analyze simplify: * 20. $10^{3} - 10^{2} + 10^{1} - 10^{0}$ (20, 57) 21. $6 + 3(2) - 4 - (5 + 3)$ (52) 22. \begin{array}{r} 1\text{ gal }2\text{ qt }1\text{ pt} \\ + 1\text{ gal }2\text{ qt }1\text{ pt} \\ \hline \end{array} (49) * 23. \begin{array}{r} 1\text{ day }3\text{ hr }15\text{ min} \\ - \ \ \ \ \ \ 8\text{ hr }30\text{ min} \\ \hline \end{array} (49) 24. $2\text{ mi} \cdot \frac{5280\text{ ft}}{1\text{ mi}}$ (50) 25. $10 - \left(5\frac{3}{4} - 1\frac{5}{6}\
ight)$ (23, 30) 26. $\left(2\frac{1}{5} + 5\frac{1}{2}\
ight) \div 2\frac{1}{5}$ (26, 30) 27. $3\frac{3}{4} \cdot \left(6 \div 4\frac{1}{2}\
ight)$ (26)

Question

Accepted Answer

### Problem 20:
# Explanation:
## Step1: Calculate each power
$10^3 = 1000$, $10^2 = 100$, $10^1 = 10$, $10^0 = 1$
## Step2: Substitute and simplify
$1000 - 100 + 10 - 1 = 900 + 10 - 1 = 910 - 1 = 909$
# Answer:
909

### Problem 21:
# Explanation:
## Step1: Simplify parentheses and multiplication
$3(2) = 6$, $(5 + 3) = 8$
## Step2: Substitute and simplify
$6 + 6 - 4 - 8 = 12 - 4 - 8 = 8 - 8 = 0$
# Answer:
0

### Problem 22:
# Explanation:
## Step1: Add gallons, quarts, pints separately
Gallons: $1 + 1 = 2$ gal
Quarts: $2 + 2 = 4$ qt (4 qt = 1 gal, so convert 4 qt to 1 gal)
Pints: $1 + 1 = 2$ pt (2 pt = 1 qt, so convert 2 pt to 1 qt)
## Step2: Combine converted units
Gallons: $2 + 1 = 3$ gal
Quarts: $0 + 1 = 1$ qt
Pints: $0$ pt
So total is $3$ gal $1$ qt
# Answer:
3 gal 1 qt

### Problem 23:
# Explanation:
## Step1: Convert 1 day to hours
1 day = 24 hours, so total time: $24 + 3$ hr $15$ min = $27$ hr $15$ min
## Step2: Subtract hours and minutes
Subtract hours: $27 - 8 = 19$ hr
Subtract minutes: $15 - 30$ (can't do, so borrow 1 hr = 60 min: $19 - 1 = 18$ hr, $15 + 60 = 75$ min)
Now subtract minutes: $75 - 30 = 45$ min
So result: $18$ hr $45$ min
# Answer:
18 hr 45 min

### Problem 24:
# Explanation:
## Step1: Cancel miles unit
$2\ 	ext{mi} \cdot \frac{5280\ 	ext{ft}}{1\ 	ext{mi}} = 2 \cdot 5280\ 	ext{ft}$
## Step2: Multiply
$2 \cdot 5280 = 10560$ ft
# Answer:
10560 ft

### Problem 25:
# Explanation:
## Step1: Simplify the inner parentheses (subtract mixed numbers)
Find common denominator (12) for $\frac{3}{4}$ and $\frac{5}{6}$:
$5\frac{3}{4} = 5\frac{9}{12}$, $1\frac{5}{6} = 1\frac{10}{12}$
$5\frac{9}{12} - 1\frac{10}{12} = 4\frac{21}{12} - 1\frac{10}{12} = 3\frac{11}{12}$ (wait, better: $5\frac{3}{4} = \frac{23}{4}$, $1\frac{5}{6} = \frac{11}{6}$; common denominator 12: $\frac{69}{12} - \frac{22}{12} = \frac{47}{12} = 3\frac{11}{12}$)
## Step2: Subtract from 10
$10 - 3\frac{11}{12} = 9\frac{12}{12} - 3\frac{11}{12} = 6\frac{1}{12}$
# Answer:
$6\frac{1}{12}$

### Problem 26:
# Explanation:
## Step1: Add the mixed numbers in parentheses
Convert to improper fractions: $2\frac{1}{5} = \frac{11}{5}$, $5\frac{1}{2} = \frac{11}{2}$
Common denominator 10: $\frac{22}{10} + \frac{55}{10} = \frac{77}{10}$
## Step2: Divide by $2\frac{1}{5} = \frac{11}{5}$
$\frac{77}{10} \div \frac{11}{5} = \frac{77}{10} \cdot \frac{5}{11} = \frac{7 \cdot 11 \cdot 5}{10 \cdot 11} = \frac{7}{2} = 3\frac{1}{2}$
# Answer:
$3\frac{1}{2}$

### Problem 27:
# Explanation:
## Step1: Simplify the division inside parentheses
$6 \div 4\frac{1}{2} = 6 \div \frac{9}{2} = 6 \cdot \frac{2}{9} = \frac{12}{9} = \frac{4}{3}$
## Step2: Multiply by $3\frac{3}{4} = \frac{15}{4}$
$\frac{15}{4} \cdot \frac{4}{3} = \frac{15 \cdot 4}{4 \cdot 3} = 5$
# Answer:
5

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QUESTION IMAGE

Question

Explanation:

Problem 20:

Step1: Calculate each power

Step2: Substitute and simplify

Step1: Simplify parentheses and multiplication

Step2: Substitute and simplify

Step1: Add gallons, quarts, pints separately

Step2: Combine converted units

Answer:

Problem 21: