The senior class sells movie tickets to students and teachers. The student tickets cost $4 each and teacher tickets cost $8 each. If they earned only $44, how many possible combinations of student and teacher tickets could have been sold?

There are 6 possible combinations:

Student | Adult .  $

      11      |     0 .    44 + 0

      9       |     1       36 + 8

      7       |     2       28 + 16

      5       |     3       20 + 24

      3       |      4       12 + 32

       1       |     5        4 +  40

Step-by-step explanation:

We can use an equation  4x + 8y = 44

Graph it and see where the graphed line crosses the grid lines at integers.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

$75.00

step-by-step explanation:

i = prt

i = 1,5000 * 0.025 * 2

i = 75