In basketball, a field goal can be worth either two or three points. During his career, an NBA player has made 49.93%of his two-point field goal attempts and 36.51% of his three-point field goal attempts. Assuming the value of a missed attempt is the average value of this player’s career field goal attempts is 1.0389 points. What percent of his career field goal attempts have been three-point attempts? Express your answer as a percent to the nearest whole number.
This is not part of an ongoing competition its i didn't know how to do it and i wanted to know how.
If you think about it, the actual number of shots does not matter. So let's just call it 1.
.4993(1-x)*2 + .3651x*3 = 1.0389
x = 0.4167
So, 41.67% of his shots were 3-pointers
Let's denote the percentage of two-point field goal attempts as T and the percentage of three-point field goal attempts as Th. We have the following information:
T = 49.93%
Th = 36.51%
Missed attempt value = 1.0389 points
To find the percentage of three-point attempts, we need to compare the values of two-point and three-point attempts.
The average value per field goal attempt can be calculated as:
Average Value = (T * 2 points) + (Th * 3 points) + (Missed attempt value * Missed attempt percentage)
Given that the average value is 1.0389 points, we can substitute in the given values:
1.0389 = (0.4993 * 2) + (0.3651 * 3) + (1.0389 * Missed attempt percentage)
Simplifying the equation:
1.0389 = 0.9986 + 1.0953 + 1.0389 * Missed attempt percentage
Rearranging the terms:
0.0389 = 1.0389 * Missed attempt percentage
Dividing both sides by 1.0389:
Missed attempt percentage = 0.0389 / 1.0389 ≈ 0.0375 (rounded to four decimal places)
To find the percentage of three-point attempts, we subtract the two-point attempt percentage from 100%:
Three-point attempts percentage = 100% - two-point attempts percentage
Three-point attempts percentage ≈ 100% - 49.93% = 50.07% (rounded to the nearest whole number)
Therefore, approximately 50% of this player's career field goal attempts have been three-point attempts.
To determine the percentage of his career field goal attempts that have been three-point attempts, we need to compare the number of three-point attempts to the total number of attempts.
Let's assume the player has attempted a total of "x" field goals in his career. Therefore, the number of two-point attempts would be 0.4993x, and the number of three-point attempts would be 0.3651x.
Now, let's calculate the average value of a missed attempt. We know that the value of a made two-point field goal is 2 points and the value of a made three-point field goal is 3 points. Since the average value of all attempts is 1.0389 points, we can set up the following equation:
[0.4993x * 2 + 0.3651x * 3 + (1 - 0.4993x - 0.3651x) * 0] / x = 1.0389
Solving this equation will give us the value of "x," representing the total number of field goal attempts.
After calculating the value of "x," we can determine the percentage of three-point attempts by dividing the number of three-point attempts by the total number of attempts and multiplying by 100. Finally, rounding the result to the nearest whole number will give us our answer.
Note: The actual calculation involves solving the equation, which can be done using algebraic methods or numerical methods such as iteration.
So, to find the percentage of his career field goal attempts that have been three-point attempts, you would need to perform the calculations described above. If you provide the values for the made two-point attempts, made three-point attempts, and the average value of a missed attempt, I can assist you in determining the percentage.