1. When 100 students took a test, the average score was 77,1. Two more students took the test, the sum of the score was 125. What is the new average ?
2. The Basket Ball Team and Baseball team have a total of 24 players. There are 12 basket players and 18 baseball players. How may players are on both the basketball and baseball team ?
Confuse..
So the total score for all 100 students is 7710
Two more students added 125 for a new total of 7835
new average = 7835/102 = 76.8
2. total = 12 bb-players + 18 baseball players
= 30 players
but there were only 24 , so 6 must have been playing both sports.
check: 12+18-6 = 24
1. To find the new average score, we need to calculate the total score of all the students after the two additional students took the test.
- The initial total score can be calculated by multiplying the average score (77.1) by the number of students (100):
Initial Total score = Average score x Number of students
Initial Total score = 77.1 x 100 = 7710
- After the two additional students took the test, we are given that the sum of the scores was 125.
- To find the new total score, we add the sum of the scores of the two additional students to the initial total score:
New Total score = Initial Total score + Sum of scores of the two additional students
New Total score = 7710 + 125 = 7835
- The new number of students is the initial number of students (100) plus the two additional students:
New Number of students = Number of students + 2
New Number of students = 100 + 2 = 102
- Finally, to find the new average score, we divide the new total score by the new number of students:
New Average score = New Total score / New Number of students
New Average score = 7835 / 102 ≈ 76.8
Therefore, the new average score is approximately 76.8.
2. To find the number of players on both the basketball and baseball teams, we can use the concept of intersection in sets.
- Given that the basketball team has 12 players and the baseball team has 18 players.
- To find the number of players on both teams, we need to find the intersection between the basketball team and the baseball team.
- In this case, the intersection represents the players who are on both teams.
- Since the total number of players between the two teams is 24, and the basketball team has 12 players, we can subtract the number of basketball players from the total number of players to find the number of players on both teams:
Number of players on both teams = Total number of players - Number of basketball players
Number of players on both teams = 24 - 12 = 12
Therefore, there are 12 players who are on both the basketball and baseball teams.
1. To find the new average score, we need to calculate the total score of all students and divide it by the total number of students. Here's how you can do it:
- Multiply the average score (77.1) by the number of students (100) to find the total score of the first group of students: 77.1 * 100 = 7710.
- Add the sum of the scores of the two additional students (125) to the total score: 7710 + 125 = 7835.
- Calculate the new average score by dividing the updated total score (7835) by the total number of students in both groups (100 + 2 = 102): 7835 / 102 ≈ 76.8.
Therefore, the new average score is approximately 76.8.
2. To determine the number of players who belong to both the basketball and baseball teams, you can use the concept of set intersection. Here's how you can do it:
- First, determine the total number of players in both teams by adding the number of basketball players (12) and baseball players (18): 12 + 18 = 30.
- Then, subtract the total number of players from both teams (24) from the total number of players in both teams (30) to find the number of players who belong to both teams: 30 - 24 = 6.
Therefore, there are 6 players who are part of both the basketball and baseball teams.