Answer:
We accept H₀ we don´t have enough evidence to support that the mean thickness is greater than 41 mm
Step-by-step explanation:
Sample Information:
Results:
41.8
40.9
42.1
41.2
40.5
41.1
42.6
40.6
From the table we get:
sample mean : x = 41.35
sample standard deviation s = 0.698
Hypothesis Test:
Null Hypothesis H₀ x = 41
Alternative Hypothesis Hₐ x > 41
The test is a one-tail test
If significance level is 0.01 and n = 8 we need to use t-student distribution
From t-table α = 0.01 and degree of freedom df = n - 1 df = 8 - 1
df = 7 t(c) = 2.998
To calculate t(s) = ( x - 41 ) / s/√n
t(s) = ( 41.35 - 41 ) / 0.698/√8
t(s) = 0.35 * 2.83/ 0.698
t(s) = 1.419
Comparing t(s) and t(c)
t(s) < t(c)
t(s) is in the acceptance region we accept H₀
V(cylinder)=πR²H
Radius of the cylinder R=x, height of the cylinder H=y.
We can write for the cylinder
V(cylinder)=πx²y
V(cone) =(1/3)πr²h
Radius of the cone r=2x.
We can write for the cone
V(cone)= (1/3)π(2x)²h=(1/3)π *4*x²h
V(cylinder) =V(cone)
πx²y=(1/3)π *4*x²h
y=(4/3)*h
h=(3/4)*y
Answer:
-5.4 that's the answer
Step-by-step explanation:
I got you trust me
The surface area of a three dimensional object is the sum of the areas of all its faces. Here we have a net of triangular prism, which if we were to fold would form a three dimensional shape.
We need to find the area of each face. Let's begin with the rectangle in the center which can be found by calculating its length times width:
26 * 10 = 260 in^2
Next, let's find the area of the other two rectangles. Although it does not specify that these rectangles are congruent (meaning the same), we know that they are because if they were different sizes, the prism would not fit together when folded. We can find the area of one rectangle and multiply by two:
26 * 13 = 338
338 * 2 = 676 in^2
Lastly, we have two triangles which are congruent for the same reason as the rectangles. The area of a triangle can be found by calculating one-half the base time the height:
0.5 * 10 * 12 = 60
Times two since there are two triangles:
60 * 2 = 120 in^2
Add up the areas:
260 + 676 + 120 = 1056 in^2
Multiply the surface area by 6 because there are 6 packages:
1056 * 6 = 6336 in^2
The answer is C.
The probability is 1/10 * 5/10 * 5/10, or 0.025.
