The volumes of two-spheres are in the ratio of 8:27. The radius of the smaller sphere is 30 inches. Find the radius of the larger sphere.

45 in

Step-by-step explanation:

Given 2 similar figures with ratio of radii = a : b , then

ratio of volumes = a³ : b³

Here ratio of volumes = 8 : 27 , then

ratio of radii = : = 2 : 3

let r be the radius of the larger sphere then by proportion

= ( cross- multiply )

2r = 90 ( divide both sides by 2 )

r = 45

The radius of the larger sphere is 45 in

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: