College Algebra 9th txtbk

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A-8 APPENDIX A
76. PHYSICS Atoms and molecules that make up the air constantly
fly about like microscopic missiles. The velocity v of a particular
particle at a fixed temperature varies inversely as the
square root of its molecular weight w. If an oxygen molecule in
air at room temperature has an average velocity of 0.3 mile/second,
what will be the average velocity of a hydrogen molecule, given
that the hydrogen molecule is one-sixteenth as heavy as the
oxygen molecule?
Problems 77 and 78 require a graphing calculator or a computer
that can calculate linear, quadratic, cubic, and exponential
regression models for a given data set.
77. Table 1 shows the life expectancy (in years) at birth for residents
of the United States from 1970 to 1995. Let x represent years
since 1970. Use the indicated regression model to estimate the life
expectancy (to the nearest tenth of a year) for a U.S. resident born
in 2010.
(A) Linear regression (B) Quadratic regression
(C) Cubic regression (D) Exponential regression
Table 1
Year
Life Expectancy
1970 70.8
1975 72.6
1980 73.7
1985 74.7
1990 75.4
1995 75.9
2000 77.0
2005 77.7
Source: U.S. Census Bureau
78. Refer to Problem 77. The Census Bureau projected the life expectancy
for a U.S. resident born in 2010 to be 77.9 years. Which
of the models in Problem 77 is closest to the Census Bureau
projection?
CHAPTERS 6–8
Cumulative Review Exercises
Work through all the problems in this cumulative review and check
answers in the back of the book. Answers to all review problems
are there, and following each answer is a number in italics
indicating the section in which that type of problem is discussed.
Where weaknesses show up, review appropriate sections in the
text. Note that Problems 4, 15, 16, 40, 41, 48, 49, and 88 are from
sections that appear online.
1. Solve using substitution or elimination by addition:
3x 5y 11
2x 3y 1
2. Solve by graphing: 2x y 4
3x y 1
3. Solve by substitution or elimination by addition:
6x 3y 2
2x y 1
4. Solve by graphing: 3x 5y 15
x, y 0
5. Determine whether each of the following can be the first three
terms of an arithmetic sequence, a geometric sequence, or neither.
(A) 20, 15, 10, . . . (B) 5, 25, 125, . . .
(C) 5, 25, 50, . . . (D) 27, 9, 3, . . .
(E) 9, 6, 3, . . .
In Problems 6–8:
(A) Write the first four terms of each sequence.
(B) Find a 8 . (C) Find S 8 .
6. a n 2 5 n 7. a n 3n 1
8. a 1 100; a n a n1 6, n 2
9. Evaluate each of the following:
32!
9!
(A) 8! (B) (C)
30! 3!(9 3)!
10. Evaluate each of the following:
(A) a 7 (B) C 7,2 (C) P 7,2
2 b
In Problems 11–13, graph each equation and locate foci. Locate
the directrix for any parabolas. Find the lengths of major, minor,
transverse, and conjugate axes where applicable.
11. 25x 2 36y 2 900 12. 25x 2 36y 2 900
13. 25x 2 36y 0
14. Find each determinant:
(A) ` 3 5
(B)
2 2 `
15. Solve x 2 y 2 2
2x y 1
5 3
5 3 `