1. Write a differential equation describing the following situation:
The rate at which people become involved in a corporate bribing scheme is jointly proportional to the number of people already involved and the number of people who are not yet involved. Suppose there are a total of 6000 people in the company. Use k for the constant, P for the number of people who are involved in the scheme, and t for time.

dP/dt = k*(600 - P)*P

Step-by-step explanation:

Given:

- Total number of people in company N = 6000

- Total people involved in bribery P

The rate at which people become involved in a corporate bribing scheme is jointly proportional to the number of people already involved and the number of people who are not yet involved.

Find:

Write a differential equation

Solution:

- The following differential equation can be used to describe the situation above:

                          Number of people not affected = N - P

- Hence we can write a differential equation:

                          dP/ dt = k *( N - P )*P

- input the value of N:

                          dP/dt = k*(600 - P)*P

d.) 48 units

step-by-step explanation:

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."