Find the maximum possible COP for a refrigerator that liquefies nitrogen at $77 \mathrm{~K}$ in a lab at $22^{\circ} \mathrm{C}$.

In this exercise, write the indicated expression in exponential form.

$$-1=\log 0.1$$

Consider the following four populations:

• $1,2,3,4,5,6,7,8$
• $1,1,1,1,8,8,8,8$
• $1,1,4,4,5,5,8,8$,
• $-6,-3,0,3,6,9,12,15$

All these populations have the same mean. Without doing the calculations, arrange the populations according to the magnitudes of their variances, from smallest to largest. Then calculate each of the variances manually.

Esta persona no pueden salir porque el/ella ocupada. Escribe lo que el/ella haciendo. (Write what the following person is doing right now.)

modelo: Alberto / correr

$\hspace{32pt}$ Alberto está corriendo.

ustedes / escribir correos electrónicos

Player Company acquired 60 percent ownership of Scout Company's voting shares on January 1, 20X2. During 20X5. Player purchased inventory for $20,000 and sold the full amount to Scout Company for$30,000. On December 31, 20X5, Scout's ending inventory included $6,000 of items purchased from Player. Also in 20X5, Scout purchased inventory for$50,000 and sold the units to Player for $80,000. Player included$20,000 of its purchase from Scout in ending inventory on December 31, 20X5.

Summary income statement data for the two companies revealed the following:

$$\begin{array}{lrr} & \textbf{Player Company} & \textbf{Scout Company}\\ \\ \text{Sales} & \$\hspace{8pt}400,000 & \$\hspace{8pt}200,000\\ \text{Income from Scout} & \underline{20,500} & \underline{0}\\ & \underline{\$\hspace{8pt}420,500} & \underline{\$\hspace{8pt}200,000}\\ \text{Cost of Goods Sold} & \$\hspace{8pt}250,000 & \$\hspace{8pt}120,000\\ \text{Other Expenses} & \underline{70,000} & \underline{35,000}\\ \text{Total Expenses} & \underline{\$(320,000)} & \underline{\$(155,000)}\\ \text{Net Income} & \underline{\underline{\$\hspace{8pt}100,500}} & \underline{\underline{\$\hspace{12pt}45,000}}\\ \end{array}$$

Required

Compute the amount to be reported as sales in the 20X5 consolidated income statement.

Determine the derivative of $\frac{d}{d x} \int_x^\pi \cos \left(t^3\right) d t$ .

Esta persona no pueden salir porque el/ella ocupada. Escribe lo que el/ella haciendo. (Write what the following person is doing right now.)

modelo: Alberto / correr

$\hspace{32pt}$ Alberto está corriendo.

tú / hacer la tarea

Compute the following integral.

$$\int_{-3}^3\left(x^2-3\right)^3 d x$$

If the function f is continuous for all real numbers, and if $F^{\prime}(x)=f(x)$, then $\int_{1}^{4} f(3 x) d x=$ (A) F(12)-F(3), (B) $\frac{1}{3}[F(4)-F(1)]$, (C) $\frac{1}{3}[F(12)-F(3)]$, (D) 3[F(4)-F(1)].

How can the present continuous be used to say what these people are doing differently than normal? Modelo: Generalmente, Juan maneja despacio. Ahora está manejando rápido.

Siempre traigo mi permiso de manejar. Hoy no ________________ el permiso conmigo.

Solve for $x$ by converting the logarithmic equation to exponential form.

$$\log _2(x)=-3$$

"a. Calculate $\langle 3,-4,1\rangle \times\langle 8,5,-2\rangle$.

b. Without doing any calculations, what is the measure of the angle between $\langle 3,-4,1\rangle$ and your answer in Part a? How do you know? "

A firm's production function is $Q(L)=12 L^2-\frac{1}{20} L^3$, where $L$ denotes the number of workers, with $L \in[0,200]$.

(a) What size of the work force $\left(L^*\right)$ maximizes output $Q(L)$ ? What size of the work force $\left(L^{* *}\right)$ maximizes output per worker, $Q(L) / L$ ?

(b) Note that $Q^{\prime}\left(L^{* *}\right)=Q\left(L^{* *}\right) / L^{* *}$. Is this a coincidence?

The function $f(t)$ satisfies the differential equation

$$\frac{d^2 f}{d t^2}+8 \frac{d f}{d t}+12 f=12 e^{-4 t}$$

For the following sets of boundary conditions determine whether it has solutions, and, if so, find them: (a) $f(0)=0, \quad f^{\prime}(0)=0, \quad f(\ln \sqrt{2})=0$ (b) $f(0)=0, \quad f^{\prime}(0)=-2, \quad f(\ln \sqrt{2})=0$.