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.

41*67/2=1373.5

step-by-step explanation:

i just used a calculator

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.