Three lighthouses on three nearby islands flash their lights every evening. On one island, the light flashes every 45 seconds. The lighthouse on the second island has a light that flashes every 2 minutes. The third lighthouse flashes a light every 1 1/4 minute. Suppose all the lights flash together at 8:35 P. M. At what time will all three lights flash together again?

Lt1 = 45; Lt2 = 120; Lt3 = 75

:

Prime factor each:

45: 3,3,5,

120: 2,2,2,3,5

75: 3,5,5

:

Lcm of all three: 2,2,2,3,3,5,5 Multiply this: 1800 secs they will all Flash

:

1800/60 = 30 min: At 9:05Pm this should occur

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.

1. sometimes

2. never true

3. sometimes

step-by-step explanation:

these are pretty self explanatory if you know what supp right and com angles are