Question

Ashley is doing some math exercises on a website called Khon Academy. In Khon Academy, you have to get at least 70% of the problems in an exercise right in order to gain proficiency. So far, Ashley has answered correctly 3 out of 7 times. Suppose she answers all of the following q questions correctly and gains proficiency in the exercise.

A. Ashley will gain proficiency if q > 3.
B. Ashley will gain proficiency if q > 4.
C. Ashley will gain proficiency if q > 5.
D. Ashley will gain proficiency if q > 6.

Answer 1

Ashley needs to answer more than 4 additional questions correctly on the Khon Academy exercises to achieve a proficiency level of 70%, considering she has already answered 3 out of 7 questions correctly.

Step-by-step explanation:

Ashley is currently working on a set of math exercises on Khon Academy and needs to achieve a proficiency level of 70% in an exercise. With 3 out of 7 questions answered correctly, she has a current correct rate of approximately 42.86%. To reach a minimum of 70%, Ashley must answer additional questions correctly.

The total number of questions Ashley will have attempted can be expressed as 7 + q, where q is the number of questions she will answer correctly next. To find the minimal value of q that will bring Ashley's success rate to at least 70%, we can set up the following inequality:

$\frac{3 + q}{7 + q} \geq 0.7$

When solving the inequality, you'll find that q must be strictly greater than 4 to satisfy the condition. Therefore, Ashley will gain proficiency if she answers more than 4 additional questions correctly, making option B the correct answer.