A market survey shows that 50% of the population used Brand Z computers last year, 4% of the population quit their jobs last year, and 2% of the population used Brand Z computers and then quit their jobs. Are the events of using Brand Z computers and quitting your job independent

the events of using Brand Z computers and quitting your job are independent.

Step-by-step explanation:

Let A be the event that the population used Brand Z computers and let B be the event that the population quit their jobs.

We are told that 50% of the population used Brand Z computers last year. Thus, the probability of event A is;

P(A) = 50% = 0.5

Also, we are told that 4% of the population quit their jobs last year. Thus the probability of event B is;

P(B) = 4% = 0.04

Since 2% of the population used Brand Z computers and then quit their jobs. Then the probability of the population used Brand Z computers and then quit their jobs is;

P(A ∩ B) = 2% = 0.02

From the law of independent events, if A and B are to be independent events, then;

P(A ∩ B) = P(A) × P(B)

Thus;

P(A ∩ B) = 0.5 × 0.04 = 0.02

This is same value as what was given in the question, thus the events of using Brand Z computers and quitting your job are independent.

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.