Answer:
A) Interval for σ² is;
0.29 < σ² < 6.74
B) The manufacturer's claim that σ² = 1 is valid.
Step-by-step explanation:
A) I have attached the explanation
B) Due to the fact that the 95% confidence interval level for σ² is from 0.29 to 6.74 and that 1 falls within that range, we can say that the manufacturer's claim that σ² = 1 is valid.
Answer:
x = -1/3 and x = 3
Step-by-step explanation:
I'm not sure, but I think you mean 3x^2 - 8x - 3 = 0
In that case:
1. Add 3 on both sides
3x^2 - 8x -3 + 3 = 3 -> 3x^2 - 8x = 3
2. Divide both sides by 3
x^2 - 8/3x = 1
3. Add ((8/3)/2)^2 to both sides
x^2 - 8/3x + ((8/3)/2)^2 = 1 + ((8/3)/2)^2
4. Simplify
x^2 - 8/3x + (4/3)^2 = 1 + (4/3)^2
x^2 - 8/3x + 16/9 = 1 + 16/9
5. Rewrite x^2 - 8/3x + 16/9 = 1 + 16/9 as a perfect square
and simplify 1 + 16/9
(x - 4/3)^2 = 25/9
6. Find the square root of both sides
7. Simplify
(x - 4/3) = ±5/3
8. Rewrite the equation as two seperate equations
(x - 4/3) = ±5/3 ->
a. (x - 4/3) = 5/3
b. (x - 4/3) = -5/3
9. Solve for x by isolating the variable (add 4/3 to both sides)
a. x = 5/3 + 4/3
b. x = - 5/3 + 4/3
10. Simplify
a. x = 9/3 -> x = 3
b. x = -1/3