After n days​ ​​\(\left(n\in Z^+\right)\), the number of cars he sold is :

\(1+2+2^2+...+2^{n-1}\)

\(=2\left(1+2+2^2+...+2^{n-1}\right)-\left(1+2+2^2+...+2^{n-1}\right)\)

\(=\left(2+2^2+2^3+...+2^n\right)-\left(1+2+2^2+...+2^{n-1}\right)\)

\(=2^n-1\)

We have : \(2^n-1\ge1000\Rightarrow2^n\ge1000\Rightarrow n\ge10\)

So, the answer is 10

1 car : First day

2 cars : Second day

4 cars : Third day

So there will be 8 cars : Fourth day.

.... 16 cars : Fifth day.

.... 32 cars : Sixth day.

..... 64 cars : Seventh day.

...... 128 cars : Eighth day.

..... 256 cars : Ninth day.

....... 512 cars : Tenth day.

So it will take him at least 11 days to sell a total of at least 1000 cars.

Dao Trong Luan was wrong because he thinks 48 is the perimeter of the garden. My solution :

Let a and 3a be the length of the length and the width of the garden in feet. We have :

\(a.3a=48\Rightarrow a^2=16\Rightarrow a=4\Rightarrow3a=12\)

The diagonal of the garden is : \(\sqrt{4^2+12^2}=4\sqrt{10}\approx12.65\) (feet)

The half perimeter of the garden is:

48: 2 = 24 [ft]

The length of this garden is:

\(24:\left(1+3\right)\cdot3=18\left(ft\right)\)

The width of this garden is:

24 - 18 = 6 [ft]

So the measure of the diagonal of the garden is:

\(\sqrt{18^2+6^2}=6\sqrt{10}=1897,366596\%\)

We have: \(n< 1\) and \(n>2\) not satisfy the question.

So n = 1 and n = 2 satisfy the question.

Because 2 > 1 so 2 is the greatest integer n.

The area of the patio is : 20 x 14 = 280 (ft²)

There are 2 cases (because there's no figure) :

+ The garden is tangent to 2 20-ft sides and 1 14-ft side

The radius of the garden is : \(14:2=7\left(ft\right)\)

The area of the garden is : \(7^2\pi=49\pi\left(ft^2\right)\) 

The answer is : \(\dfrac{100\left(280-49\pi\right)}{280}\%\approx45\%\)

+ The garden is tangent to 2 14-ft sides and 1 20-ft side

The radius of the garden is : \(20:2=10\left(ft\right)\)

The area of the garden is : \(10^2\pi=100\pi\left(ft^2\right)\) (asburd because \(100\pi>280\))

So, the answer is 45%

The book has the number of page is: 

480 x 600 = 288000 (pages)

So it takes her the number of minutes is: 

288000 : 240 = 1200 (mins) = 20 (hrs)

Time to turn all of them into decimal
1111₃=3³+3²+3¹+3⁰=27+9+3+1=40
1111₂=2³+2²+2¹+2⁰=8+4+2+1=15
So the decimal difference is 40-15=25

1 KOD (Kondlo Dollars) = 4.28466 POD (Ponplos Dollar)

\(\Rightarrow\) \(\dfrac{1}{4.28466}\) KOD = \(\dfrac{4.28466}{4.28466}\) POD

\(\Leftrightarrow\) 0.23339 KOD = 1 POD