Balloons are often filled with helium gas because it weighs only about one-seventh of what air weighs under identical conditions. The buoyancy force, which can be expressed as $F_b=\rho_{\text {airg }} V_{\text {balloon }}$, will push the balloon upward. If the balloon has a diameter of $12 \mathrm{~m}$ and carries two people, $70 \mathrm{~kg}$ each, find the acceleration of the balloon when it is first released. Assume the density of air is $\rho=1.16 \mathrm{~kg} / \mathrm{m}^3$, and neglect the weight of the ropes and the cage.

Fill in the blanks. If the term does not a particular word element, leave the blank empty.

pesticide ___________ / ___________ / ___________

$$\text{ \ \ \ \ \ \\ \ \ \ \ \ \ \ \ \ \ \\ \ \ \ \ \ \ \\ \ \ \ P\ \ \ \ \ \ \ \ \ \ \ R/CF\ \ \ \ \ \ \ \ \ \ \ S}$$

An elevator without a ceiling is ascending with a constant speed of 10 m/s. A boy on the elevator shoots a ball directly upward, from a height of 2.0 m above the elevator floor, just as the elevator floor is 28 m above the ground. The initial speed of the ball with respect to the elevator is 20 m/s. (a) What maximum height above the ground does the ball reach? (b) How long does the ball take to return to the elevator floor?

Use the above method to evaluate the following expression.

$$\sec ^{-1}(-0.5)$$

Solve each equation. Then tell whether the equation is conditional, an identity, or a contradiction. 8p-4p-(p-7)+9p+6=12p-7

Graph each function over a one-period interval. See the example in this section.

$$y=2 \tan x$$

Determine whether

$$\cot{\left( x + \frac{\pi}{4} \right)} = \frac{1-\tan{x}}{1 + \tan{x}}$$

is a conditional equation or an identity.

Use the method earlier to graph the line with $m=-2$, through $(-1,-4)$.

Suppose the total demand for wheat and the total supply of wheat per month in the Kansas City grain market are as shown in the table below. Suppose that the government establishes a price ceiling of $3.70$ dollars for wheat. What might prompt the government to establisah this price ceiling? Explain carefully the main effects. Demonstrate your answer graphically. Next, suppose that the government establishes a price floor of $4.60$ dollars for wheat. What will be the main effects of this price floor? Demonstrate your answer graphically.

Solve each conjunction or disjunction and graph each solution set that is not empty. w<0 and

$$w \geq 4$$

Solve each inequality and graph each solution that is not empty. 4s+3(2-3s)<5(2-s)

Use the roster method to write the set.

the integers between $-4$ and $0$

Pro Corporation purchased 11,000 shares of Schroeder Corporation on January 1, 20X3, at book value. At that date, the fair value of the non-controlling interest was equal to 26.6 percent of Schroeder's book value. On December 31, 20X8, Schroeder reported these balance sheet amounts:

$$\begin{array}{lrlr} \text{Cash} & \$\hspace{5pt}80,000 & \text{Accounts Payable} & \$\hspace{5pt}50,000\\ \text{Accounts Receivable} & \text{120,000} & \text{Bonds Payable} & \text{100,000}\\ \text{Inventory} & \text{200,000} & \text{Common Stock} & \text{150,000}\\ \text{Buildings \& Equipment} & \text{600,000} & \text{Additional Paid-In Capital} & \text{50,000}\\ \text{Less: Accumulated Dep.} & \underline{\text{(250,000)}} & \text{Retained Earnings} & \underline{\text{400,000}}\\ \text{Total Assets} & \underline{\underline{\$750,000}} & \text{Total Liabilities \& Equity} & \underline{\underline{\$750,000}} \end{array}$$

On January 1, 20X9, Schroeder issued an additional 5,000 shares of its $10 par value common stock to Nonaffiliated Company for$80 per share.

Required

Record the consolidation entry needed to prepare a consolidated balance sheet immediately after Schroeder's issuance of additional shares.

Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample. If a number is odd, then it is divisible by 5.