At westwood middleschool, 648 students responded to a survey asking about their favorite type of exercise. twice as many students chose jogging as swimming. the same number of students chose yoga as jogging. twice as many students chose biking as jogging. how many students chose each type of exercise?

The number of students chose jogging is 144, chose swimming is 72, chose yoga is 144 and chose biking is 288.

Step-by-step explanation:

Given:

At westwood Middle School, 648 students responded to a survey asking about their favorite type of exercise.

Twice as many students chose jogging as swimming.

The same number of students chose yoga as jogging.

Twice as many students chose biking as jogging.

Now, to find the number of students chose each type of exercise.

Let the students chose jogging be

The student chose swimming be

The student chose yoga be

And the student chose biking be

As per given in question:

Twice as many students chose jogging as swimming.

.........(1)

The same number of students chose yoga as jogging.

.........(2)

Twice as many students chose biking as jogging.

 .........(3)

Total students surveyed = 648.

According to question:

Putting the value from above equations (1), (2) and (3) we :

Multiplying both sides by 2 we get:

Dividing both sides by 9 we get:

The students chose jogging = 144.

The student chose swimming:

The students chose yoga:

The student chose biking :

Therefore, the number of students chose jogging is 144, chose swimming is 72, chose yoga is 144 and chose biking is 288.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.