One light flashes every 18 seconds and another light flashes every 12 seconds. If they flash together at 8:00 p. M., what is the next time that they will flash together?

They will flash together at 36 seconds after 8:00 p.M which can be written as 8:00:36 PM.

Step-by-step explanation:

This question can be solved using concept of LCM

LCM is the least number which is divisible by all the set of given number.

LCM is found by finding the prime factors of given set of numbers and then taking the each numbers highest power and then multiplying all.

for example

lets find LCM of 20 and 75

prime factor of 20 = 2*2*5

prime factor of 75 = 3*5*5

highest power of 2 is 2*2 = 4

highest power of 3 is 3 = 3

highest power of 5 is 5*5 = 25

thus LCM is 4*3*25 = 300

Thus, 300 is the least number which will be commonly divisible by 20 and 75.

Now in the problem given One light flashes every 18 seconds and another light flashes every 12 seconds.

Thus, they will will flast together at time when the time will be commonly divisible by both 12 and 18.

to find that time, lets find the LCM of 12 and 18

The number is 12 , 18

prime factor of 12 = 2*2*3

prime factor of 18 = 2*3*3

highest power of 2 is 2*2 = 4

highest power of 3 is 3*3 = 9

thus LCM is 9*4 = 36

Thus, the lights will flash together after 36 seconds.

Given that they flash together at 8:00 p.M

They will flash together at 36 seconds after 8:00 p.M which can be written as 8:00:36 PM.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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