Fill in the letter of the choice that best answers the question. Abe built this setup to investigate how far a toy car would travel after it left the ramp. He used a meterstick to measure distance.

$$\begin{matrix} \text{Number of Books} & \text{Distance Traveled (m)}\\ \text{2} & \text{1.50}\\\text{4} & \text{2.50}\\ \text{6} & \text{3.75}\\ \end{matrix}$$

Which is a conclusion that Abe can draw? A. The toy car would have traveled farther if Abe had used a different ramp. B. Adding two books to the height doubled the distance the car traveled. C. A toy car will travel 6 meters if there are 8 books under the end of the ramp. D. The greater the number of books under the ramp, the farther the car traveled.

Tell whether the statement is a propositional function. For each statement that is a propositional function, give a domain of discourse. Choose an integer between 1 and 10.

Graph the function and its inverse.

$$f ( x ) = \left( \frac { 1 } { 9 } \right) ^ { x }$$

The sum of two integers with different signs is 8. Give two possible integers that fit this description .

Convert the equation to cylindrical coordinates and sketch its graph in $\mathbb{R}^{3}$.

$$z=x^{2}+y^{2}$$

Of the four moments of insight, which came as the greatest surprise to you? Explain your answer.

Determine whether the function is a polynomial function, rational function, or neither. For those that are polynomial functions, state the degree. For those that are not polynomial functions, tell why not. $f(x)=4 x^{5}-3 x^{2}+5 x-2$

Determine the following indefinite integrals. Check your work by differentiation.

$$\int \left( \frac { 3 } { x ^ { 4 } } + 2 - \frac { 3 } { x ^ { 2 } } \right) d x$$

Use properties of power series substitution, and factoring of constants to find the first four nonzero terms of the Maclaurin series for the following functions. Use the Maclaurin series $( 1 + x ) ^ { - 2 } = 1 - 2 x + 3 x ^ { 2 } - 4 x ^ { 3 } + \cdots$, for -1<x<1. $\frac { 1 } { \left( 4 + x ^ { 2 } \right) ^ { 2 } }$

Show that there are infinitely many integers $n$ for which $\phi(n)$ is a perfect square.

Involve discounted loans. In each exercise, determine a. the loan 's discount . b. the net amount of mon ey you receive. c. the loan's actual interest rate, to the nearest tenth of a percent. You borrow $2000 on a 7% discounted loan for a period of 8 months.

What economic compromise was made in order to fund the Great Society programs?

(a) What type of music does the speaker sing? (b) Considering the loneliness, death, and defeat that occur in Homer's Odyssey, why is the speaker's musical style appropriate? Explain.

How does active transport differ from passive transport?