Question

1. during the month of august, the mean of the daily rainfall in a city was 0.01 inches with a standard deviation of 0.15 inches. in another city, the mean was 0.01 inches with a standard deviation of 0.05 inches. han says that both cities had a similar pattern of precipitation in the month of august. do you agree with han? explain your reasoning. (from unit 1, lesson 13.) 6. in a video game, players form teams and work together to earn as many points as possible for their team. each team can have between 2 and 4 players. each player can score up to 20 points in each round of the game. han and three of his friends decided to form a team and play a round. write an expression, an equation, or an inequality for each quantity described here. if you use a variable, specify what it represents. a. the allowable number of players on a team b. the number of points hans team earns in one round if every player earns a perfect score c. the number of points hans team earns in one round if no players earn a perfect score d. the number of players in a game with six teams of different sizes: two teams have 4 players each and the rest have 3 players each e. the possible number of players in a game with eight teams (from unit 2, lesson 1.)

Explanation:

Step1: Analyze part a

Let \( n \) be the number of players on a team. Since each team can have between 2 and 4 players, the inequality is \( 2\leq n\leq4 \).

Step2: Analyze part b

Han's team has 4 players (\( n = 4 \)), and each player can score up to 20 points. If every player earns a perfect score, the number of points \( p=4\times20 = 80 \).

Step3: Analyze part c

Let \( x_i \) be the score of the \( i - \)th player (\( i = 1,2,3,4 \)), and \( 0\leq x_i<20 \). The number of points \( P=\sum_{i = 1}^{4}x_i \), so \( 0\leq P<80 \).

Step4: Analyze part d

There are six teams. Two teams have 4 players each (\( 2\times4 \)), and the remaining \( 6 - 2=4 \) teams have 3 players each (\( 4\times3 \)). The total number of players \( N=2\times4 + 4\times3=8 + 12=20 \).

Step5: Analyze part e

Let \( m \) be the number of players in a team. Since \( 2\leq m\leq4 \) and there are 8 teams. The minimum number of players is \( 2\times8 = 16 \), and the maximum number of players is \( 4\times8=32 \). So the inequality is \( 16\leq N\leq32 \).

Answer:

a. \( 2\leq n\leq4 \) (where \( n \) is the number of players on a team)
b. \( p = 80 \)
c. \( 0\leq P<80 \) (where \( P \) is the number of points Han's team earns)
d. \( N=2\times4+4\times3 = 20 \)
e. \( 16\leq N\leq32 \) (where \( N \) is the number of players in the game)