The marginal opportunity cost of the second unit of pizza is:

a. 2 units of robots.

b. 3 units of robots.

c. 7 units of robots.

d. 9 units of robots.

A vocabulary word appears in italics in the passage below. The meaning of its root is given in parentheses. Look at the prefix and think about how the word is used in the passage. Then write a definition for the vocabulary word.

The candidates differed on most issues, but they did $concur$ on the need for clean air. (Root word: $currere$, "to run")

Let X and Y have a bivariate normal distribution with respective parameters $\mu _ { x } = 2.8 , \mu _ { y } = 110 , \sigma _ { x } ^ { 2 } = 0.16 , \sigma _ { y } ^ { 2 } = 100 ,$ and $\rho = 0.6$ Using R, compute: (a) P(106 < Y < 124). (b) P(106 < Y < 124|X = 3.2).

The following questions ask about objects that you may see in your classroom. Answer each question in a complete sentence that includes a direct object pronoun. ¿Ven Uds. los mapas?

In a source-free vacuum region; $\mathbf{H}=\frac{1}{\rho} \cos (\omega t-3 z) \mathbf{a}_{\phi} A / m$ (a) Express Hin phasor form. (b) Find the associated E Field. (c) Determine $\omega$.

The standard normal distribution has a mean of 0 and a standard deviation of 1 . To convert an $x$-value from a normal distribution with a mean of $\bar{x}$ and a standard deviation of $\sigma$ to a $z$-value from a standard normal distribution, use this formula:

$$z=\frac{x-\bar{x}}{\sigma}$$

A z-value gives the number of standard deviations an $x$-value is from the mean $\bar{x}$. You can use z-values to compare $x$-values from different normal distributions.

What percent of your class would originally have had scores between 54 and 78 ? What will be the new range of scores for this part of the class? How can you answer this question without using the formula from part (c)?

Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, $y=x^{2} )$ and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. $g(x)=4 \sqrt{x}$

In the following sentence, underline the subject of the verb in parentheses. Then, underline twice the verb in parentheses that agrees in number with its subject.

Kites and other flying objects (was, were) the main attraction at the fair.

How can you increase the molarity of a solution? (A) Add solute. (B) Add solvent. (C) Pour out some of the solution. (D) All of the above.

What is the magnitude of the vector $\langle 5, 7 \rangle$, to the nearest whole unit? A. 6 units B. 7 units C. 8 units D. 9 units

Let $V=\frac{\sin 3 \phi}{\rho} V$ in a dielectric material for which $\boldsymbol{\varepsilon}=2.8 \boldsymbol{\varepsilon}_{0}$. (a) Find E and P at point $A\left(1,20^{\circ}, 4\right)$. (b) Calculate the volume charge density at A.

Show that a homogeneous lamina of density $\rho$ and mass m that covers the circular region $x^{2}+y^{2}=a^{2}$ will have moment of inertia $\text{ma}^{2} / 4$ with respect to both the x- and y-axes. What is the moment of inertia of the lamina with respect to the z-axis?

Graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, $y=x^{2})$ and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. $f(x)=-4 \sqrt{x-1}$

In the given exercise, indicate a good method for evaluating the integral (but do not evaluate). The choices are substitution (specify u and du ), Integration by Parts (specify u and dv ), a trigonometric method, or trigonometric substitution (specify). If it appears that these techniques are not sufficient, state this.

$$\displaystyle \int \sin ^{3 / 2} x d x$$