HELP Latisha owns two spas, one in Pine township and the other in Adams township. Each spa offers a 30-minute face, head, and neck massage to reduce muscle tension. However, therapists first ask each patient questions about their type of tension and stop about five minutes before the end of the 30 minutes to have time to prepare for the next patient. The number of minutes each therapist massages the patients at both spas is approximately Normally distributed, with the Pine spa having a mean of 22.6 minutes and a standard deviation of 1.7 minutes and the Adams spa having a mean of 21.0 minutes and a standard deviation of 2.8 minutes. If Latisha randomly selects 8 massage times from Pine and 9 from Adams, what is the probability that the mean time for Pine is longer than the mean time for Adams?

Let x represent number of massages and y represent number of pedicure + 90-minute massage packages.

We have been given that a spa charges $125 for a one hour massage, so amount earned from x massages would be .

The spa charges $250 for a pedicure + 90-minute massage package, so amount earned from y pedicure + 90-minute massages will be .

We have been given that one day the spa had 27 customers. We can represent this information in an equation as:

Since spa made $5,250, so amount earned from both massages would be equal to 5,250. We can represent this information in an equation as:

Upon substituting equation (1) in equation (2), we will get:

Let us solve for x.

Upon substituting  in equation (1), we will get:

Therefore, the spa performed 12 one hour massages and 15 pedicure + 90-minute massage  packages that is .

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: