<h2>
Answer with explanation:</h2>
The confidence interval for population mean is given by :-
(1)
, where
= sample mean
z* = critical value.
SE = standard error
and
,
= population standard deviation.
n= sample size.
As per given , we have


n= 15
It is known that ring diameter is normally distributed.
By z-table ,
The critical value for 95% confidence = z*= 1.96
A 99% two-sided confidence interval on the true mean piston diameter :
(using (1))

[Rounded to three decimal places]
∴ A 99% two-sided confidence interval on the true mean piston diameter = (74.020, 74.022)
By z-table ,
The critical value for 95% confidence = z*= 1.96
A 95% lower confidence bound on the true mean piston diameter:
(using (1))
[Rounded to three decimal places]
∴ A 95% lower confidence bound on the true mean piston diameter= 74.020
Answer:
yes
Step-by-step explanation:
The line intersects each parabola in one point, so is tangent to both.
__
For the first parabola, the point of intersection is ...
y^2 = 4(-y-1)
y^2 +4y +4 = 0
(y+2)^2 = 0
y = -2 . . . . . . . . one solution only
x = -(-2)-1 = 1
The point of intersection is (1, -2).
__
For the second parabola, the equation is the same, but with x and y interchanged:
x^2 = 4(-x-1)
(x +2)^2 = 0
x = -2, y = 1 . . . . . one point of intersection only
___
If the line is not parallel to the axis of symmetry, it is tangent if there is only one point of intersection. Here the line x+y+1=0 is tangent to both y^2=4x and x^2=4y.
_____
Another way to consider this is to look at the two parabolas as mirror images of each other across the line y=x. The given line is perpendicular to that line of reflection, so if it is tangent to one parabola, it is tangent to both.
Answer:
Step-by-step explanation:
3x^2 * 2x^3= 6x^5
Multiply the 3 and 2 to get 6. Add the exponents.
Answer:
29.3 feet
Step-by-step explanation:
Okay I don't know the equation to put it in, but all you need to do is add the two values together.
12.4 + 16.9 = 29.3 feet
I rounded each number to the nearest whole number and added those.
29 + 79 + 42 = 150
If you add the original numbers you would get 149.5, which rounds to 150.