Alist of measurements in increasing order is 4, 5, 6, 8, 10, and x. if the median of these measurements is \small \frac{6}{7} times their arithmetic mean, what is the value of x ?

Given:

(i) The measurements of the data in increasing order are 4,5,6,8,10 and X

(ii) Total number of observations (n) = 6 which is even

(iii) Median = (6 / 7)× Arithmetic Mean

Concept: If there are even number of observations then the median can be calculated as

Median = [(n /2)the term + {(n/2)+1} term] / 2

Here, n = 6,

Median = [(6 /2)the term + {(6/2)+1} term] / 2 = [ 3rd term + 4th term] /2

Median = [ 6 + 8] /2 = 7

Arithmetic Mean (AM) = Sum of the observation / Number of observations

or, = [ 4 + 5 + 6 + 8 + 10 + X] / 6

or, = [33 + X] / 6

According to the problem,

Median = (6 / 7)× AM

or, 7 = ( 6 / 7 ) × ( 33 + X) /6

or, 49 = 33 + X

or, X = 16

Hence, the value of X will 16

i leave the calculator work to you.

7. diameter 4 miles, circumference 4π miles

8. radius 0.2 miles, circumference 0.4π miles

[this is a bad problem because the actual radius of a car on the track is less than 0.2 miles so the answer is less than 0.4π miles]

9. radius 6 feet, circumference 12π feet

10. diameter 14 cm, circumference 14π cm

11. diameter 4.8 feet, circumference 4.8π feet

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol