Item 9
On a 15-question online quiz, you correctly answer five 1-point questions and nine 2-point questions. You earn 92% of the possible points on the quiz.
a. How many possible points is the quiz worth?
b. How many questions did you miss?
How many points was each missed question worth?
5*1 + 9*2 = 0.92x
Once you have solved for x, you can answer the questions (assuming that all the missed questions counted the same).
To find the answers to these questions, we can use the given information and some basic algebra.
Let's start with part a. The problem states that you earned 92% of the possible points on the quiz. Since we know the number of correct answers for each type of question, we can calculate the total number of points you earned.
For the 1-point questions, you answered five correctly, so you earned 5 points.
For the 2-point questions, you answered nine correctly, so you earned 18 points.
Now, let's calculate the total points you earned:
Total points = points earned from 1-point questions + points earned from 2-point questions
Total points = 5 + 18 = 23
Since you earned 92% of the possible points, we can set up the equation:
23 = 0.92 * (total possible points on the quiz)
To solve for the total possible points, divide both sides of the equation by 0.92:
total possible points on the quiz = 23 / 0.92
Evaluating the right side of the equation gives us:
total possible points on the quiz = 25
Therefore, the quiz is worth a total of 25 points.
Moving on to part b, to find the number of questions you missed, we need to know the total number of questions on the quiz. We can calculate this by dividing the total possible points by the number of points each question is worth.
Since we know that there are both 1-point and 2-point questions, we need to find the number of each type. Let's assume there are x 1-point questions and y 2-point questions.
The number of questions you missed is equal to the total number of questions minus the number of questions you answered correctly, which can be expressed as:
Questions missed = total number of questions - (number of 1-point questions answered correctly + number of 2-point questions answered correctly)
Since the total number of questions on the quiz is equal to the number of 1-point questions plus the number of 2-point questions, we can rewrite the equation as:
Questions missed = (x + y) - (number of 1-point questions answered correctly + number of 2-point questions answered correctly)
We know that you answered five 1-point questions correctly and nine 2-point questions correctly, so we can substitute these values into the equation:
Questions missed = (x + y) - (5 + 9)
We don't know the values of x and y, but we can find the value of x + y using the fact that the total number of questions is equal to the number of 1-point questions plus the number of 2-point questions. We can write an equation for this:
Total number of questions = number of 1-point questions + number of 2-point questions
Substituting the variable values into the equation, we get:
Total number of questions = x + y
So, we can rewrite the equation for the number of questions missed as:
Questions missed = (Total number of questions) - (5 + 9)
Since we now know the total number of questions is equal to x + y, we can substitute this value into the equation:
Questions missed = (x + y) - (5 + 9)
To find the value of x + y, we need more information. The problem does not provide any additional information regarding the number of questions or the values of x and y. Therefore, without any further information, we cannot calculate the exact number of questions missed or determine the value of x and y.
Apologies, but without additional information, we cannot determine how many points each missed question was worth either.
Item 9
On a 15-question online quiz, you correctly answer five 1-point questions and nine 2-point questions. You earn 92% of the possible points on the quiz.
a. How many possible points is the quiz worth?
b. How many questions did you miss?
How many points was each missed question worth?