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Math 10B Quiz 1-
1. Explain why the following statement is true: For any positive integer n, the number of subsets of a set with n different elements is 2n.
2. We say that a string of five decimal digits is valid if it satisfies both of the following two conditions:
(i) At least one of the five digits is a "0".
(ii) The five digits are all distinct.
How many valid strings are there?
3. You are giving an exam in a classroom where 24 chairs are arranged in a circle. To discourage heating, you do not want students to sit next to each other. What is the maximum number of students that can take the exam in this room? Explain your answer carefully.
What fraction of the time does he take the bus
Find the slope of the tangent line to f(x) = e2X2+3x at the point where x = 0. The function g is differentiable, and the tangent line to the graph of y = g(x) at x = -5 is y = 2x - 2. Let f(x) = -3g(x) + 5x + 5. Give f' (-5).
Write and solve an equation to determine the selling price of the house. Jamie sold her house for x dollars. The real estate agent received a 5% commission and Jamie received $197,125.
the number of assists per match for the setter on your schools volleyball team has a mean of 58 and a standard
If bacteria grows exponentially, and it takes 12 hours for bacteria to double in number, what is the growth rate
X and Y are sets. ζu refers to the usual topology, ζH is the half-open interval topology. ζC is the open half-line topology, ζF is the finite complement topology and ζcc. is the countable complement topology. R is the set of real numbers, Z is the ..
Approximate f by a taylor polynomial with degree n at the number a, and use taylors inequality to estimate the accuracy of the approximation f(x)=T(x) when x lies in the given interval
How many revolutions will the graph of the circular helix r(t)=acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis?
Use the improved Euler method with h=0.05 to find approximate values of the solution of the given initial value problem at t=0.1,0.2,0.3, and 0.4 y'=3+t-y, y(0)=1.
When identifying and evaluating brand extensions, it is helpful to have a summary tool to judge their viability. The following checklist can provide some guidance:
Find the average RAM installed on PCs in the year 2007. b-f this trend continues, in which year will the average RAM installed on PCs be 14 GB?
a college administrator wants to study the average age of students who drop out of college after only attending one
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