Paul a dentist determined that the number of cavities that develops in his patients mouth each year varies inversely to the number of seconds spent brushing each night.

Lori will have cavity if she brushed for each night.

Step-by-step explanation:

As the question suggests cavities developed varies inversely with the number of seconds spent on brushing.

Lets take the terms as ,where is the constant of proportionality.

And

c = Number of cavities developed each year

t = Number of minutes spent on brushing per night

Now we will plugging the values of the given terms and find the value of ,for this we can re-arrange it as...

and

Now as Lori will increase her brushing time so as the cavity will decrease.

So for this we have been given, and .

As

So as per Paul's observation if Lori brushed for at night she will have cavity on that year.

8 apples are left.

step-by-step explanation:

10-2=8

10 apples

take 2

now u have 8

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: