Since you did not select any specific options (ExplainAnswer, TeachTopic, or GeneratePractice are all false), I will provide the final answers extracted from the provided Solutions Key image.
Final Answer:
ARE YOU READY? PAGE 791
1. B
2. E
3. A
4. C
5.
- $p_1 \rightarrow r_2$
- $p_2 \rightarrow r_1$
- $p_3 \rightarrow r_3$
*(Note: The diagram shows connections between P and R nodes)*
6. $\frac{1}{20}, \frac{20}{20}, \frac{20}{20}$
7. $\frac{8}{24}, \frac{6}{24}, \frac{20}{24}$
8. $\frac{8}{15}, \frac{2}{15}, \frac{8}{15}$
9. $\frac{1}{12}, \frac{1}{60}, \frac{5}{60}$
10. $\frac{1}{2}, \frac{3}{7}, \frac{3}{14}$
11. $\frac{1}{4}, \frac{7}{12}, \frac{1}{12}$
12. $\frac{4}{5}, \frac{1}{5}, \frac{2}{5}, \frac{2}{5}, \frac{1}{1}$
13. $\frac{1}{3}, \frac{1}{4}, \frac{1}{3}, \frac{1}{18}, \frac{4}{3}$
14. 7% of $150 = x$; $0.07(150) = x$; $x = 10.5$
15. 90% of $x = 45$; $0.9x = 45$; $x = 50$
16. Price increased by 12% of 24 = $0.12(24) = \$2.88$
17. The amount of water to be changed is 20% of 65 = $0.20(65) = 13$ gal.
18. Data: 2, 4, 4, 6, 9
- mean: 5
- median: 4
- mode: 4
19. Data: 1, 1, 2, 2, 2
- mean: 1.5
- median: 1.5
- mode: 1, 2
20. Data: 1, 2, 3, 4, 5, 6
- mean: 3.5
- median: 3.5
- mode: none
21. Data: 3, 14, 14, 18, 18, 20
- mean: 15
- median: 16
- mode: 14, 18
CHECK IT OUT!
1a. Start plot and end plot: $6 \times 4 \times 5 = 120$. There are 120 adventures.
1b. Letter letter letter letter digit: $52 \times 52 \times 52 \times 52 \times 10 = 73,116,160$. There are 73,116,160 possible passwords.
2a. $_8P_3 = \frac{8!}{(8-3)!} = \frac{8!}{5!} = 8 \cdot 7 \cdot 6 = 336$. There are 336 ways to award the costumes.
2b. $_5C_3 = \frac{5!}{(5-3)!3!} = \frac{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{3 \cdot 2 \cdot 1 \cdot 2 \cdot 1} = 10$. There are 10 ways a 2-digit number can be formed.
3. The order does not matter. It is a combination. $_8C_2 = \frac{8!}{2!(8-2)!} = \frac{8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{2 \cdot 1(6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1)} = 28$. There are 28 ways to select 2 swimmers from 8.
THINK AND DISCUSS
1. Possible answer: selecting a 9-player batting order from 20 players; selecting 3 magazine subscriptions from a list of 20.
2. 1; possible answer: there is only 1 way to choose the entire group from a group.
3. Possible answer: the number of ways to select 4 items from 5 if you can select more than the total number of items.
4. Table values:
-
Permutation Formula: $\frac{n!}{(n-r)!}$ | Example: $_5P_3 = \frac{5!}{2!} = 60$
-
Combination Formula: $\frac{n!}{r!(n-r)!}$ | Example: $_5C_3 = \frac{5!}{3!2!} = 10$
EXERCISES GUIDED PRACTICE
1. Important; permutation
2. Blouse jacket skirt: $3 \times 3 \times 2 = 18$. There are 18 different outfits.
3. Digit letter: $9 \times 25 = 225$. There are 225 different codes.
4. $_7P_2 = \frac{7!}{(7-2)!} = \frac{7!}{5!} = 7 \cdot 6 = 42$. There are 42 ways to schedule the 2 activities.
Parent Tip: Review the logic above to help your child master the concept of holt algebra 2 worksheet.
