Sorry, I don't understand.

From 1 to 100 have: (100 - 1) : 1 + 1 = 100 (terms).

Let A be the set of natural numbers from 1 to 100 which are multiples of 3 and 7.

=> A is the set of natural numbers from 1 to 100 which are multiples of 3*7=21.

=> A = {21;42;63;84}

We see: set A has 4 elements.

=>The number of natural numbers ranging from 1 to 100 which are not multiples of 3 and 7 are:

                                      100 - 4 = 96 (numbers)

60s*60'*24h*365*100 = 3153600000s

We have: a < b < c  =>\(\dfrac{1}{a}>\dfrac{1}{b}>\dfrac{1}{c}\).

=> \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=1=\dfrac{3}{3}< \dfrac{1}{a}+\dfrac{1}{a}+\dfrac{1}{a}=\dfrac{3}{a}\)

=> a < 3. Since a > 0 (positive integer).

=> a = 1 or a = 2.

*If a = 1 => \(\dfrac{1}{a}=1\).

=> \(\dfrac{1}{b}+\dfrac{1}{c}=1-1=0\) (false)

*If a = 2 => \(\dfrac{1}{a}=\dfrac{1}{2}\).

=> \(\dfrac{1}{b}+\dfrac{1}{c}=1-\dfrac{1}{2}=\dfrac{1}{2}=\dfrac{2}{4}< \dfrac{1}{b}+\dfrac{1}{b}=\dfrac{2}{b}\).

=> b < 4. Since b > 2 (a < b).

=> b = 3.

=> \(\dfrac{1}{c}=\dfrac{1}{2}-\dfrac{1}{3}=\dfrac{1}{6}\) => c = 6

Hence a + b + c = 2 + 3 + 6 = 11.

It's incorrect.Because...

We have: 2³ = 8 divided by 7 remaining 1

=> (2³)⁴ divided by 7 remaining 1⁴

=> 2¹² divided by 7 remaining 1.

Hence 2¹² is not divisible by 7.

Let the number of student who took the test (the number of mark) be x.

We have: 81x - 100 = 80(x - 1)

=>           81x - 100 = 80x - 80

=>           81x - 80x = -80 + 100

=>           x = 20

Hence there are 20 student including Kate in the class who took the test.

We have: A team of 4 people has just finished \(\dfrac{1}{2}\) of a project in 10 days.

Let the number of people are needed to be done the rest of the project in 5 days be x.

Due the number of people and the project are two inversely proportional variable, so we have:

\(\dfrac{4}{x}=\dfrac{5}{10}=\dfrac{1}{2}\)

So \(x=\dfrac{4}{\dfrac{1}{2}}=8\)

Hence 8-4=4 more people are needed.

Before they meet 1 hour, the distance between each other is:

                                70*1+40*1=110 (miles)