Answer:
The volume in terms of π is 144 ft³
The volume rounded to the nearest tenth is 452.4 ft³
Step-by-step explanation:
The formula of the volume of a cone is V = π r² h , where r is its radius and h is its height
The formula of the area of a circle is A = π r²
∵ The area of the base of the cone is 36π ft²
- Equate the formula of the area of the circle by 36π to find r
∵ πr² = 36π
- Divide both sides by π
∴ r² = 36
- Take √ to both sides
∴ r = 6 ft
∵ The height of the cone is equal to twice the radius
∵ The radius of the cone is 6 ft
- Multiply 6 by 2 to find the height
∴ h = 2(6) = 12 ft
∴ The height of the cone is 12 ft
Substitute the values of h and r in the formula of the volume of the cone to find it
∵ V = π(6)²(12)
∴ V = 144 π ft³
∴ V = 452.3893421 ft³
- Round it to the nearest tenth
∴ V = 452.4 ft³
Answer:
The decision rule is
Reject the null hypothesis
The test statistics is
Step-by-step explanation:
From the question we are told that
The first sample size is
The mean at first deployment is
The standard deviation is
The second sample size is
The mean at second deployment is
The standard deviation is
The null hypothesis is
The alternative hypothesis is
The level of significance is
Generally the degree of freedom is mathematically represented as
=>
=>
Generally the pooled variance is mathematically represented as
=>
=>
Generally the test statistics is mathematically represented as
=>
=>
Generally from the t distribution table the probability corresponding to the t statistics value to the left is
Generally the p -value is mathematically represented as
=>
=>
From the obtained value we see that the hence
The decision rule is
Reject the null hypothesis