Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
The hypothesis :
H0 : σ²= 47.1
H1 : σ² > 47.1
α = 5% = 0.05
Population variance, σ² = 47.1
Sample variance, s² = 83.2
Sample size, n = 15
The test statistic = (n-1)*s²/σ²
Test statistic, T = [(15 - 1) * 83.2] ÷ 47.1
Test statistic = T = [(14 * 83.2)] * 47.1
Test statistic = 1164.8 / 47.1
Test statistic = 24.73
The degree of freedom, df = n - 1 ; 10 = 9
Critical value (0.05, 9) = 16.92 (Chisquare distribution table)
Reject H0 ; If Test statistic > Critical value
Since ; 24.73 > 16.92 ; Reject H0 and conclude that variance is greater.
Complete question is;
The lengths of two sides of a right triangle ABC are given.
Find the length of the missing side.
b = 16 ft and c = 30 ft
Answer:
25.377 ft
Step-by-step explanation:
From online sources, c is the hypotenuse of the triangle.
Thus, we can use pythagoras theorem to solve for the other side of the right angle triangle.
c² = a² + b²
Where a is the length of the missing side.
Thus;
30² = a² + 16²
a² + 256 = 900
a² = 900 - 256
a² = 644
a = √644
a = 25.377 ft
5x-6=29
+6 +6
5x=35
/5 /5
x=7
Here, it is helpful to use the formulae for the volume of a cone and a cylinder. I am assuming we are dealing with a right cone and a right cylinder.
and
.
The volumes of both of these figures are equal to 34 cubic inches, as you said. Notice in our formulae, everything is identical EXCEPT that the volume of a cone is basically that of a cylinder divided by three. To reverse this, that is, to find the volume of the cylinder, we would multiply by 3. 34 cubic inches times 3 is
102 cubic inches.
I would like to add that sometimes these formulae seem totally arbitrary. But when you think about the cylinder like a circle with a rolled-up rectangle, you can see that the
part is the area of a circle, and the height is because it's three dimensional. To translate this into the volume of a cone is a bit trickier. It involves calculus...
. If that looks like nonsense to you, then you can just remember that a cone is kind of a pointy cylinder and must be smaller than a cylinder!