A baseball player's batting average is calculated by dividing the number of times a player got a hit by the total number of times the player was at bat. It is expressed as a decimal rounded to three decimal places. After the first ten games of the season,Sam had 12 hits out of 33 times at bat.
a) What is his batting average after the first ten games?
b) How many hits in a row would he need to get his batting average to above 0.5?
12/33 = 0.364
To find Sam's batting average after the first ten games, you need to divide the number of hits by the number of times at bat. In this case, Sam had 12 hits out of 33 times at bat.
a) Batting average = Number of hits / Number of times at bat
Batting average = 12 / 33
Batting average ≈ 0.364
Therefore, Sam's batting average after the first ten games is approximately 0.364.
b) To determine how many hits in a row Sam would need to get his batting average to above 0.5, we can set up an equation.
Batting average = Number of hits / (Number of hits + Number of at-bats)
We need to find the number of hits where the batting average is greater than 0.5, so we can write:
0.5 < Number of hits / (Number of hits + Number of at-bats)
To find the number of hits that meets this condition, we can set up the following inequality:
0.5 < x / (x + 33)
Solving this inequality, we get:
0.5(x + 33) < x
Distributing the terms, we have:
0.5x + 16.5 < x
Subtracting 0.5x from both sides, we get:
16.5 < 0.5x
Dividing both sides by 0.5, we have:
33 < x
This means that Sam would need more than 33 consecutive hits to raise his batting average above 0.5.
a) To find Sam's batting average after the first ten games, we need to calculate the ratio of the number of hits to the number of times at bat:
Batting average = (Number of hits) / (Number of times at bat)
Number of hits = 12
Number of times at bat = 33
Batting average = 12 / 33 = 0.364 (rounded to three decimal places)
So, Sam's batting average after the first ten games is 0.364.
b) To find how many hits in a row Sam would need to get his batting average above 0.5, we can use the following formula:
(Number of hits + x) / (Number of times at bat + x) > 0.5
Where 'x' represents the number of hits in a row Sam needs.
Let's solve the equation:
(12 + x) / (33 + x) > 0.5
Cross multiplying, we have:
0.5(33 + x) > 12 + x
16.5 + 0.5x > 12 + x
0.5x - x > 12 - 16.5
-0.5x > -4.5
Dividing both sides by -0.5 (or multiplying both sides by -2), we get:
x < 9
So, Sam would need to get 9 hits in a row to have a batting average above 0.5.