What is the quotient StartFraction 2 m Superscript 9 Baseline n Superscript 4 Baseline Over Negative 4 m Superscript negative 3

Answer:

1.21 g/day

Step-by-step explanation:

We start with the fact that

The mass of the bacterial colony (in grams) is described by

Where t=Time(in days)

Next, we differentiate with respect to t

Using the formula

We know that P(t)=6

Now, substitute this value

Insert the given value of t

We understand that

Applying the formula

By employing

g/day

Consequently, the instantaneous rate at which the mass of the colony changes is=1.21g/day

Answer:

a) True

b) True

c) False

d) True

e) True

f) True

g) True

Step-by-step breakdown:

Let A denote a set. The element a is part of A if and only if a∈A.

a) The sole element of {∅} is ∅, so it follows that ∅∈{∅}.

b) The elements of {∅, {∅}} are ∅ and {∅}, thus ∅ ∈ {∅, {∅}}.

c) As {∅} solely contains ∅, it is clear {∅}≠∅ due to {∅} having one element while ∅ has no elements. Hence, {∅} ∉ {∅} since {∅} is not an element of {∅}.

d) The one element in {{∅}} is {∅}. Thus, {∅} ∈ {{∅}}.

e) The items in {∅, {∅}} include ∅ and {∅}. The only element of {∅} is ∅. Thus, every element of {∅} appears in {∅, {∅}} too, leading to {∅} ⊂ {∅, {∅}}.

f) With elements of {∅, {∅}} being ∅ and {∅}, and since the only element of {{∅}} is {∅}, we determine that {{∅}} appears in {∅, {∅}}, which means {{∅}} ⊂ {∅, {∅}}.

g) The only element of {{∅}, {∅}} equals {{∅}} which is {∅}. Each element of {{∅}} is also within {{∅}}, therefore {{∅}} ⊂ {{∅}, {∅}}={{∅}}.