1. hooke's law states that the distance d that a spring is stretched by a hanging object varies directly as the mass m of the object. if the distance is 20 cm when the mass is 3kg, what is the distance when the mass is 8kg?
2. the time t required to do a job varies inversely as the number of people p working. it takes 5 hours for 7 volunteers to pick up rubbish from 1 mile of roadway. how long would it take 12 volunteers to complete the job.
3. it takes two painters 9 hours to scraps a house. how long would it take three painters to scrape the same house?
4. the trane air conditioner cooled off 1000 cubic feet in 10 minutes. how long would it take the same unit to cool off 3000 cubic feet?

Step-by-step explanation:

4. The Trane air conditioner cooled off 1000 cubic feet in 10 minutes. How long would it take the same unit to cool off 3000 cubic feet?

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

fahrenheit

step-by-step explanation:

fahrenheit is more precise than celsius. the ambient temperature on most of the inhabited world ranges from -20 degrees fahrenheit to 110 degrees fahrenheit—a 130-degree range. on the celsius scale, that range is from -28.8 degrees to 43.3 degrees—a 72.1-degree range. this means that you can get a more exact measurement of the air temperature using fahrenheit because it uses almost twice the scale.