If x varies jointly as y and z, and x = 8 when y = 4 and z = 9, find z when x = 16 and y = 6. 3

Joint variation says that:

if and

then the equation is in the form of:

, where, k is the constant of variation.

As per the statement:

If x varies jointly as y and z

then by definition we have;

          ......[1]

Solve for k;  

when x = 8 , y=4 and z=9

then

Substitute these in [1] we have;

⇒

Divide both sides by 36 we have;

Simplify:

⇒

to find z when x = 16 and y = 6

Substitute these value we have;

⇒

Multiply both sides by 9 we have;

Divide both sides by 12 we have;

12 = z

or

z = 12

Therefore, the value of z is, 12

15%

step-by-step explanation:

use the table and count the number of guesses that has two correct answers.

the following are two correct answers

10010, 01100, 11000

a total of 3 numbers having 2 correct guesses out of 20 questions.

probability of getting 2 correct guesses = the number of questions getting 2 correct answers / total number of questions.

= 3/20

to convert it into percent multiply by 100, we get

= 3/20 * 100

= 15%

the answer is 15%

you.

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2