To find the lowest original score that will result in an A if the professor uses (i)(f*g)(x) and (ii)(g*f)(x). Professor Harsh gave a test to his coll

hexacordoK 2021-03-05 Answered

To find the lowest original score that will result in an A if the professor uses
\((i)(f \times g)(x)\ and\ (ii)(g \times f)(x)\).
Professor Harsh gave a test to his college algebra class and nobody got more than 80 points (out of 100) on the test.
One problem worth 8 points had insufficient data, so nobody could solve that problem.
The professor adjusted the grades for the class by
a. Increasing everyone's score by 10% and
b. Giving everyone 8 bonus points
c. x represents the original score of a student

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

liannemdh
Answered 2021-03-06 Author has 11412 answers

The function \(f(x) = 1.1\) xrepresents the score increased by 10%
The function \(g(x) = x + 8\) represents the score increased by 8 points
The function \((f \times g)(x) = 1.1(x + 8)\) represents the final score when the score is first increased by 8 bonus points and then by 10%
The function \((g \times f)(x) = l.lx + 8\) represents the final score when the score is first increased by 10% and then by 8 bonus points
A score of 90 or better results in an A
Calculation:
(i) Consider \((f \times g)(x) = 1.1 (x+8)\)
Plugging the final score of 90,
\(90 = 1.1 (x+8)\)
Dividing by 1.1 on both the sides,
\(\frac{90}{1.1}=\frac{1.1(x+8)}{1.1}\)
\(81.8181... =x+8\)
\(x+8=818181...\)
\(x+8= 81.82\)
Subtracting 8 from both the sides,
\(x+8-8=81.82-8\)
\(x= 73.82\)
(ii) Consider \((g \cdot f)(x) = 1.1x +8\)
Plugging the final score of 90,
\(90 = 1.1x+8\)
Subtracting 8 from both the sides,
\(90-8 = 1.1x+8-8\)
\(82= 1.1x\)
\(1.1x = 82\)
Dividing by 1.1 on both the sides,
\(\frac{1.1x}{1.1}=\frac{82}{1.1}\)
\(x= 74.5454...\)
\(x= 74.55\).

Have a similar question?
Ask An Expert
22
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-02-05

To calculate:To check if \((f*g)(x)=(g*f)(x)\). Professor Harsh gave a test to his college algebra class and nobody got more than 80 points (out of 100) on the test. One problem worth 8 points had insufficient data, so nobody could solve that problem.
The professor adjusted the grades for the class by
a. Increasing everyone's score by 10% and
b. Giving everyone 8 bonus points
c. x represents the original score of a student

asked 2021-03-07

A multiple regression equation to predict a student's score in College Algebra \((\hat{y})\) based on their high school GPA (\(x_1x_1\)), their high school Algebra II grade (\(x_2x_2\)), and their placement test score (\(x_3x_3\)) is given by the equation below.
\(\hat{y}=-9+5x_1x_1+6x_2x_2+0.3x_3x_3\)
a) According to this equation, what is the predicted value of the student's College Algebra score if their high school GPA was a 3.9, their high school Algebra II grade was a 2 and their placement test score was a 40? Round to 1 decimal place.
b) According to this equation, what does the student's placement test score need to be if their high school GPA was a 3.9, their high school Algebra II grade was a 2, and their predicted College Algebra score was a 67? Round to 1 decimal place.

asked 2021-07-03
The sum of three times a first number and twice a second number is 43. If the second number is subtracted from twice the first number, the result is -4. Find the numbers.
asked 2020-10-18
The sum of three times a first number and twice a second number is 43. If the second number is subtracted from twice the first number, the result is -4. Find the numbers.
asked 2021-06-10
Eastside Golden Eagles scored 60 points on a combination of two-polnt shots and three-point shots. If they made a total of 27 shots. how many of each kind of shot was made ?
asked 2021-03-02
Eastside Golden Eagles scored 60 points on a combi: nation of two-polnt shots and three-point shots. If they made a total of 27 shots. how many of each kind of shot was made”?
asked 2021-05-28
Lee buys a parcel of land in the shape of a rectangle. It has an area of 1,125 square feet and a width of 25 feet. What is the length of the parcel of land?
...