Answer: x = 3, y = 1, z = 2
<u>Step-by-step explanation:</u>
EQ 1: x - y - z = 0
EQ 3:<u> -x + 2y + z = 1 </u>
y = 1
EQ 2: 2x - 3y + 2z = 7 → 1(2x - 3y + 2z = 7) → 2x - 3y + 2z = 7
EQ 3: -x + 2y + z = 1 → -2( -x + 2y + z = 1) → <u>-2x + 4y + 2z = 2</u>
y + 4z = 9
y = 1 ⇒ 1 + 4z = 9
4z = 8
z = 2
Input y = 1 and z = 2 into one of the equations to solve for x:
EQ 1: x - y - z = 0
x - (1) - (2) = 0
x - 3 = 0
x = 3
Check:
EQ 2: 2x - 3y + 2z = 7
2(3) - 3(1) + 2(2) = 7
6 - 3 + 4 = 7
3 + 4 = 7
7 = 7 
Answer:
0.2 ; 100 ; 4.84
Step-by-step explanation:
Given that the probability of each of the 5 groups is the same :
Sum of probability = 1
Hence, Probability of each group = 1 / number of groups = 1 / 5 = 0.2
Expected number for each interval for a sample of 500 : ; X = 500
E(X) = X * P(x) = 500 * 0.2 = 100
Goodness of fit (X²) :
X² = Σ(X - E)² ÷ E
Groups :
113, 95, 108, 99, and 85
X : 113 ____ 95 ____ 108 ____ 99 _____ 85
(113 - 100)^2 / 100 = 1.69
(95 - 100)^2 / 100 = 0.25
(108 - 100)^2 / 100 = 0.64
(99 - 100)^2 / 100 = 0.01
(85 - 100)^2 / 100 = 2.25
(1.69 + 0.25 + 0.64 + 0.01 + 2.25) = 4.84
