Answer:
The radius of sphere with volume 4500 cubic inches is 10.24 inches.
Step-by-step explanation:
Let V be the volume of the sphere
Given
Volume of sphere = V = 4500 cubic inches
Let r be the radius of the sphere
The volume of the sphere is given by the formula

Putting the known values

Taking cube root on both sides
![\sqrt[3]{r^3} = \sqrt[3]{1073.8636} \\r = 10.2403](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Br%5E3%7D%20%3D%20%5Csqrt%5B3%5D%7B1073.8636%7D%20%5C%5Cr%20%3D%2010.2403)
Rounding off to nearest hundredth
The radius is: 10.24 inches.
Hence,
The radius of sphere with volume 4500 cubic inches is 10.24 inches.
Answer:
c) 50
Step-by-step explanation:
We have been given that the mean life of a particular brand of light bulb is 1200 hours. About 95% of this brand of bulbs will last between 1100 and 1300 hours.
We will use z-score formula to solve our given problem.
, where,
,
,
,

We know that 95% of data points lies within two standard deviation of mean, so 1100 will correspond to a z-score of -2 and 1300 will correspond to a z-score of 2.




We can use sample score 1300 and get same answer as:




Therefore, the standard deviation of the light bulbs’ life is 50 years.
To do this question you need to multiply base times height. So it would be 24*17. After that, you should get 408 square feet.
Answer:

Step-by-step explanation:
Given expression is
.
Now we need to find the cube root of given expression
.
![\sqrt[3]{27a^{12}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27a%5E%7B12%7D%7D)
![=\sqrt[3]{3*3*3a^{4*3}}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7B3%2A3%2A3a%5E%7B4%2A3%7D%7D)
![=\sqrt[3]{3^3\left(a^4\right)^3}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7B3%5E3%5Cleft%28a%5E4%5Cright%29%5E3%7D)
![=\sqrt[3]{\left(3a^4\right)^3}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7B%5Cleft%283a%5E4%5Cright%29%5E3%7D)
Since cube root and cube are opposite operations of each other. So they will cancel each other.

Hence correct choice is the last choice
.