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lands that are 12 miles apart (see figure). For a trip between the islands, there is enough fuel for a 20-mile trip. 6 7 0 0 f t 1.10 radians 3250 ft 0.84 radian (a) Find the angle between the two lines of sight to the peaks. (b) Approximate the amount of vertical climb that is necessary to reach the summit of each pea... |
length. An interval that does not have a finite length is unbounded (see page A3). a, b a, b a, b Open Graph 333202_0A01.qxd 12/6/05 2:09 PM Page A3 Appendix A.1 Real Numbers and Their Properties A3 or , Note that whenever you write intervals containing you always use a parenthesis and never a bracket. This is because ... |
hich numbers in the set are (a) natural numbers, (b) whole numbers, (c) integers, (d) rational numbers, and (e) irrational numbers. 1. 2. 3. 4. 5. 6. 3, 2, 0, 1, 4, 2, 11 3, 0, 3.12, 5 4 , 3, 12, 5 2, 5, 2 9, 7 5, 7, 7 2.01, 0.666 . . . , 13, 0.010110111 . . . , 1, 6 2.3030030003 . . . , 0.7575, 4.63, 10, 475, , 1 3, 1... |
bra. For instance, you might prefer the following steps for Example 2(d). 3x 2 y 2 y 3x 22 y 2 9x4 Note how Property 3 is used in the first step of this solution. The fractional form of this property is m a b b a m . 333202_0A02.qxd 12/6/05 2:12 PM Page A13 Appendix A.2 Exponents and Radicals A13 Scientific Notation Ex... |
rs. For square roots, you can use the square root key . For cube roots, you can use the cube root key 3 roots, you can first convert the radical to exponential form and then use the exponential key or you can use the xth root key . Consult the user’s guide x for your calculator for specific keystrokes. > , Example 14 C... |
Exercise 11. A polynomial that has all zero coefficients is called the zero polynomial, denoted by 0. No degree is assigned to this particular polynomial. For polynomials in more than one variable, the degree of a term is the sum of the exponents of the variables in the term. The degree of the polynomial is the highes... |
terms. Factor each group. Distributive Property Now try Exercise 147. Factoring a trinomial can involve quite a bit of trial and error. Some of this trial and error can be lessened by using factoring by grouping. The key to this method of factoring is knowing how to rewrite the middle term. In general, to ac factor a t... |
x x (a) (b) 12x 8x 6x 9x 210. Stopping Distance The stopping distance of an automobile is the distance traveled during the driver’s reaction time plus the distance traveled after the brakes are applied. In an experiment, these distances were measured (in feet) when the automobile was traveling at a speed of x miles per... |
ning the fractions in its numerator into a single fraction and then combining the fractions in its denominator into a single fraction. Then invert the denominator and multiply. Example 8 Simplifying a Complex Fraction 3 2 x 1 1 x 1 x 2 3x 1x 1 1 x 1 2 3x x x 2 x 1 2 3x x x 1 x 2 2 3xx 1 xx 2 Combine fractions. Simplify... |
the relationship between the length of a thighbone and the height of a person, helping researchers learn about ancient cultures. Equations and Solutions of Equations An equation in example x is a statement that two algebraic expressions are equal. For 3x 5 7, x2 x 6 0, and 2x 4 are equations. To solve an equation in m... |
ic Formula to solve 8x2 24x 18 0. Solution 8x2 24x 18 0 4x2 12x 9 0 x b ± b2 4ac 2a Write original equation. Divide out common factor of 2. Quadratic Formula x 12 ± 122 449 24 Substitute b 12, a 4, and c 9. x 12 ± 0 8 3 2 Simplify. This quadratic equation has only one solution: equation. x 3 2. Check this in the origin... |
x 3 0 33x 1 5 0 x 31 9x 5 x 5 x 5 x 332 8 x 223 9 x2 x 2232 27 4x 3x 2 7 x 2 6x 3x 18 x 10 x 2 10x 176. 178. 180. 182. 184. 185. Anthropology The relationship between the length of an adult’s femur (thigh bone) and the height of the adult can be approximated by the linear equations y 0.432 x 10.44 Female y 0.449x 12.15... |
equality symbol is reversed. Remember that when you multiply or divide by a negative number, you must reverse the inequality symbol. Example 2 Solving Linear Inequalities Checking the solution set of an inequality is not as simple as checking the solutions of an equation. You can, however, get an indication of the vali... |
e interval(s) on the real number line for which the radicand is nonnegative. 75. 77. 79. x 5 x 3 47 2x 76. 78. 80. x 10 3 x 46x 15 81. Think About It The graph of can be described as all real numbers within three units of 5. Give x 10 < 8. a similar description of x 5 < 3 82. Think About It The graph of can be describe... |
ors. Correct Form Comment Leave as a x b . Do not add denominators when adding fractions ab 1 a 1 b x ab 1 1 1 x 3x 3 13x 1 3 x x 3 Multiply by the reciprocal when dividing fractions. Use the property for adding fractions. Use the property for multiplying fractions. Be careful when using a slash to denote division. 1x ... |
. 35. (a6 −4 −2 2 4 6 8 x − 4 −6 37. (a) 9. 3, 4 7. 13. Quadrant II 17. Quadrant III 21. y 11. Quadrant IV 5, 5 15. Quadrant III or IV 19. Quadrant I or III y 5 4 3 (− 1, 2) − 1 − 1 ( 5 ,− 2 4 3 ) −4 −6 (4, − 5) (b) (c) 210 2, 3 (5, 4 82 3 1, 7 6 (b) (c) C H A P T E R 1 5000 4500 4000 3500 3000 10 11 12 13 Year (6 ↔ 19... |
x Yes, V is a function of x. V x24 2x2, 0 < x < 12 (c) 91. A x2 2x 2, x > 2 C 12.30x 98,000 R 17.98x P 5.68x 98,000 97. (a) (b) (c) 93. Yes, the ball will be at a height of 6 feet. 95. 1990: $27,300 1991: $28,052 1992: $29,168 1993: $30,648 1994: $32,492 1995: $34,700 1996: $37,272 1997: $40,208 1998: $41,300 1999: $43... |
e2 −3 −4 −5 −6 4 3 2 1 −2 −3 −4 −5 −6 −4 −2 −2 −4 −6 −8 x g 65 Section 1.8 (page 89) Vocabulary Check (page 89) 1. addition; subtraction; multiplication; division gx 4. inner; outer 2. composition 3. x 4 5 6 1 g 1. y 3. y 4 3 2 1 5. (a) (d) 7. (a) g 4 2 x 6 8 10 c) x2 4 all real numbers x except x 2 (b) 4 2x x 2 x 2 x2... |
. No t2 2t 2 69. Yes (d) 5 ≤ x ≤ 5 (b) F 30 25 20 15 10 c) 12.5 pounds 47. slope: 0 y-intercept: 6 y 8 4 2 x 24 − 6 −4 −2 10 12 20 Length (in inches) 16 49. slope: 3 y-intercept: 13 y 12 6 3 −3 −6 3 6 9 x 75. All real numbers x except y x 3, 2 6 4 2 −2 −4 −6 x 4 6 77. (a) 16 feet per second (b) 1.5 seconds −9 −6 −3 51.... |
r (c) −9 6 −6 9 39. (a) No real zeros (b) number of turning points: 1 (c) 40 45. (a) −6 4 −4 6 49. 0, 0, ±1, 0, ±2, 0 x -intercepts: x 0, 1, 1, 2, 2 x f x x2 4x 12 (b) (c) (d) The answers in part (c) match the -intercepts. f x x2 10x f x x3 5x2 6x f x x 4 4x3 9x2 36x f x x2 2x 2 57. f x x3 2x2 3x f x x4 x3 15x2 23x 10 ... |
ers x except x ±4; horizontal asymptote: x 1, horizontal asymptote: 3; x 1, 1 2; y 1 y 1 2 x 2 Vertical asymptote: horizontal asymptote: x 1 2; 27. (a) Domain: all real numbers x except 0, 1 (b) y-intercept: (c) Vertical asymptote: x 2 Horizontal asymptote 333200_02_AN.qxd 12/9/05 1:27 PM Page A112 A112 (d) Answers to ... |
y 6 (b) Intercept: 0, 0 3 2 1 (0, 0) −3 − 2 −1 1 2 3 −2 −3 x 133. (a) Domain: all real numbers x except (b) y-intercept: x-intercepts: (c) Vertical asymptote: Slant asymptote: y (d) 0, 0.5 2 3, 0, 1( ( 0, − 1 2 ( −2 −1 −2 (1, 0) 2 3 4 x 135. $0.50 is the horizontal asymptote of the function. 333200_02_AN.qxd 12/9/05 1... |
30,788 24,394 11,606 V 30,788e0.268t 23,550 13,779 (e) Answers will vary. St 1001 e0.1625t 45. (a) (b) 5. d Time to Double 19.8 yr 7.75 yr 6.3 yr 15.4 yr 6. f Amount After 10 years $1419.07 $1834.36 $1505.00 $10,000.00 4. a 3. b Annual % Rate 3.5% 8.9438% 11.0% 4.5 ( 120 90 60 30 5 10 20 15 25 Time (in years) (c) 55,6... |
nute 140° 35 109. False. A measurement of A 476.39 square meters 1496.62 square meters 4 radians corresponds to two complete revolutions from the initial to the terminal side of an angle. 333200_04_AN.qxd 12/9/05 1:32 PM Page A133 Answers to Odd-Numbered Exercises and Tests A133 111. False. The terminal side of the ang... |
−3 approaches 0 and f approaches cosecant is the reciprocal of the sine. g because the 2 − 2 3 The expressions are equivalent except that when y1 is undefined. sin x 0, 55. −2 4 −4 2 The expressions are equivalent. f → 0 as x → 0. g → 0 as x → 0. 58. a, 60. c, f → 0 as x → 0. g → 0 as x → 0. 57. d, 59. b, 61. y 3 2 1 ... |
x 8 x 5x 8 117. 111. An identity because sin 1 0.1987 0.3894 0.5646 0.7174 0.8415 121. 0.1987 0.3894 0.5646 0.7174 0.8415 1.2 1.4 0.9320 0.9854 0.9320 0.9854 y2 y 2 1 −1 −2 −3 −4 x π2 π3 2 0.2 0.4 0.6 0.8 1.0 Section 5.2 (page 387) 1.2230 1.5085 1.8958 2.4650 3.4082 1.2230 1.5085 1.8958 2.4650 3.4082 1.2 1.4 5.3319 11.... |
ter than 90, then the other two angles must be acute and therefore less than The triangle is oblique. 90. arcsin0.5 sin 47. (a) (b) (c) (d) (e) 1 0 0 Domain: 0 < < Range: 0 < < 6 c 18 sin arcsin0.5 sin sin 27 0 0 c c Domain: Range: 0 < < 9 < c < 27 0.4 0.8 1.2 1.6 0.1960 0.3669 0.4848 0.5234 25.95 23.07 19.19 15.33 2.0... |
5.1 meters 37. 39. 45. (a) (d) 47. (a) (d) 49. (a) (d) 51. (a) 53. feet 33. 9.80 u v 61, slopeu 7, 5 7, 7 41. 4, 3 11, 3 1, 6 17, 18 7i 2j 20i j 3i 6j slopev 43. 9, 2 3i 4j 22, 7 2, 9 5i 6j 12.6 feet, (b) (b) (b) (b) (c) (c) 35. 8.36 5 6 4, 43 3, 9 (c) 15, 6 6i 3j (d) 18i 12j 12i 30, 9 (c) 55. y y v − 5 2 −2 −4 −6 −8 −... |
a, 35a, 67a 39. s 16t 2 32t 500 y 1 2x 2 2x 45. 35. 0, 0, 0 s 16t 2 144 5 −4 −3 x2 y 2 4x 0 47. −3 3 −3 8 6 y x2 6x 8 10 −2 −6 49. x2 y 2 6x 8y 0 10 −2 6 −12 51. 6 touchdowns, 6 extra-point kicks, and 1 field goal 53. $300,000 at 8% $400,000 at 9% $75,000 at 10% 250,000 1 2s 125,000 1 2s 125,000 s s in growth stocks in... |
0 25 30 a (70, 130) (35,130) (c) No, because the total cholesterol is greater than 200 milligrams per deciliter. 50 100 150 250 x (d) LDL: 140 milligrams per deciliter HDL: 50 milligrams per deciliter Total: 190 milligrams per deciliter 50, 120; 170 50 3.4 < 4; (e) answers will vary. Chapter 8 Section 8.1 (page 582) Vo... |
M23 19 12, C13 19, C23 19 2, C33 107. 4, 7 115. Collinear 21, 22, 103. 130 111. 16 117. 121. Uncoded: Encoded: 109. 1, 4, 5 12 15 2 12, 5 21 6 0 20 21 99 119. 15, 15 68 30 11 2x 6y 13 0 15, 0 21 23 0 20 0, 42 60 53 8 45 102 69 123. SEE YOU FRIDAY 125. False. The matrix must be square. 127. The matrix must be square and... |
0_09_AN.qxd 12/12/05 11:32 AM Page A184 A184 Answers to Odd-Numbered Exercises and Tests 41. 360 x3y2 37. 39. 45. 49. 180 55. 57. x5 10x4y 40x3y2 80x2y3 80xy4 32y5 120x7y3 1,259,712 x2y7 32,476,950,000x4y8 51. 43. 47. 1,732,104 326,592 53. 210 x2 12x32 54x 108x12 81 x 2 3x 43y 13 3x 23y 23 y 59. 3x 2 3xh h 2, h 0 61. 1... |
bottom half of a double-napped cone, is parallel to the side of the cone, and does not intersect the vertex. 7. d 8. f 6. b 5. e 11. Vertex: Focus: Directrix: 0, 0 0, 1 2 y 1 2 9. a 13. Vertex: Focus: Directrix: 10. c 0, 0 3 21 −6 −5 −4 −3 −3 −4 333200_10a_AN.qxd 12/9/05 2:42 PM Page A188 A188 Answers to Odd-Numbered E... |
s r a 47. 3x y 0 y 4 57. x2 y 22 6x2y 2y 3 4x2 5y 2 36y 36 0 r 2a cos 53. x2 y2 x23 0 49. x2 y2 16 43. 45. 51. 55. 59. 63. x2 y 2 4y 0 61. x2 4y 4 0 Answers to Odd-Numbered Exercises and Tests A195 65. The graph of the polar equation consists of all points that are six units from the pole. x2 y2 36 y 8 4 2 −8 −4 −2 2 4... |
1 7 3, 9, 5, 0, 1, 4, 2, 11 13, 1, 6 (b) 1 (c) 2.01, 13, 1, 6, 0.666 . . . 0.010110111 . . . 6 (b) 3, 8 1 6 3, 8 3, 7.5, 1, 8, 22 11. 0.123 3, 6 (c) 9. 6 (c) (d) 3. (a) 1 (d) (e) 5. (a) (d) 7. 0.625 13. −8 − 7 − 6 −5 −4 15. 3 2 3, 1, 8, 22 (e) 1 < 2.b 17. 19. (a) (b) 21. (a) (b) 23. (a) (b) 25. (a) (b) 27. (a) (b) 1 0 ... |
estimated height of a male with a 19-inch femur is 69.4 inches. (c) Height, x Female femur length Male femur length 60 70 80 90 100 110 15.48 19.80 24.12 28.44 32.76 37.08 14.79 19.28 23.77 28.26 32.75 37.24 (d) 100 inches x 100.59; There would not be a problem because it is not likely for either a male or a female to ... |
a binomial, A25 Cube root, A14 Cubic function, 68 Curtate cycloid, 778 Curve butterfly, 810 plane, 771 rose, 788, 789 sine, 321 Cycloid, 775 curate, 778 D Damping factor, 337 Decreasing function, 57 Defined, 47 Definitions of trigonometric functions of any angle, 312 Degenerate conic, 735 Degree, 285 conversion to rad... |
of, A7 factors of, A7 irreducible over, A26 Intercept form of the equation of a line, 36 Intercepts, 17 finding, 17 Intermediate Value Theorem, 146 Interval bounded, A2 on the real number line, A2 unbounded, A3 Invariant under rotation, 767 Inverse additive, A5 multiplicative, A5 Inverse function, 93 cosine, 345 defini... |
index of, A14 like, A17 properties of, A15 simplest form, A16 symbol, A14 Radicand, A14 Radius of a circle, 20 Random selection with replacement, 691 without replacement, 691 Range of a function, 40, 47 Rate, 31 Rate of change, 31 average, 59 Ratio, 31 Rational exponent, A18 Rational expression(s), A36 improper, 154 pr... |
ngle definitions, where Adjacent e t i s o p p O sin opp. hyp. cos adj. hyp. tan opp. adj. csc hyp. opp. sec hyp. adj. cot adj. opp. Circular function definitions, where is any angle 2 2 y θ y r x x sin y r cos x r tan , csc r y sec r x cot 120° 4 135° 150° − ( 1, 0) π 180° y (0, 1) 90° 601, 0) π 3 45° π 4 30° 0° 360° ... |
participate. The variable could be the amount of extracurricular activities by one high school student. Let X = the amount of extracurricular activities by one high school student. The data are the number of extracurricular activities in which the high school students participate. Examples of the data are 2, 5, 7. 1.1 ... |
nd e are qualitative or categorical. 1.9 Determine the correct data type, quantitative or qualitative, for the number of cars in a parking lot. Indicate whether quantitative data are continuous or discrete. Example 1.10 A statistics professor collects information about the classification of her students as freshmen, so... |
of students and the relative sizes of each category at each school are important points to be made. For the pie graph, they should point out which color represents part-time students and which represents full-time students. They should also be sure that the numbers and colors are visible when displayed. For the bar gra... |
or organization in order to support their claim. Is the study impartial? Read the study carefully to evaluate the work. Do not automatically assume that the study is good, but do not automatically assume the study is bad either. Evaluate it on its merits and the work done. • Misleading use of data—: These can be impro... |
ng the entire population. If the survey is done well, the answer is yes. 1.14 A local radio station has a fan base of 20,000 listeners. The station wants to know if its audience would prefer more music or more talk shows. Asking all 20,000 listeners is an almost impossible task. The station uses convenience sampling an... |
als. DATA VALUE FREQUENCY RELATIVE FREQUENCY or .15 or .25 or .15 or .30 or .10 or .05 3 20 5 20 3 20 6 20 2 20 1 20 Table 1.13 Frequency Table of Student Work Hours with Relative Frequencies The sum of the values in the relative frequency column of Table 1.13 is 20 20 , or 1. Cumulative relative frequency is the accum... |
tive frequency for 2006? Explain what this number tells you about the data. 1.4 | Experimental Design and Ethics Does aspirin reduce the risk of heart attacks? Is one brand of fertilizer more effective at growing roses than another? Is fatigue as dangerous to a driver as speeding? Questions like these are answered usin... |
iederik Stapel is a former professor at Tilburg University in the Netherlands. Over the past two years, an extensive investigation involving three universities where Stapel has worked concluded that the psychologist is guilty of fraud on a colossal scale. Falsified data taints over 55 papers he authored and 10 Ph.D. di... |
ts stratified by city into columns and grouped horizontally by entree cost (clusters). Restaurants Stratified by City and Entree Cost Entree Cost San Jose Under $10 $10 to under $15 $15 to under $20 Over $20 El Abuelo Taq, Pasta Mia, Emma’s Express, Bamboo Hut Emperor’s Guard, Creekside Inn Agenda, Gervais, Miro’s Blak... |
y a study in which data is collected as reported by individuals. systematic sampling a method for selecting a random sample; list the members of the population Use simple random sampling to select a starting point in the population. Let k = (number of individuals in the population)/(number of individuals needed in the ... |
in months patients live once starting the treatment. Two researchers each follow a different set of 40 patients with the viral disease from the start of treatment until their deaths. The following data (in months) are collected: Researcher A: 3; 4; 11; 15; 16; 17; 22; 44; 37; 16; 14; 24; 25; 15; 26; 27; 33; 29; 35; 44... |
mple of the data. 57. number of tickets sold to a concert This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 1 | Sampling and Data 57 58. percent of body fat 59. favorite baseball team 60. time in line to buy groceries 61. number of students enrolled at Evergreen Valley College 62. ... |
blanks in Table 1.37. b. What percent of students take exactly two courses? c. What percent of students take one or two courses? lastbaldeagle. Retrieved from http://www.youpolls.com/details.aspx?id=12328. 5. 6. Keeter, S., et al. (2006). Gauging the impact of growing nonresponse on estimates from a national RDD teleph... |
iteraryDigest.html. The Mercury News. Retrieved from http://www.mercurynews.com/. 1.3 Frequency, Frequency Tables, and Levels of Measurement Levels of Measurement. Retrieved from http://cnx.org/content/m10809/latest/. National Hurricane Center. Retrieved from http://www.nhc.noaa.gov/gifs/table5.gif. ThoughtCo. Retrieve... |
ersonal schedules, decreased willingness to be interviewed b. When a large number of people refuse to participate, then the sample may not have the same characteristics of the population. Perhaps the majority of people willing to participate are doing so because they feel strongly about the This OpenStax book is availa... |
omes of high school students to the school. Create a stemplot using the following data and identify any outliers. 0.5, 0.7, 1.1, 1.2, 1.2, 1.3, 1.3, 1.5, 1.5, 1.7, 1.7, 1.8, 1.9, 2.0, 2.2, 2.5, 2.6, 2.8, 2.8, 2.8, 3.5, 3.8, 4.4, 4.8, 4.9, 5.2, 5.5, 5.7, 5.8, 8.0 This OpenStax book is available for free at http://cnx.or... |
bar width/bin size; however, consistency is key when determining which data values to place inside each interval. Example 2.9 The following data are the heights (in inches to the nearest half inch) of 100 male semiprofessional soccer players. The heights are continuous data since height is measured. 60, 60.5, 61, 61, ... |
hown in Table 2.18. Age at Inauguration Frequency 41.5–46.5 46.5–51.5 51.5–56.5 56.5–61.5 61.5–66.5 66.5–71.5 Table 2.18 4 11 14 9 4 2 Frequency polygons are useful for comparing distributions. This comparison is achieved by overlaying the frequency polygons drawn for different data sets. 90 Chapter 2 | Descriptive Sta... |
smallest to largest: 114,950; 158,000; 230,500; 387,000; 389,950; 479,000; 488,800; 529,000; 575,000; 639,000; 659,000; 1,095,000; 5,500,000 M = 488,800 Q1 = 230,500 + 387,000 2 = 308,750 Q3 = 639,000 + 659,000 2 = 649,000 IQR = 649,000 – 308,750 = 340,250 (1.5)(IQR) = (1.5)(340,250) = 510,375 Q1 – (1.5)(IQR) = 308,75... |
The percentage of individuals or items with data values above the percentile 100 Chapter 2 | Descriptive Statistics Example 2.20 On a timed math test, the first quartile for time it took to finish the exam was 35 minutes. Interpret the first quartile in the context of this situation. Solution 2.20 • Twenty-five percent... |
cores for Mr. Ramirez's class held during the day are as follows: 99, 56, 78, 55.5, 32, 90, 80, 81, 56, 59, 45, 77, 84.5, 84, 70, 72, 68, 32, 79, 90. Test scores for Ms. Park's class held during the evening are as follows: 98, 78, 68, 83, 81, 89, 88, 76, 65, 45, 98, 90, 80, 84.5, 85, 79, 78, 98, 90, 79, 81, 25.5. a. Fi... |
yellow, purple, black, blue, the mode is red. Statistical software will easily calculate the mean, the median, and the mode. Some graphing calculators can also make these calculations. In the real world, people make these calculations using software. 2.30 Five credit scores are 680, 680, 700, 720, 720. The data set is ... |
and the standard deviation is two minutes. The standard deviation can be used to determine whether a data value is close to or far from the mean. A z-score is a standardized score that lets us compare data sets. It tells us how many standard deviations a data value is from the mean and is calculated as the ratio of the... |
he variance may be calculated by using a table. Then the standard deviation is calculated by taking the square root of the variance. We will explain the parts of the table after calculating s. Data Frequency Deviations Deviations2 (Frequency)(Deviations2) x 9 9.5 10 10.5 11 11.5 f 1 2 4 4 6 3 Table 2.32 (x – x¯ ) 9 – 1... |
numerically the expected deviation a data value has from the mean. In simple English, the standard deviation allows us to compare how unusual individual data are when compared to the mean. Example 2.35 Find the standard deviation for the data in Table 2.34. Class Frequency, f Midpoint, m m2 0–2 3–5 6–8 9–11 12–14 15–1... |
a value of the data occurs in the set of all outcomes to the number skewed used to describe data that is not symmetrical; when the right side of a graph looks chopped off compared to the left side, we say it is skewed to the left. When the left side of the graph looks chopped off compared to the right side, we say the ... |
cars, nine generally sell six cars, and 11 generally sell seven cars. Complete the table. Data Value (Number of Cars) Frequency Relative Frequency Cumulative Relative Frequency Table 2.45 13. What does the frequency column in Table 2.45 sum to? Why? 136 Chapter 2 | Descriptive Statistics 14. What does the relative fre... |
, 22, 22, 23 51. 87, 87, 87, 87, 87, 88, 89, 89, 90, 91 52. When the data are skewed left, what is the typical relationship between the mean and median? 53. When the data are symmetrical, what is the typical relationship between the mean and median? 54. What word describes a distribution that has two modes? 55. Describ... |
gles as they do person by person as a couple? Explain why in one or two complete sentences. 152 Chapter 2 | Descriptive Statistics 82. 25 randomly selected students were asked the number of movies they watched the previous week. The results are as follows: Number of Movies Frequency Relative Frequency Cumulative Relati... |
1,890 Table 2.76 104. Calculate the mean, median, standard deviation, the first quartile, the third quartile, and the IQR. Round to one decimal place. 105. Construct a box plot for the FTES for 2005–2006 through 2010–2011 and a box plot for the FTES for 1976–1977 through 2004–2005. 106. Compare the IQR for the FTES fo... |
ineering conferences. h. Calculate the sample standard deviation of days of engineering conferences. i. Find the mode. j. If you were planning an engineering conference, which would you choose as the length of the conference, mean, median, or mode? Explain why you made that choice. k. Give two reasons why you think tha... |
Fredo: z = .158 – .166 .012 = –0.67. For Karl: z = .177 – .189 .015 = –.8. Fredo’s z score of –.67 is higher than Karl’s z score of –.8. For batting average, higher values are better, so Fredo has a better batting average compared to his team. 77 a. s x = b. s x = c. s x = ∑ f m2 n ∑ f m2 n ∑ f m2 n 79 − x¯ 2 = 193,15... |
sment of likely results. You may have visited a casino where people play games chosen because of the belief that the likelihood of winning is good. You may have chosen your course of study based on the probable availability of jobs. You have, more than likely, used probability. In fact, you probably have an intuitive s... |
ead "the probability of A, given B." P(A|B) is the probability that event A will occur given that the event B has already occurred. A conditional probability reduces the sample space. We calculate the probability of A from the reduced sample space B. The formula to calculate P(A|B) is P(A|B) = P(A AND B) P(B) where P(B... |
the second card from the 51 cards remaining in the deck. It is the three of diamonds. You put this card aside and pick the third card from the remaining 50 cards in the deck. The third card is the J of spades. Your picks are {K of hearts, three of diamonds, J of spades}. Because you have picked the cards without repla... |
ards. The red cards are marked with the numbers 1, 2, and 3, and the blue cards are marked with the numbers 1, 2, 3, 4, and 5. The cards are well-shuffled. You reach into the box (you cannot see into it) and draw one card. Let R = red card is drawn, B = blue card is drawn, E = even-numbered card is drawn. The sample sp... |
wimmers practice four times a week. Suppose one member of the swim team is chosen randomly. a. What is the probability that the member is a novice swimmer? Solution 3.16 a. There are 150 members; 75 of these are advanced, and 47 of these are intermediate swimmers. So there are 150 − 75 − 47 = 28 novice swimmers. The pr... |
___ 14 ___ 45 55 ___ a. Complete the table. Solution 3.21 a. There are 45 females in the sample; 18 prefer the coastline and 16 prefer hiking near lakes and streams. So, we know there are 45 − 18 − 16 = 11 female students who prefer hiking on mountain peaks. Continue reasoning in this way to complete the table. 206 Cha... |
t a blue marble is selected first, we need only follow the left set of branches on the tree diagram. In this case, there are three ways to obtain red on the second draw and 11 possible outcomes. Figure 3.11 P(R on 2nd draw GIVEN B on 1st) = P(R on 2nd | B on 1st) = 3 11 You can also use the formula This OpenStax book i... |
r buys a novel is .6, and the probability that the customer buys a nonfiction book is .4. Suppose that the probability that the customer buys both is .2. a. Draw a Venn diagram representing the situation. b. Find the probability that the customer buys either a novel or a nonfiction book. c. In the Venn diagram, describ... |
A) = P(B). If A and B are mutually exclusive, P(A OR B) = P(A) + P(B) and P(A AND B) = 0. 3.3 Two Basic Rules of Probability The multiplication rule—P(A AND B) = P(A|B)P(B) The addition rule—P(A OR B) = P(A) + P(B) − P(A AND B) Chapter 3 | Probability Topics 227 PRACTICE 3.1 Terminology 1. In a particular college class... |
provided. Suppose that one person from the study is randomly selected. Find the probability that person used the product 11 to 20 times a day. Product Use (times per day) African Americans Native Hawaiians Latinos Japanese Americans Whites TOTALS 1–10 11–20 21–30 31+ TOTALS Table 3.17 Product Use by Ethnicity 60. Suppo... |
is the side the coin lands on. a. List the sample space. b. Let A be the event that there are at least two tails. Find P(A). c. Let B be the event that the first and second tosses land on heads. Are the events A and B mutually exclusive? Explain your answer in one to three complete sentences, including justification. ... |
the probability that his shirt number is from 1 to 33. b. Find the probability that he weighs at most 210 pounds. c. Find the probability that his shirt number is from 1 to 33 AND he weighs at most 210 pounds. d. Find the probability that his shirt number is from 1 to 33 OR he weighs at most 210 pounds. e. Find the pro... |
pril). Language use in the United States: 2007 (American Community Survey Reports, ACS-12). Washington, DC: United States Census Bureau. Retrieved from http://www.census.gov/hhes/socdemo/ language/data/acs/ACS-12.pdf The Roper Center for Public Opinion Research. (n.d.). Archives. Retrieved from http://www.ropercenter.u... |
9 a. b. c. 255 3059 196 3059 718 3059 This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 3 | Probability Topics 251 d. 0 e. f. 463 3059 136 196 g. Figure 3.25 252 Chapter 3 | Probability Topics This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 4... |
bility that they play zero days is .2, the probability that they play one day is .5, and the probability that they play two days is .3. Find the long-term average or expected value, μ, of the number of days per week the men's soccer team plays soccer. To do the problem, first let the random variable X = the number of d... |
ou guess the right suit every time, you get your money back and $256. What is your expected profit of playing the game over the long term? Example 4.6 Suppose you play a game with a biased coin. You play each game by tossing the coin once. P(heads) = 2 3 and . If you toss a head, you pay $6. If you toss a tail, you win... |
bability question can be stated mathematically as P(x = 15). If you define X as the number of losses, then a success is defined as a loss and a failure is defined as a win. A success does not necessarily represent a good outcome. It is simply the outcome that you are measuring. X still takes on the values of 0, 1, 2, 3... |
, calculate the (i) mean and (ii) standard deviation of X. c. Use your calculator to find the probability that at most eight people develop the disease. d. Is it more likely that five or six people will develop the disease? Justify your answer numerically. Solution 4.14 a. This is a binomial experiment since all three ... |
. Solution 4.18 a. Let X = the number of students you must ask until one says yes. b. What values does X take on? Solution 4.18 b. 1, 2, 3, . . ., (total number of students) c. What are p and q? Solution 4.18 c. p = .55; q = .45 d. The probability question is P(_______). Solution 4.18 d. P(x = 4) 4.18 You need to find ... |
: r = the size of the group of interest (first group), b = the size of the second group, n = the size of the chosen sample. Example 4.24 A school site committee is to be chosen randomly from six men and five women. If the committee consists of four members chosen randomly, what is the probability that two of them are m... |
e seismic activity for the next 48 hours in the Kuril Islands off the coast of Japan was reported at about 1.43 percent. Use this information for the next 100 days to find the probability that there will be low seismic activity in 5 of the next 100 days. Use both the binomial and Poisson distributions to calculate the ... |
nder the same conditions. Under these circumstances the binomial RV X is defined as the number of successes in n trials. The notation is: X ~ B(n, p). The mean is μ = np and the standard deviation is σ = npq . The probability of the following exactly x successes in n trials is n P(X = x) = ⎛ ⎝ x ⎞ ⎠ pxqn − x expected v... |
and n = the size of the chosen sample. X = the number of items from the group of interest that are in the chosen sample, and X may take on the values x = 0, 1, . . . , up to the size of the group of interest. The minimum value for X may be larger than zero in some instances. n ≤ r + b The mean of X is given by the for... |
be used to approximate? When would you do this? Use the following information to answer the next six exercises: On average, eight teens in the United States die from motor vehicle injuries per day. As a result, states across the country are debating raising the driving age. 63. Assume the event occurs independently in... |
08 Chapter 4 | Discrete Random Variables 88. A school newspaper reporter decides to randomly survey 12 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 18 percent of students attend Tet festivities. We are interested in the number of students who w... |
wl. In words, define the random variable X. a. b. List the values that X may take on. c. Give the distribution of X. X ~ _____(_____,_____) d. How many adults in America do you expect to survey until you find one who will watch the Super Bowl? e. Find the probability that you must ask seven people. f. Find the probabil... |
ion of X. X ~ _____(_____,_____) d. Find the probability that she has no children. e. Find the probability that she has fewer children than the Spanish average. f. Find the probability that she has more children than the Spanish average. 122. Fertile, female cats produce an average of three litters per year. Suppose th... |
p/english/ policy/children/children-childrearing/index.html Pew Internet. (2013). How Americans use text messaging. Retrieved from http://pewinternet.org/Reports/2011/Cell-PhoneTexting-2011/Main-Report.aspx South Carolina Department of Mental Health. (2006). Eating disorder statistics. Retrieved from http://www.state.s... |
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