math problem:
pedro wants to calculate his gpa.
he has the lab grades:90/100,98/100,90/100,94/100,90/100,90/100,95/100,98/100. Labs are worth 20%.
He has the test grades: 9/10,6/10,10/10,10/10,5/10,7/10,7/10,7/10,10/10,10/10,8/10,10/10. Homework is worth 20%
test grades are: 35/100, 20/100, 26/100, 34/100. Exams are worth 40%.
What is his grades so far? What would his grade be is he had a 90 on the final which is worth 20%?
To calculate Pedro's grades so far, we need to find the weighted average of his lab grades, test grades, and exam grades.
Let's start with the lab grades. We have 8 lab grades, and each lab is worth 20%. To calculate the weighted average of the lab grades, multiply each grade by 20% and then sum them up:
(90/100) x 20% + (98/100) x 20% + (90/100) x 20% + (94/100) x 20% + (90/100) x 20% + (90/100) x 20% + (95/100) x 20% + (98/100) x 20%
= 0.9 x 20% + 0.98 x 20% + 0.9 x 20% + 0.94 x 20% + 0.9 x 20% + 0.9 x 20% + 0.95 x 20% + 0.98 x 20%
= 0.18 + 0.196 + 0.18 + 0.188 + 0.18 + 0.18 + 0.19 + 0.196
= 1.45
So, Pedro's lab average is 1.45.
Now let's move on to the test grades. We have 12 test grades, and each test is worth 20%. To calculate the weighted average of the test grades, multiply each grade by 20% and then sum them up:
(9/10) x 20% + (6/10) x 20% + (10/10) x 20% + (10/10) x 20% + (5/10) x 20% + (7/10) x 20% + (7/10) x 20% + (7/10) x 20% + (10/10) x 20% + (10/10) x 20% + (8/10) x 20% + (10/10) x 20%
= 0.9 x 20% + 0.6 x 20% + 1 x 20% + 1 x 20% + 0.5 x 20% + 0.7 x 20% + 0.7 x 20% + 0.7 x 20% + 1 x 20% + 1 x 20% + 0.8 x 20% + 1 x 20%
= 0.18 + 0.12 + 0.2 + 0.2 + 0.1 + 0.14 + 0.14 + 0.14 + 0.2 + 0.2 + 0.16 + 0.2
= 2.38
So, Pedro's test average is 2.38.
Finally, let's calculate the weighted average of the exam grades. We have 4 exam grades, and each exam is worth 40%. To calculate the weighted average of the exam grades, multiply each grade by 40% and then sum them up:
(35/100) x 40% + (20/100) x 40% + (26/100) x 40% + (34/100) x 40%
= 0.35 x 40% + 0.2 x 40% + 0.26 x 40% + 0.34 x 40%
= 0.14 + 0.08 + 0.104 + 0.136
= 0.468
So, Pedro's exam average is 0.468.
To calculate Pedro's overall grade so far, we need to combine the weighted averages of the lab, test, and exam grades. Since labs are worth 20%, tests are worth 20%, and exams are worth 40%, we can calculate the overall grade as:
lab average x 20% + test average x 20% + exam average x 40%
= 1.45 x 20% + 2.38 x 20% + 0.468 x 40%
= 0.29 + 0.476 + 0.1872
= 0.9532
So, Pedro's overall grade so far is approximately 0.9532.
If Pedro had a 90 on the final, which is worth 20%, we can calculate his final grade by combining the weighted averages of all the components again:
(lab average x 20% + test average x 20% + exam average x 40% + final grade x 20%)
= 1.45 x 20% + 2.38 x 20% + 0.468 x 40% + 90 x 20%
= 0.29 + 0.476 + 0.1872 + 18
= 18.9532
So, if Pedro had a 90 on the final, his grade would be approximately 18.9532.