had a population of 50.000. By the 2010, the population had reached 74,012. If the population grows by the same percent each year, when will the population reach 100,000?
The probability of a couple getting a boy child is 0.5 and getting a girl is 0.65 . If the couple plans to get three children find the probability that at least there is a boy.
In an essay two to three pages in length, compare and contrast act-utilitarianism and rule-utilitarianism, then make an argument for why you think one is better than the other.
Formulate an appropriate hypothesis and state your conclusion.
How many ATM cells (described in Example 28) can be transmitted in 10 seconds over a link operating at the following rates?
an object is thrown upward from the top of a 64-foot building with an initial velocity of 48ft per second, which implies that the position function is s = -16t squared + 48t +64 where the time t is measured in seconds.
Audrey's 300-mile trip took six hours to complete. Find the ratio of average speed.
The appropriate alternative hypotheses for study is that gender and acceptance are associated.
The projected number of Americans age 65 and older for the years 1995-2030 can be modeled by the equation N(x)= 0.03x^2+0.315x+34.23 million people, where x is the number of years after 2000.
"G has subgraphs H1, H2, . . . , Ht, with Ht = G and Hi a subgraph of Hi+1 for each i, satisfying the following properties: H1 is a cycle
Resistors R1, and R2, have resistances of 50.0 Ohms, and 10.0 Ohms. R1 and R2 are connected in series-parallel circuit. What is the total resistance in ohms?
Describe algorithms for drawing a graph on paper or on a display given the vertices and edges of the graph. What considerations arise in drawing a graph so that it has the best appearance for understanding its properties?
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