Students deliver catalogues and leaflets to houses.

307.80

Step-by-step explanation:

Minimum number of students = maximum amount of work done by each student. This is because if students did less than the maximum amount of work, we would need more students. Therefore, we can assume that each student works for 8 hours a day delivering the maximum number of leaflets/catalogs.

Let's say students work for a total of z hours each day. They work for x hours delivering catalogs and y hours delivering leaflets.

For each hour a student delivers catalogs, 16 are delivered. Therefore, 16x = number of catalogs delivered. Similarly, 90y = number of leaflets delivered. We therefore have

x+y=z

16x = 384

divide both sides by 16 to isolate x

x=24

90y = 1890

divide both sides by 90 to isolate y

y=21

Therefore, 45 hours must be worked, and 5 5/8 students must be hired. Since a student working partially must be paid for a full day, we must round up to 6 students, causing us to pay 51.3 * 6 = 307.80 for their wages

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:

the answer

b. they are parallel and will never intersect.