回答 - Ch 1:真实数字和代数表达式

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Section 1.2: Sets
::第1.2节:一套

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Review Questions
::回顾问题

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1. M = {January, June, July},  $\begin{array}{r}\left|M\right|\end{array}$  = 3
   ::M = { 1月, 6月, 7月} {M = 3 {1月, 6月, 7月} {M = 3
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2. a.  $\begin{array}{r}\left|F\right|\end{array}$  = 6,  $\begin{array}{r}\left|M\right|\end{array}$  = 6. Therefore,  $\begin{array}{r}F\sim M\end{array}$ . However, since $\begin{array}{r}F\end{array}$  and  $\begin{array}{r}M\end{array}$  do not contain the same elements, they are not equal.                                                                                    
   b.  $\begin{array}{r}\left|X\right|\end{array}$  = 10,  $\begin{array}{r}\left|Y\right|\end{array}$  = 10. Therefore,  $\begin{array}{r}X\sim Y\end{array}$ . Also, since $\begin{array}{r}X\end{array}$  and  $\begin{array}{r}Y\end{array}$  contain the same elements (even though they are arranged in a different order),  $\begin{array}{r}X=Y\end{array}$ .                                        
   ::a. * * * *=6,******* *=6,**********************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************************
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3. Many possible answers: one is A = {a}, A' = {b, c, d, e}.
   ::许多可能的答案:一个是 A = {a}, A = {b, c, d, e}。
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4. Many possible answers: one is A = {physics, chemistry, biology}, A' = {engineering, computer science, accounting, business, liberal arts}.
   ::许多可能的答案:一个是A={物理、化学、生物},A'={工程、计算机科学、会计、商业、自由艺术}。
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5. Many possible answers: one is A = {Paul, Ringo, John}, A' = {George}.
   ::许多可能的答案是 A = {Paul, Ringo, John}, A = {George} 。
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6. Let A = {m, a, t, h, e, m, a, t, i, c, s} and B = {c, o, l, l, e, g, e} and C = {a, l, g, e, b, r, a}.    
   a.  $\begin{array}{r}A\cup B\end{array}$  = {m, a, t, h, e, i, c, s, o, l, g}                                                                                
   b.  $\begin{array}{r}A\cap B\end{array}$   = {c, e}                                                                                                  
   c. $\begin{array}{r}B\cap C\end{array}$  = {e, l, g}                                                                                                
   d. $\begin{array}{r}A\cap B\cap C\end{array}$  = {e}
   ::让 A = {m, a, t, h, e, m, a, t, i, c, s} 和 B = {c, o, l, l, e, g, e, e} 和 C = {a, l, g, e, b, r, a} = {m, a, t, h, e, e, i, c, s, o, l, g} b = {B = {c, e} c. B = {e, l, g} d {B = {e}
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7.   $\begin{array}{r}x\end{array}$  
   ::x x
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8.   $\begin{array}{r}y,x\end{array}$  
   ::y,x y,x
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9.   $\begin{array}{r}x,y,z\end{array}$  
   ::x,y,z 十,y,z
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10.   $\begin{array}{r}y\end{array}$  
    ::y y , y
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11.   $\begin{array}{r}w,y,z\end{array}$  
    ::W,y,z,z,w,y,z
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12.   $\begin{array}{r}w\end{array}$  
    ::时 时 时
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13.   $\begin{array}{r}w,z\end{array}$  
    ::w,z z
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14.   $\begin{array}{r}w,y,x\end{array}$  
    ::w,y,x

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Explore More
::探索更多

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1.  

   

    

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   15 dog or cat, no other
   ::15只狗或猫

   
   ::15只狗或猫

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7 only dog
::7只7只只狗

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20 no pets
::20个无宠物

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8 other with dog or cat, but not both
::另外8只狗或猫,但不是两只

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2. 76 customers said they like only chocolate.
   ::76个顾客说他们只喜欢巧克力
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3. The power set of X = {{3}, {4}, {5}, {6}, {3, 4}, {3, 5}, {3, 6}, {4, 5}, {4, 6}, {5, 6}, {3, 4, 5}, {3,4,6}, {3, 5, 6}, {4, 5, 6}, {3, 4, 5, 6}, {}}. 
   ::X = {% 3}, {4}, {5}, {6}, {3, 4}, {3, 5}, {3, 6}, {4, 5}, 4, 5}, 6}, {4, 5, 6}, 4, 4, 5, 6}, 3, 3, 4, 5, 6} 3, 4, 4, 5, 6} 。
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4. a. No, this is not an empty set because all negative numbers are less than 20, so there are actually infinitely many elements in this set.  b. Yes, this is an empty set because no months contain exactly 27 days. 
   ::a. 否,这不是一个空套件,因为所有负数小于20,所以这个套件中实际上有无限多的元素。b. 是的,这是一个空套件,因为没有任何月份包含确切的27天。
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5. Answers will vary.
   ::答案将各有不同。
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6. Answers will vary.
   ::答案将各有不同。

 

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Section 1.3: Subsets of Real Numbers
::第1.3节:真实数字子集

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Review Questions
::回顾问题

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1. $\begin{array}{r}5.67\end{array}$ : r ational number
   ::5.67:合理数目
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2. $\begin{array}{r}\text{-}\sqrt{6}\end{array}$ : i rrational number
   
   ::-6:非非理性数字
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3. $\begin{array}{r}\frac{9}{5}\end{array}$ : r ational number
   
   ::95: 合理数字
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4.  0: w hole number
   
   ::零:整数
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5. $\begin{array}{r}\text{-}75\end{array}$ : i nteger
   
   ::-75:整数
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6. $\begin{array}{r}\sqrt{16}\end{array}$ : natural  number
   
   ::16:自然数
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7.   $\begin{array}{r}4\end{array}$ : r eal, rational, integer, whole, and natural number
   ::4:真实、合理、整数、整数和自然数
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8.   $\begin{array}{r}\frac{6}{9}\end{array}$ : r eal and rational number
   ::69:实际合理数字
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9.   $\begin{array}{r}\pi \end{array}$ : r eal and irrational number
   ::? :真实和不合理的数字
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10. True
    ::真实
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11. True
    ::真实
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12. False
    ::假假
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13. True
    ::真实
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14. True
    ::真实
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15. False
    ::假假

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::探索更多

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1.                                                       
   a. 0.4646464646... is  $\begin{array}{r}\frac{46}{99}.\end{array}$                                                                        
   b.0.81212121212... is  $\begin{array}{r}\frac{134}{165}.\end{array}$                                                                                             
   ::a. 0.4646464646... 是4699. b. 0. 0.81212121212...
2. $\begin{array}{r}\sqrt{3}=1.7,1.73,1.732,1.7320,1.73205\end{array}$  
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3. Quiz 1: 86%                                                                                                                    
   Quiz 2: 88%                                                                                                                  
   Quiz 3: 84%                                                                                                                  
   Quiz grades from least to greatest are Quiz 3, Quiz 1, Quiz 2.
   ::问题1:问题1:问题1:问题2:问题88% 问题3:问题3:问题3:问题3:问题2:问题3、问题1、问题2:问题2:问题3、问题2:问题2:问题2:问题3:问题2:问题2:问题2:问题3:问题2:问题2:问题3:问题2:问题2:问题2:问题3:问题3:问题3:问题3:问题3:问题3:问题3:问题3:问题44%是问题3,问题2。
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4. 4 questions
   ::4个问题
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5. a. Rational numbers         
   b. Rational numbers
   ::a. 合理数字 b. 合理数字
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6. a. Rational numbers
   b. Natural numbers
   c. Rational numbers
   ::a. 合理数字 b. 自然数字 c. 合理数字

 

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Section 1.4: Ordering Real Numbers and Absolute Value
::第1.4节:定序实际数字和绝对值

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Review Questions
::回顾问题

1. 
   
2. 
   
3. 
   
4. 
   
   
   
   
5.    $\begin{array}{r}\text{-}\frac{9}{2},\text{-}4,\text{-}\pi ,\text{-}\frac{1}{3},\text{-}\frac{1}{4}\end{array}$
6.   $\begin{array}{r}\text{-}\sqrt{\frac{1}{3}},\text{-}\frac{1}{2},0,\frac{1}{6},\frac{4}{5}\end{array}$
   
   
7.  5, 4 $\begin{array}{r}\frac{1}{2}\end{array}$ , 3 $\begin{array}{r}\frac{11}{12}\end{array}$ , 3.68, $\begin{array}{r}\sqrt{10}\end{array}$  
   
   
8.   $\begin{array}{r}\text{-}\frac{6}{5},\text{-}\sqrt{3},\text{-}2,\text{-}\sqrt{5},\text{-}\frac{11}{4}\end{array}$
   
   
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9. Answer: >
   ::答复: >
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10. Answer: <
    ::答复: <
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11. Answer: <
    ::答复: <
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12. Answer: =
    ::答复:=
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13. Answer: =
    ::答复:=
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14. Answer: <
    ::答复: <
15. 5
16. 1
17. 1
18. 5
19. 5
20. 1

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::探索更多

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1. Water:  $\begin{array}{r}\frac{71}{100}.\end{array}$  Land: $\begin{array}{r}\frac{29}{100}.\end{array}$   
   ::水:71100.土地:29100。
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2. a. 2.718281828.  b. irrational number. c. π > e.  d.  $\begin{array}{r}e>\sqrt{7}\end{array}$  
   ::a. 2.718281828. b. 不合理的编号. c. > e. d. e. 7
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3. Find the  $\begin{array}{r}\sqrt{6}\end{array}$  by guessing and checking. 2.4494897427
   ::通过猜测和检查发现6号,2.4494897427
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4. a. Yes, systolic.  b. Yes, diastolic.  c. Yes, both.  d. No.
   ::a.是的,是的,是的,是的,是的,是的,是的,是的,都是的。 d. 否。

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If you have answered, "I want to work for Company B because I will be that employee making $3,500," that means you are competitive and ready to embrace the challenge. It's a positive attitude, but you should also keep in mind the possibility of becoming the person earning $2,600. If you worked for Company A, on the other hand, you would have a better chance of being treated more fairly. 
::如果你回答说,“我想为B公司工作,因为我会是雇员,挣3500美元。” 这意味着你具有竞争力,愿意接受挑战。这是一个积极的态度,但你也应该记住成为挣2600美元的人的可能性。另一方面,如果你为A公司工作,你将更有可能得到更公平的对待。

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Let's take a look at the mean absolute deviations of the salaries for each company. 
::让我们来看看每家公司工资的绝对偏差。

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For Company A, the mean salary is  $\begin{array}{r}\frac{3,000+3,100+3,100+3,200}{4}=\$3,100.\end{array}$  
::A公司的平均工资为3 000+3 100+3 100+3 100+2004=3 100美元。

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The absolute deviations from this mean are: 
::绝对偏离这一平均值的是:

 

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Therefore, the mean absolute deviation for Company A is  $\begin{array}{r}\frac{100+0+0+100}{4}=\$50\end{array}$ .
::因此,A公司的平均绝对偏差为100+0+0+1004=50美元。

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For Company B, the mean salary is also $\begin{array}{r}\frac{2,600+3,000+3,300+3,500}{4}=\$3,100.\end{array}$   
::B公司的平均工资为2 600+3 000+3 300+3 544=3 100美元。

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However, the mean absolute deviation for Company B is  $\begin{array}{r}\frac{500+100+200+400}{4}=\$300.\end{array}$  
::然而,B公司的平均绝对偏差为500+100+200+4004=300美元。

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Although both companies pay the same average salary, Company A is fairer towards its employees. 
::虽然两家公司平均工资相同,但A公司对其雇员更为公平。

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Section 1.5: Intervals

::第1.5节:间隔

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Review Questions
::回顾问题

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1. 
   $\begin{array}{rl}& \text{-}2<x<3\\ & (\text{-}2,3)\\ & \left\{x\in \mathrm{I}\mathrm{R}|\text{-}2<x<3\right\}\end{array}$  
   
   ::-2 <x <3( 2, 3) {xIR} -2 <x <3}
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2. 
   $\begin{array}{rl}& \text{-}3\le x\le 4\\ & [\text{-}3,4]\\ & \left\{x\in \mathrm{I}\mathrm{R}|\text{-}3\le x\le 4\right\}\end{array}$  
   ::- 3x4[3、4、4]{xIR} -3x4}
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3. 
   $\begin{array}{rl}& 0<x\le 2\\ & (0,2]\\ & \left\{x\in \mathrm{I}\mathrm{R}|0<x\le 2\right\}\end{array}$  
   ::0 < x% 2( 2/ 2/ 0. 2) {xIR 0 < x% 2}
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4. 
   $\begin{array}{rl}& \text{-}4\le x<1\\ & [\text{-}4,1)\\ & \left\{x\in \mathrm{I}\mathrm{R}|\text{-}4\le x<1\right\}\end{array}$  
    
   ::-=YTET -伊甸园字幕组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=- 翻译组=
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5. 
   $\begin{array}{rl}& x>1\\ & (1,\mathrm{\infty })\\ & \left\{x\in \mathrm{I}\mathrm{R}|x>1\right\}\end{array}$  
   ::x1( 1, ) {x} IR x>1}
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6. 
   $\begin{array}{rl}& x\le \text{-}2\\ & (\text{-}\mathrm{\infty },\text{-}2]\\ & \left\{x\in \mathrm{I}\mathrm{R}|x\le \text{-}2\right\}\end{array}$  
   ::x--2(-)-(-)-(-)-(-)-(-)-(-){x--(IR)-(x)-(x)-(I)-(x)-(x)-(x)-(x)-(x)-(x)-(x)-(x)-(x)-(x)-(x)-(x)-(x)-(x)-(x)-(x)
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7. 
   $\begin{array}{rl}& x\ge \text{-}1\\ & [\text{-}1,\mathrm{\infty })\\ & \left\{x\in \mathrm{I}\mathrm{R}|x\ge \text{-}1\right\}\end{array}$  
   ::x-1[ 1, ]{xIR x-1}
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8. 
   $\begin{array}{rl}& x\le 2\\ & (\text{-}\mathrm{\infty },2]\\ & \left\{x\in \mathrm{I}\mathrm{R}|x\le 2\right\}\end{array}$  
   ::x% 2 (- , 2) {x} IR x% 2}
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9. 
   $\begin{array}{rl}& x\le \text{-}1\mathrm{o}\mathrm{r}x>2\\ & (\text{-}\mathrm{\infty },\text{-}1]\cup (2,\mathrm{\infty })\\ & \left\{x\in \mathrm{I}\mathrm{R}|x\le \text{-}1\mathrm{o}\mathrm{r}x>2\right\}\end{array}$  
     
   ::x-1 或 x>2(-) {x} x-1 或 x>2 或 x>2}
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10. 
    All real numbers
    $\begin{array}{r}(\text{-}\mathrm{\infty },\mathrm{\infty })\\ \left\{x\in \mathrm{I}\mathrm{R}\right\}\end{array}$  
    ::所有实际数字 (- , ){xIR}

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Explore More
::探索更多

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1. { x | x $\begin{array}{r}\in \end{array}$   $\begin{array}{r}\mathbb{N}\end{array}$ , 1 ≤ x ≤ 5}
   ::{ x x n, 1 x 5}
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2. { x | x   $\begin{array}{r}\in \end{array}$   $\begin{array}{r}\mathrm{Z}\end{array}$ , x is even, and | x | ≤ 6} or { x | x   $\begin{array}{r}\in \end{array}$   $\begin{array}{r}\mathbb{Z}\end{array}$ , x is even, and -6 ≤ x   ≤ 6}
   ::{ x { { { } x { { { { { { { { Z , x 是 均 , 和 {x 6} 或 {x { { { x { { Z , x 是 均 , 和 - 6 x 6}
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3. { x | x   $\begin{array}{r}\in \end{array}$ $\begin{array}{r}\mathrm{Z}\end{array}$ , x is odd, and | x | ≤ 5} or { x | x   $\begin{array}{r}\in \end{array}$   $\begin{array}{r}\mathbb{Z}\end{array}$ , x is odd, and -5 ≤ x  ≤ 5}
   ::{x {{{{{{{{{{{{{{{{{{{{{{{{{{{{{{}{{{{{{{{{{{}}{{{{{{{{{{{{{{{{{{{{{{{{}}}{{{{{{{{}}}{{{{{{{{{{{{{{{}}}}{{{{{{{{{{{{{{}}}}}{{{{{{{{{{{{}{{{{{{{{{{{{{{{}}}}}}}}}{{{{{{{{{{{{{{{{{{{{{{{{{{}}}}}}}}{{{{{{{{{{{{{{{}}}}}}}}}}}}}{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
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4. { x | x   $\begin{array}{r}\in \end{array}$   $\begin{array}{r}\mathrm{Z}\end{array}$ , x is odd, and x is multiple of 5, | x | ≤ 15} 
   ::{ x x Z, x 是奇数, x 是 5 的倍数 , {x 15}
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5. {  x | x   $\begin{array}{r}\in \end{array}$   $\begin{array}{r}\mathrm{Z}\end{array}$ , x solves 6 y + 27 = x , for y ∈ $\begin{array}{r}\mathbb{N}\end{array}$  and y  ≤ 4}
   ::{x {% x {Z} x 解答 6y + 27 = x, y {N 和 y {4}

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Section 1.6: Operating with Real Numbers and Real Number Properties
::第1.6节:使用实数和实数属性操作

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Review Questions
::回顾问题

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1. commutative
   ::平平
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2. distributive
   ::分配
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3. inverse (multiplicative)
   ::反向( 重复)
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4. associative
   ::结合
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5. identity (additive)
   ::身份( 添加)
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6. inverse (additive)
   ::反向( 相加)
7. 47
8. 8
9. $\begin{array}{r}\frac{1}{2}\end{array}$  
   
10. 2
11. 17
12. 30
13. 26
14. $\begin{array}{r}\frac{1}{3}\end{array}$  
    
15. 17

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1. a) 24 – 54 + 30 = 0
   b) 6 × 0 = 0
   c) both are valid ways to simplify an expression
   :a) 24 - 54 + 30 = 0 b) 6 × 0 = 0 c) 两者都是简化表达式的有效方法
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2. a)  $\begin{array}{r}6+5\cdot (2-9)÷(3+4)=1\end{array}$  
   b) $\begin{array}{r}(6+5)\cdot 2-9÷3+4=23\end{array}$  
   :a) 6+5_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________(3+4+4=1 b (6++__________________________________________________________________________________________(+_________________________________________________________________(+_________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Section 1.7: Operating with Integers and the Fundamental Theorem of Arithmetic
::第1.7节:用整数和自学基本理论进行操作

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Review Questions
::回顾问题

1. -50
2. 8
3. 97
4. -2
5. 48
6. -99
7. -44
8. 364
9. 1,716
10. -1,875
11. -13
12. 49
13. -41

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1. 48 minutes
   ::48分钟 48分钟
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2. a) -2 times -5 is positive 10. Answer is 2.   
   b) -6 should be distributed to both 2 and -3. Answer is 6.
   ::10. 答复为2.b)-6,应分发给2和3。 答复为6。
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3. 30,340 feet
   ::30,340英尺
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4. 70°F
   ::70°F 70°F
5. $257

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Section 1.8: Operating with Fractions

::第1.8节:分数操作

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Review Questions
::回顾问题

1. $\begin{array}{r}\text{-}\frac{17}{9}=\text{-}1\frac{8}{9}\end{array}$  
2. $\begin{array}{r}\frac{15}{6}=2\frac{1}{2}\end{array}$  
3. $\begin{array}{r}\frac{103}{70}=1\frac{33}{70}\end{array}$  
4. $\begin{array}{r}2\end{array}$  
5. $\begin{array}{r}\text{-}\frac{41}{24}=\text{-}1\frac{17}{24}\end{array}$  
6. $\begin{array}{r}\frac{89}{40}=2\frac{9}{40}\end{array}$  
7. $\begin{array}{r}\frac{32}{21}=1\frac{11}{21}\end{array}$  
8. $\begin{array}{r}\text{-}\frac{2}{11}\end{array}$  
9. $\begin{array}{r}\frac{6}{13}\end{array}$  
10. $\begin{array}{r}\text{-}\frac{8}{9}\end{array}$  

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1. a)  $\begin{array}{r}\text{-}\frac{127}{90}=\text{-}1\frac{37}{90}\end{array}$    
   b) $\begin{array}{r}\frac{71}{30}=2\frac{11}{30}\end{array}$  
   :a) - 12790=- 13790 b) 7130= 21130
2. $\begin{array}{r}\frac{1}{15}\end{array}$  
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3. $\begin{array}{r}\frac{7}{3}=2\frac{1}{3}\end{array}$  cups of sugar
   ::73=213杯糖
4. $\begin{array}{r}\frac{7}{12}\end{array}$  
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5. $\begin{array}{r}209\frac{1}{3}\end{array}$  feet
   ::20913英尺

 

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Section 1.9: Operating with Decimals
::第1.9节:以十进制操作

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Review Questions
::回顾问题

1. 17.685
2. 0.907
3. -44.086
4. -6.092
5. 3.311
6. -16.419
7. 8.432
8. -342.3
9. 309
10. 70.224

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1. 92.249
2. 7.42333...
3. $40.51
4. $127.86
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5. 10.1 L
   ::10.1 L案
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6. 12,500 yards
   ::12 500码

 

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Section 1.10: Rates and Percents
::第1.10节:比率和百分比

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Review Questions
::回顾问题

1.   $\begin{array}{r}0.5,\frac{1}{2}\end{array}$  
   
   
2. $\begin{array}{r}0.12,\frac{3}{25}\end{array}$  
   
   
3. $\begin{array}{r}\mathrm{0.3333...},\frac{1}{3}\end{array}$  
   
   
4. $\begin{array}{r}0.75,75\mathrm{\%}\end{array}$  
   
5. $\begin{array}{r}0.625,62.5\mathrm{\%}\end{array}$  
   
6. $\begin{array}{r}1.25,125\mathrm{\%}\end{array}$  
   
7. $\begin{array}{r}10\mathrm{\%}\end{array}$  
   
8. $\begin{array}{r}220\end{array}$  
   
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9. equivalent
   ::等值
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10. not equivalent
    ::不相等
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11. equivalent
    ::等值

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1. 62 copies
   ::62份
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2. a) $0.30 per ounce  
   b) $0.28 per ounce  
   c) The 12-ounce cheese is a better buy by 2 cents per ounce. 
   :a) 每盎司0.30美元(b) 每盎司0.28美元(c) 12盎司芝士最好每盎司2美分。
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3. a) $80.50  
   b) $84  
   c) $87.50
   :a)80.50(b)84(c)87.50美元
4. $10.64
5. $618
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6. 42% English, 24% History, 20% Biology, 14% Math
   ::42%英语、24%历史、20%生物学、14%数学

 

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Section 1.11: Simplifying and Operating with Square Roots
::第1.11节:简化和用平根操作

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Review Questions
::回顾问题

1. $\begin{array}{r}5\sqrt{3}\end{array}$  
2. $\begin{array}{r}4\sqrt{3}\end{array}$  
3. $\begin{array}{r}10\end{array}$  
4. $\begin{array}{r}12\sqrt{7}\end{array}$  
5. $\begin{array}{r}80\end{array}$  
6. $\begin{array}{r}18\sqrt{2}\end{array}$  
7. $\begin{array}{r}4+4\sqrt{2}\end{array}$  
8. $\begin{array}{r}\text{-}10\sqrt{3}\end{array}$  
9. $\begin{array}{r}\sqrt{2}\end{array}$  
10. $\begin{array}{r}5\sqrt{10}+7\sqrt{5}\end{array}$  
11. $\begin{array}{r}\frac{4\sqrt{6}}{11}\end{array}$  
12. $\begin{array}{r}\sqrt{5}\end{array}$  
13. $\begin{array}{r}\frac{3\sqrt{42}}{4}\end{array}$  

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1. $\begin{array}{r}\frac{5\sqrt{15}-6\sqrt{6}}{6}\end{array}$  
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2. 4.2 nautical miles per hour
   ::4.2海里/小时每小时4.2海里
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3. v = 16.155
   ::五=16.155
4. $\begin{array}{r}2\sqrt{14}\end{array}$

 

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Section 1.12: Exponent Properties and Scientific Notation
::第1.12节:指数属性和科学标记

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Review Questions
::回顾问题

1. 46,656
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2. $\begin{array}{r}\frac{1}{x^9}\end{array}$  
   ::1x9
3. $\begin{array}{r}\frac{1}{7}\end{array}$  
4. $\begin{array}{r}{2}^3\cdot 3^3=216\end{array}$
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5. $\begin{array}{r}{d}^{14}\cdot f^{10}\end{array}$  
   ::d14-f10
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6. $\begin{array}{r}\frac{1}{x{y}^2}\end{array}$
    
   ::1xy2
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7. $\begin{array}{r}\frac{b}{a^6}\end{array}$  
   ::重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重六重
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8. $\begin{array}{r}\frac{2c^4}{3d}\end{array}$  
   ::2c43d
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9. $\begin{array}{r}\frac{4g}{15h}\end{array}$  
   ::4g15小时
10. $\begin{array}{r}{2}^{15}=32,768\end{array}$  
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11. $\begin{array}{r}{3}^4{x}^4=81x^4\end{array}$  
    ::34x4=81x4
12. $\begin{array}{r}\frac{4^2}{5^2}=\frac{16}{25}\end{array}$  
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13. $\begin{array}{r}\frac{1}{4^2{x}^{16}}=\frac{1}{16x^{16}}\end{array}$
     
    ::142x16=116x16
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14. $\begin{array}{r}\frac{2^3{x}^{21}}{5^3{y}^9}=\frac{8x^{21}}{125y^9}\end{array}$  
    ::23x2153y9=8x21125y9
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15. $\begin{array}{r}{3}^4{m}^4{n}^{48}=81m^4{n}^{48}\end{array}$  
    ::34m4n48=81m4n48

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1. 15 bacteria
   ::15种细菌
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2. $\begin{array}{r}\frac{b^{66}}{12a^{17}}\end{array}$  
   ::b6612a17(b6612a17)
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3. Elise  is correct:  $\begin{array}{r}\frac{2^5\cdot 2^4}{2^2}=2^7\end{array}$ . 
   ::Elise是正确的: 252422=27。
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4. a.  $\begin{array}{r}{(\text{-}2)}^1=\text{-}2\end{array}$  
   b.  $\begin{array}{r}{(\text{-}2)}^2=4\end{array}$  
   c.  $\begin{array}{r}{(\text{-}2)}^3=\text{-}8\end{array}$  
   d.  $\begin{array}{r}{(\text{-}2)}^4=16\end{array}$  
   e.  $\begin{array}{r}{(\text{-}2)}^5=\text{-}32\end{array}$  
   f.  $\begin{array}{r}{(\text{-}2)}^6=64\end{array}$  
   When starting with a base that is negative, even powers have positive answers while odd powers have negative answers.
   ::a. (2-2)1=2 b. (2-2)2=4 c. (2-2)3=8 d. (2-2)4=16 e. (2-2)5=-32 f. (2-2)6=64),从否定的基数开始,即使权力也有肯定的答复,而奇异的强国也有否定的答复。
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5. Yes. When the negative is included in the parentheses, it is also raised to the power.
   $\begin{array}{r}{(\text{-}2)}^4=16\\ \text{-}{(2)}^4=\text{-}16\end{array}$  
   ::是。 括号内括号内含负数时,也向权力机关提出负数。 (-2)4=16-(2)4=16

 

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Section 1.13: Evaluating Algebraic Expressions
::第1.13节:评价代数表达式

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Review Questions
::回顾问题

1. 9
2. 37
3. -13
4. 0
5. 23
6. 50
7. 2
8. 4
9. -2
10. -10

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1. a. yes
   b. no
   c. no
   ::a. 是 b. 否 c. 否
2. $32
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3. 14 m/s
   ::14米/秒

 

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Section 1.14: Simplifying Algebraic Expressions
::第1.14节:简化代数表达式

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Review Questions
::回顾问题

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1. $\begin{array}{r}\text{-}10b+15d\end{array}$  
   ::-10b+15d
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2. $\begin{array}{r}\text{-}4g^2+21\end{array}$  
   
   ::-4g2+21
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3. $\begin{array}{r}{5u}^2-4u+14\end{array}$  
   
   ::5u2-4u+14
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4. cannot be simplified:  $\begin{array}{r}2a-5f\end{array}$
   
   ::不能简化: 2a-5f
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5. $\begin{array}{r}{\text{-}p}^2-{4q}^2+16p-10\end{array}$  
   
   :2-4q2+16p-10
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6. $\begin{array}{r}{\text{-}5n}^2+17n+12\end{array}$  
   
   ::-5n2+17n+12
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7. $\begin{array}{r}{4rs}^2\end{array}$  
   
   ::4架2
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8. cannot be simplified:  $\begin{array}{r}\frac{7c^3}{11d}\end{array}$   
   
   ::不能简化: 7c311d
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9. $\begin{array}{r}2a-6\end{array}$  
   
   ::2a-6
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10. $\begin{array}{r}2b-5\end{array}$  
    ::2b-5
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11. $\begin{array}{r}14x-15\end{array}$   
    ::14-15岁
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12. $\begin{array}{r}8x+21\end{array}$  
    ::8x+21
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13. $\begin{array}{r}\text{-}12x+35\end{array}$  
    ::-12x+35
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14. $\begin{array}{r}37x+19\end{array}$  aa
    ::37x19 aa

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1. $\begin{array}{r}\frac{3x^2{z}^4}{y^2}=\frac{9x^2{z}^4}{y^2}\end{array}$  
   ::3x2z4y2=9x2z4y2

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Section 1.15: Unit Conversion

::第1.15节:部队改划

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Review Questions
::回顾问题

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1. 5,280 feet
   ::5 280英尺
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2. 4 cups
   ::4杯4杯
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3. 100,000 centimeters
   ::100 000厘米
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4. 8 pints
   ::8 品脱
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5. 160,934 centimeters
   ::160,934厘米
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6. 0.25 gallons
   ::0.25加仑
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7. 189 inches
   ::189英寸
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8. 60 pints
   ::60 品脱
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9. 5,200 pounds
   ::5 200磅
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10. 475 centimeter
    ::475厘米

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1. 10.5 cups of flour; 24 total oz of chips; 6 oz of semi-sweet chips, and 18 oz of bittersweet chips
   ::10.5个面粉杯;24个共奥兹薯片;6个半甜薯片和18个苦甜薯片
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2. Approximately 11.88 gallons
   ::约11.88加仑
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3. Approximately 2,174.8 miles
   ::约2,174.8英里
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4. Approximately 113 mg
   ::约113毫克

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Section 1.16: Geometric Formulas
::第1.16节:几何公式

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Review Questions
::回顾问题

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1. Perimeter = 32
   Area = 48
   ::周边 = 32 区域 = 48
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2. Perimeter = 30
   Area ≈ 25.98
   ::周边 = 30 区域 = 25.98
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3. Perimeter = 24.1
   Area = 34.8
   ::周边 = 24.1 区域 = 34.8
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4. Perimeter = 36
   Area = 60
   ::周边 = 36 区域 = 60
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5. Circumference = 22π
   Area = 121π
   ::环形 = 22 区域 = 121
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6. Surface area ≈ 536.79
   Volume ≈ 538.42
   ::表面面积 536.79 卷 538.42
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7. Surface area = 232π
   Volume = 400π
   ::表面面积 = 232 体积 = 400
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8. Surface area = 253.5
   Volume = 274.625
   ::表面面积 = 253.5 卷 = 274.625
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9. Surface area  ≈ 9,372.8π
   Volume ≈ 870.67π
   ::表面面积 9,372.8 卷 870.67
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10. Surface Area = 536.78
    Volume = 538.35
    
    ::表面面积 = 536.78 卷 = 538.35
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11. Surface Area = 576π
    Volume - 2,304 π
    ::表面面积 = 576 体积 - 2 304

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1. 4,953,312 cubic feet
   ::4 953 312立方英尺
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2. Difference in surface area is 44,953,780π square miles, or approximately 141,226,465 square miles.
   Approximately 1,950,718,677 people could live on Mars.
   ::面积差异为44,953,780平方英里,约141,226,465平方英里,约1,950,718,677人可在火星上生活。
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3. Area of shape = 600 square units
   Surface area of the matching cube = 600 square units
   ::方形面积 = 600平方单位