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Math 10B Quiz 3-
1. (a) Fill in the blanks: The Stirling number S(n, k) counts the number of ways to ________________ (arbitrarily/surjectively/injectively) put n _______________________ (distinguishable/indistinguishable) balls into k ____________________ (distinguishable/indistinguishable) boxes.
(b) Compute S(7, 5). (It's a three digit number.)
2. In a class, there are 30 students taking a quiz. Each quiz score will be an integer between -10 and 10 inclusive. How many different quiz score distributions are possible for the class? Here, a quiz score distribution records only the number of -10 scores, the number of -9 scores, . . . , the number of 10 scores.
3. A weather forecaster says:
Assuming mathematical consistency of the weather forecaster's statements, what is the probability there is no rain in Berkeley today nor tomorrow?
Every complex number can be expressed in the form a + bi, where a and b are real numbers and i^2 = -1. Which of the following is equivalent to (1 + ci)2. What are the real numbers x, if any that are in the domain of the function f(x) = -x^5 but not..
two angles are complementary. The sum of the measure of the first and the one-fourth of the second angle is 62.25 degrees find the measures of the angle.
At a General Electric Plant they produced 12,000 jet engines in May. General Electric was able to sell 11,000 of these engines. Calculate total ending inventory cost assuming each engine cost $290,000.
the perimeter of a rectangle is 900 feet. The ratio of the length to breadth is 7:3. What is the length and breadth
In a sample batch of 52 mechanical pencils it is assumed that 20 are defective. If 3 mechanical pencils are randomly selected, what is the probability that none of them are defective?
How do I get the answer to this 3.55x(4/1)x(5/6)= How do I express these as percentages 0.45 and 2/3 ? Respectively
a soft drink company has recently received customer complaints about its one-liter-sized soft drink products. customers
What percent of new expansion should be financed by equity?
Show that x = 0 is a regular singular point. Find two linearly independent solutions about this point using the Frobenius Method. Find the first four non-zero terms of two linearly independent solutions y1 (x) and y2 (x) .
Three of your friends decide to take the same chemistry class together at the local university along with 21 other students. On the first day of class, the professor indicates that this class is graded on a bell-shaped curve.
If the graph of x2 + y2 = 9 is horizontally compressed by a factor of 1/4, and then reflected in the y-axis, determine an equation for the new graph.
Write a formula for the velocity of the object as a function of time t. What should be the velocity of the object when it reaches its highest point? What is the maximum height reached by the object?
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