Answer:
The p-value for the test is 0.0459.
Explanation:
The question involves a chi-squared test whose p-value is to be determined.
H₀: σ² ≤ 0.027 (null hypothesis)
H₁: σ² > 0.027 (alternative hypothesis)
Standard deviation = s = 0.2
Hence, s² = (0.2)² = 0.04
Sample size = n = 30
Degree of freedom = n - 1 = 30 - 1 = 29
Significance level = 0.05
Test statistic: X² = (n - 1)s² / σ²
= (30 - 1) x 0.04 / 0.027
= 42.9629
The p-value can now be determined using the Excel function:
CHISQ.DIST.RT(42.9629,29) = 0.0459
Hence, the p-value for the test is 0.0459.
The value of the height of the cylinder is 25cm.
According to the statement
we have to find that the height pf the cylinder with the given value of the volume.
So, For this purpose we know that the
The volume of a cylinder is the density of the cylinder which finds that the amount of material it can carry. Cylinder's volume is given by the formula, πr^2h.
From the given information:
The volume of a cylinder is 225π cubic inches, and the radius of the cylinder is 3 inches.
Then
volume = πr^2h
225π = π3^2h
Now, solve it then
225 = 9h
h = 25.
The value becomes 25.
So, The value of the height of the cylinder is 25cm.
Learn more about volume of a cylinder here
brainly.com/question/9554871
#SPJ9
Answer: The length of BC is 7
Step-by-step explanation: Assuming the lengths of the opposite sides of the quadrilateral are congruent, then
AB=DC and
AD=BC
Inputting the values of AB, DC and AD as given in the question:
x + 8 = 3x ...(1)
x + 3=? ...(2)
We have to solve for the value of x to get the actual lengths and thus ascertain BD.
From equation (1):
8 = 3x - x
8 = 2x
8/2 = x
Therefore, x = 4.
If x = 4 then equation(2) would be
4 + 3= 7.
Hence, the actual lengths of the quadrilateral are:
AB = 4 + 8. DC = 3(4)
=12. =12.
AD = 4 + 3. AD = BC
= 7. Therefore, BC = 7.
Hence, it is confirmed that quadrilateral ABCD is a parallelogram since both the opposite sides are proven to be congruent.
Answer:
a. 4r² b. 2r c. 6 cm
Step-by-step explanation:
The surface area A of the cube is A = 24r². We know that the surface area, A of a cube also equals A = 6L² where L is the length of its side.
Now, equating both expressions, 6L² = 24r²
dividing both sides by 6, we have
6L²/6 = 24r²/6
L² = 4r². Since the area of one face is L², the polynomial that determines the area of one face is A' = 4r².
b. Since L² = 4r² the rea of one face of the cube, taking square roots of both sides, we have
√L² = √4r²
L = 2r
So, the polynomial that represents the length of an edge of the cube is L = 2r
c. The length of an edge of the cube is L = 2r. When r = 3 cm.
L = 2r = 2 × 3 cm = 6 cm
So, the length of an edge of the cube is 6 cm.
