Question

5 from unit 1, lesson 13
during the month of august, the mean of the daily rainfall in one city was 0.04 inches with a standard deviation of 0.15 inches. in another city, the mean of the daily rainfall 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? no
explain your reasoning.
because the standard deviations are different

6 from unit 2, lesson 1
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

Explanation:

Step1: Define variable for part a

Let $p$ be number of players.

Step2: Calculate for perfect - score in part b

4 players, 20 points each.

Step3: Define scores for non - perfect scores in part c

Use $x_i$ for player scores.

Step4: Calculate number of players in part d

Multiply number of teams by players per team.

Step5: Find min and max for part e

Use min and max players per team for 8 teams.

Answer:

a. Let $p$ represent the number of players on a team. The inequality is $2\leq p\leq4$.
b. Han and three of his friends form a team, so there are 4 players on the team. If each player can score up to 20 points in a round and every player earns a perfect - score, the expression for the number of points Han's team earns in one round is $4\times20 = 80$.
c. Let $x_1,x_2,x_3,x_4$ be the scores of the 4 players on Han's team. The expression for the number of points Han's team earns in one round is $x_1 + x_2+x_3 + x_4$, where $0\leq x_i<20$ for $i = 1,2,3,4$.
d. Two teams have 4 players each and the remaining $6 - 2=4$ teams have 3 players each. The expression for the number of players in the game is $2\times4+4\times3=8 + 12=20$.
e. Let $n$ be the number of players in a game with 8 teams. The minimum number of players occurs when each team has 2 players, so $n_{min}=8\times2 = 16$. The maximum number of players occurs when each team has 4 players, so $n_{max}=8\times4 = 32$. The inequality is $16\leq n\leq32$.