Complete question :
The IQ scores of the middle 50% of a population can be written as (x - 100) / 15 ≤ 2/3
Answer: 90 ≤ x ≤ 110
Oxs 90 and x 2 110
Step-by-step explanation:
Given the inequality:
The middle 50% of the population :
(x - 100) / 15 ≤ 2/3
The upper bound :
(x - 100) / 15 ≤ 2/3
multiply both sides by 15
(x - 100) / 15 * 15 ≤ 2/3 * 15
(x - 100) ≤ 2/3 * 15
x - 100 ≤ 10
x ≤ 10 + 100
x ≤ 110
The lower bound :
- (x - 100) / 15 ≤ 2/3
(-x + 100) / 15 ≤ 2/3
multiply both sides by 15
(-x + 100) / 15 * 15 ≤ 2/3 * 15
(-x + 100) ≤ 2/3 * 15
-x + 100 ≤ 10
-x ≤ 10 - 100
-x ≤ - 90
x ≤ 90
90 ≤ x ≤ 110
Senior tickets (x)
Child tickets (y)
First day: 3x + 5y = 70
second day: 12x + 12y = 216
Solve the system of equations (use elimination)
Multiply first equation by -4 -4(3x + 5y = 70), which makes it
-12x - 20y = -280
(+)12x + 12y = 216 add to second equation
-8y = -64
divide by -8. y = 8
Plugin the y value to either equation ( I will choose first equation)
3x + 5(8) =70
3x+ 40 = 70
3x = 30
x = 10
Senior tickets are $10, child tickets are $8
3.62
Find roots of 13 and 14
Pick any number between them
Mark brainliest please
Answer:
3x-2y-1=0
or, 3x-2y=1
or, x=(1+2y)/3...(i)
4x+y=27... ...(ii)
solving (i) and (ii)
(4+8y)+3y=27x3
4+11y= 81
11y=77
y=7
now,
x=(1+2x7)/3
x=5
hence, the passing point is (5,7)
now, for the radius of circle
radius of circle= distance betn (5,7) and (2,3)
r= √(5-2)²+(7-3)²
r=5units
finally,
the eqn of circle
(x-h)²+(y-k)²=r² (where (h,k)=(2,3) )
(x-2)²+ (y-3)²=5²
x²-4x+4+y²-6y+9=25
x²+y²-4x-6y=12....this is the required answer.