Evaluate each expression. 8 - 3 - 4

Find $\int \frac{1}{1+e^{-x}} d x.$ [Hint: Write $e^{-x}$ as $\frac{1}{e^{x}},$ and simplify the complex fraction before making an appropriate substitution.]

Write a sentence explaining its significance to electing leaders. precincts

¿Qué hizo el grillo para llegar primero a la roca?

Find the general solution of the non-homogeneous Cauchy–Euler equation

$$\begin{gather*} t^{2} y'' - 2ty' + 2y = 4t^2, \,\,\,\,\, t > 0. \end{gather*}$$

Test your understanding of stockholders’ equity by answering the following questions. Select the best choice from among the possible answers given. These account balances at December 31 relate to Aqua Sport, Inc.: $$ \begin{matrix} \text{Accounts Payable........................ } & \text{\$ 51,400 } & \text{Paid-in Capital in Excess of Par—Common.................................} & \text{\$260,000 }\\ \text{Accounts Receivable....................} & \text{81,950} & \text{Preferred Stock, 10\\%, \$100 Par................ } & \text{81,000}\\ \text{Common Stock...........................} & \text{313,000 } & \text{Retained Earnings..................................... } & \text{71,600 }\\ \text{Treasury Stock............................} & \text{5,700} & \text{Notes Receivable.......................................} & \text{12,300}\\ \text{Bonds Payable.............................} & \text{3,900}\\ \end{matrix} $$ What is total stockholders’ equity for Aqua Sport, Inc.? a. $719,900 b.$725,600 c. $731,300 d.$654,000 e. None of the above

On a separate sheet of paper, explain the following term by using it correctly in a sentence. Slavs

Given the points A(4, 2, -1), B(2, 1, 5), and C(9, 4, 1): Find the equation of the line through: (i) A and B (ii) A and C.

What aspects of Pablo Neruda's life made him a famous poet throughout the world?

In the journal Knowledge Quest (January/February 2002), education professors at the University of Southern California investigated children’s attitudes toward reading. One study measured third through sixth graders’ attitudes toward recreational reading on a 140-point scale (where higher scores indicate a more positive attitude). The mean score for this population of children was 106 points, with a standard deviation of 16.4 points. Consider a random sample of 36 children from this population, and let

$$\overline { x }$$

represent the mean recreational reading attitude score for the sample. a. What is

$$\mu _ { \overline { x } } ?$$

b. What is

$$\sigma _ { \overline { x } } ?$$

c. Describe the shape of the sampling distribution of

$$\overline { x }$$

d. Find the z -score for the value

$$\overline { x } = 100$$

points . e. Find

$$P ( \overline { x } < 100 )$$

Write the contrapositive of the following statement. If a polygon is a triangle, then it has three sides.

Jan sold her house on December 31 and took a $10,000 mortgage as part of the payment. The 10-year mortgage has a 10% nominal interest rate, but it calls for semiannual payments beginning next June 30. Next year Jan must report on Schedule B of her IRS Form 1040 the amount of interest that was included in the two payments she received during the year. a. What is the dollar amount of each payment Jan receives? b. How much interest was included in the first payment? How much repayment of principal was included? How do these values change for the second payment? c. How much interest must Jan report on Schedule B for the first year? Will her interest income be the same next year? d. If the payments are constant, why does the amount of interest income change over time?

A $D_0 = 8-m$-diameter tank is initially filled with water 2 m above the center of a D = 10-cm-diameter valve near the bottom. The tank surface is open to the atmosphere, and the tank drains through $a_L = 80-m$-long pipe connected to the valve. The friction factor of the pipe is given to be f = 0.015, and the discharge velocity is expressed as $V=\sqrt{rac{2 g z}{1.5+f L/ D}}$ where z is the water height above the centerof the valve. Determine (a) the initial discharge velocity from the tank and (b) the time required to empty the tank. The tank can be considered to be empty when the water level drops to the center of the valve.

What is the difference between pronation and supination of the hand and the foot?