1A Review of the Basics (Answers to Exercises)

1.1 Algebraic Expressions

1. [latex]5a+1[/latex]
2. [latex]20b^2+10b[/latex]
3. [latex]2x^2+4x+4.5[/latex]
4. [latex](1+i)^{17}[/latex]
5. [latex]4[/latex]
6. [latex]I =[/latex]55.48$
7. [latex]15r^2 +3r+5[/latex]
8. [latex]1,024x^{40}[/latex]
9. [latex]0.75t+3.5t^3[/latex]
10. [latex]2 + 3(1+i)^3 -5(1+i)^6[/latex]
11. [latex]3.995628R[/latex]
12. [latex]0.0256[/latex]
13. [latex]PV=\$2,550[/latex]
14. [latex]PMT= \$246.64[/latex]
15. [latex]a^4 -9a^2 +18[/latex]
16. [latex]-2x^2 -0.6xy+4.8y^2 -7.2x+4.2y[/latex]
17. [latex]-\frac{3}{16}z^{-13}[/latex]
18. [latex]$15,223.10[/latex]
19. [latex]$39,963.05[/latex]
20. [latex]$12,466.44[/latex]

1.2 Linear Equations

1. [latex]x=10[/latex]
2. [latex]b=1[/latex]
3. [latex]m=2[/latex]
4. [latex]x=4, y=2[/latex]
5. [latex]h=5, q=1[/latex]
6. [latex]a=8, b=0.6[/latex]
7. [latex]y=[/latex]620.14$
8. [latex]t=6.1513̅[/latex]
9. [latex]\text{Delay} = 1.5 hours[/latex]
10. [latex]\text{10. Users in } 2000 = 107,998,376[/latex]
11. [latex]\text{ Direct cost} = \$3,000[/latex]
12. [latex]\text{Gross income} = \$140,000[/latex]
13. [latex]\text{Single tickets} = 10,363; \text{3-pack Tickets} = 1,879[/latex]
14. [latex]A = 700 \text{units}; B = 550 \text{ units}[/latex]
15. [latex]\text{Company shares} =[/latex]975,000$
16. [latex]240 \text{ minutes}[/latex]
17. [latex]\text{Marianne} = \$50,000; \text{William} = \$40,000; \text{Hendrick} = \$65,000; \text{Charlotte} =[/latex]20,000$
18. [latex]\text{Regular stalls} = 10,860; \text{Handicap stalls} = 240; \text{Small car stalls} = 720; \text{RV stalls} = 180[/latex]
19. [latex]Z = \$25,000[/latex]
20. [latex]q = 2.78; r = 9.31[/latex]

1.3 Natural Logarithms
[latex]e^1.367188 = 3.9243[/latex]
[latex]e^-0.295042 = 0.7445[/latex]
[latex]e^0.609336 = 1.83921[/latex]
[latex]e^2.585852 =12.2746[/latex]
[latex]e^-2.051398 = 0.128555[/latex]
[latex]0.392393[/latex]
[latex]2.302585[/latex]
[latex]1.811554[/latex]
[latex]0.455460[/latex]
[latex]0.519446[/latex]
[latex]1.529094[/latex]
[latex]50.517191[/latex]
[latex]22.48254[/latex]
[latex]36.904108[/latex]
[latex]N=87.808096[/latex]
[latex]N=160.423164[/latex]
[latex]0.583198[/latex]
[latex]1.451535[/latex]
[latex]403.428793[/latex]
[latex]33.115452[/latex]