The members of a band are arranged in a rectangular formation. When they are arranged in 8 rows, there are 2 positions unoccupied in the formation. When they are arranged in 9 rows, there are 3 positions unoccupied. How many members are in the band if the membership is between 100 and 200

150

Step-by-step explanation:

Using 8 rows leaves  2 positions unoccupied implies that the population of the number  of members in the band is 2 less than a  multiple of 8. That makes this an even  number.

Similarly, we understand that the number  of members is 3 less than a multiple of  9. So, If we list the even numbers  that are 3 less than multiples of 9  between 100 and 200 and are even; we have:

117 – 3, 135 – 3, 153 – 3, 171 – 3,  189 – 3

= 114, 132, 150, 168, 186  

Also, the numbers that are two less than  a multiple of 8:  

102, 110, 118, 126, 134, 142, 150, 158,  166, 174, 182, 190, 198

From above, we will realize that the number common in both is 150

Let's check if that satisfy our calculation;

SO:

150/8 = 18 remainder 6 ; Thus 8 - 6 = 2 (positions)

150/9 =  16 reminder 6 ;  Thus  9 - 6 = 3 (positions)

Hence the number of members in the band if the membership is between 100 and 200 is 150

ab will be equal to

option c) graph of line going through 1, 4 and 3, 10

step-by-step explanation:

let y equal to margo's coin collection

let x equal to number of years

at the begining x=0, y=1 → point=(x,y)→point=(0,1)

she adds 3 coins per year, then y=1+3x

at x=1, y=1+3(1)=1+3→y=4→point=(x,y)→point=(1,4)

at x=3, y=1+3(3)=1+9→y=10→point=(x,y)→point=(3,10)

the graph of line going through (1, 4) and (3, 10), then the option c is the correct.