Use the formula for the sum of an infinite geometric series to solve this exercise.

How much additional spending will be generated by a $\$ 10$ billion tax rebate if $60 \%$ of all income is spent?

Balance the following chemical equations: (a) $\mathrm{CaCl}_{2}+\mathrm{Na}_{2} \mathrm{CO}_{3} \rightleftharpoons \mathrm{CaCO}_{3}+\mathrm{NaCl}$ (b) $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+\mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}$ (c) $\mathrm{NO}_{2}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{HNO}_{3}+\mathrm{NO}$ (d) $\mathrm{C}_{4} \mathrm{H}_{10}+\mathrm{O}_{2} \rightleftharpoons \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}$ (e) $\mathrm{Al}(\mathrm{OH})_{2}^{-} \rightleftharpoons \mathrm{Al}^{3+}+\mathrm{OH}^{-}$

For a certain bowling league, a beginning bowler computes her handicap by taking 90% of the difference between 220 and her average score in league play. Determine the average scores that would produce a handicap of 72 or less. Also assume that a negative handicap is not possible in this league.

What is the momentum of a $\lambda=0.010 \mathrm{nm}$ X-ray photon?

In order to cool 1 ton of water at 20$^\circ{}$C in an insulated tank, a person pours 130 kg of ice at -5$^\circ{}$C into the water. Determine the final equilibrium temperature in the tank. The melting temperature and the heat of fusion of ice at atmospheric pressure are 0$^\circ{}$C and 333.7 kJ/kg, respectively. Answer: 8.2$^\circ{}$C

Assume that $X$ is a hypergeometric random variable with N=25, S=3, and n=4. Calculate the following probabilities.

a. P(X=0)

b. P(X=1)

c. P(X \leq 1)

Consider the single-input, single-output system is described by

$$\begin{aligned} . \mathbf{x}(t) & =\mathbf{A} \mathbf{x}(t)+\mathbf{B} u(t) \\ y(t) & =\mathbf{C x}(t) \end{aligned}$$

where

$$\mathbf{A}=\left[\begin{array}{cc} 0 & 1 \\ 3-K & -2-K \end{array}\right], \mathbf{B}=\left[\begin{array}{l} 0 \\ 1 \end{array}\right], \mathbf{C}=\left[\begin{array}{ll} 1 & -1 \end{array}\right]$$

Compute the characteristic polynomial and plot the root locus as $0 \leq K<\infty$. For what values of $K$ is the system stable?

La Caja de Ahorros Ridgewood cobra $\$ 27$ por cheque en concepto de protección contra sobregiros. El 8 de julio, Nancy tenía $\$ 1,400$ en su cuenta. Durante los cuatro días siguientes, llegaron al banco los siguientes cheques:

• 9 de julio, $\$1.380.15$;
• 10 de julio, $\$ 670$ y $\$ 95.67$;
• 11 de julio, $\$ 130$; y
• 12 de julio, $\$ 87.60$.

¿Cuánto pagará en concepto de comisiones por descubierto? ¿Cuánto deberá al banco después del 12 de julio?

From the list below, supply the words needed to complete the paragraph. Some words will not be used.

$$\begin{array}{llll}\text { veritable } & \text { discretionary } & \text { moribund } & \text { draconian } \\ \text { analgesic } & \text { flummox } & \text { noisome } & \end{array}$$

Randy's decision to go camping was entirely _____ , but after the experience, he knew that he wouldn't be returning to the great outdoors again in the near future. On the first day, a bee stung him near his eye and caused it to swell shut. That night, as he applied a topical _____ to reduce the pain of the sting, he was overwhelmed by the _____ odor of a skunk-a skunk in his tent. Once he'd taken an emergency bath in the river, after being sprayed by the skunk, Randy helped his family pack up the car and leave, three days early. Randy's bad luck on the trip _____ him; he had never had such a miserable time in the wilderness. He thought that the trip might renew his _____ sense of adventure after working eight years in an office cubicle as a computer network administrator, but instead it caused him to think of how great it would be to go home to a clean shower, relax on the sofa, and maybe watch a movie in his skunk- and insect-free living room.

The following list of matrices and their respective characteristic polynomials is referred to in Exercise.

$$A=\left[\begin{array}{rr} 2 & -1 \\ -1 & 2 \end{array}\right]$$

, $p(t) = (t − 3)(t − 1),$

$$B=\left[\begin{array}{cc} 1 & -1 \\ 1 & 3 \end{array}\right]$$

, $p(t)=(t-2)^{2}$,

$$C=\left[\begin{array}{rrr} -6 & -1 & 2 \\ 3 & 2 & 0 \\ -14 & -2 & 5 \end{array}\right]$$

, $p(t)=-(t-1)^{2}(t+1)$,

$$D=\left[\begin{array}{rrr} -7 & 4 & -3 \\ 8 & -3 & 3 \\ 32 & -16 & 13 \end{array}\right]$$

, $p(t)=-(t-1)^{3}$,

$$E=\left[\begin{array}{llll} 6 & 4 & 4 & 1 \\ 4 & 6 & 1 & 4 \\ 4 & 1 & 6 & 4 \\ 1 & 4 & 4 & 6 \end{array}\right]$$

, $p(t) =(t + 1)(t + 5)^2(t − 15),$,

$$F=\left[\begin{array}{rrr} 1 & -1 & -1 & -1 \\ -1 & 1 & -1 & -1 \\ -1 & -1 & 1 & -1 \\ -1 & -1 & -1 & 1 \end{array}\right]$$

, $p(t)=(t+2)(t-2)^{3}$. Find a basis for the eigenspace $E_{\lambda}$ for the given matrix and the value of $\lambda$. Determine the algebraic and geometric multiplicities of $\lambda$. $E, \lambda=-1$

A triangular field has sides of lengths 22, 36, and 44 yd. Find the largest angle.

check whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation $x-y-z=-6$ is satisfied by $(2,-3,5)$.

The following reaction occurs when a burner on a gas stove is lit:

$$\mathrm{CH}_4(\mathrm{~g})+2 \mathrm{O}_2(\mathrm{~g})=\mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$$

Is an equilibrium among $\mathrm{CH}_4, \mathrm{O}_2, \mathrm{CO}_2$, and $\mathrm{H}_2 \mathrm{O}$ established under these conditions? Explain your answer.

Which of the following reaction mixtures would produce the greatest amount of product, assuming all went to completion? Justify your choice.
Each involves the reaction symbolized by the equation

$$2 \mathrm{H}_2+\mathrm{O}_2 \rightarrow 2 \mathrm{H}_2 \mathrm{O}$$

a. 2 moles of $\mathrm{H}_2$ and 2 moles of $\mathrm{O}_2$.
b. 2 moles of $\mathrm{H}_2$ and 3 moles of $\mathrm{O}_2$.
c. 2 moles of $\mathrm{H}_2$ and 1 mole of $\mathrm{O}_2$.
d. 3 moles of $\mathrm{H}_2$ and 1 mole of $\mathrm{O}_2$.
e. Each would produce the same amount of product.