What is the expected result when you roll a single die? Specify 40 rolls, and then click on "roll the dice." After the last roll, click on "show mean." Does your expected sum agree with the green mean? What happens to the plotted points as the number of rolls increases? If the picture is not clear, click on "roll the dice" for a new total of 80 rolls. Describe what you see in a sentence. What is the name for this principle?

In the theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized. Suppose $M$ denotes the total amount of a subject to be memorized and $A(t)$ is the amount memorized in time $t$. Assume that the rate at which material is forgotten is proportional to the amount memorized in time $t$. Determine a differential equation for $A(t)$ when forgetfulness is taken into account.

Distinguish between a hypothesis and a prediction.

Find a pattern for each sequence. Describe the pattern and use it to show the next two terms. 6, 24, 96, 384, ...

If two opposite sides of a rectangle increase in length, how must the other two opposite sides change if the area of the rectangle is to remain constant?

At Suburban Community College, 10% of all business majors switched to another major the next semester, while the remaining 90% continued as business majors. Of all nonbusiness majors, 20% switched to a business major the following semester, while the rest did not. Set up these data as a Markov transition matrix, and calculate the probability that a business major will no longer be a business major in two semesters’ time.

The coordinates of three vertices of a square are (-1, -1), (3, -1), and (3, 3). What are the coordinates of the fourth vertex?

Convert each polar equation to a rectangular equation. Then use a rectangular coordinate system to graph the rectangular equation.

$$r = \cos \theta$$

Find the centroid of the region lying underneath the graph of the function over the given interval. f(x) = 6 - 2x, [0, 3]

Write an equation that expresses each relationship.Then solve the equation for y. x varies directly as z and inversely as the difference between y and w.

Katie has read 32% of a book. If she has read 80 pages, how many more pages does Katie have left to read? A. 40 B. 170 C. 200 D. 250

Find the fifth term and the nth term of the geometric sequence whose initial term $a_1$ and common ratio r are given. $a_{1}=0 ; \quad r=\frac{1}{\pi}$

Factor each polynomial.

$$36 y ^ { 2 } - 16$$

Estimate the difference of $23.07 and$6.94 by rounding both amounts to the nearest dollar and then subtracting.