To make the sum of the integers 0, the biggest number he wrote is 37.

Because 38,39,40,41,42 are the consecutive integers after 37 and their sum is 200 so the greatest integer of the sequence is 42.

There are: \(9-1+1=9\left(numbers\right)\) from 100 to 199.

There are: \(9-2+1=8\left(numbers\right)\) from 200 to 299.

................................................................

There are: \(9-9+1=1\left(number\right)\) from 900 to 999.

So there are total is: \(9+8+7+6+5+4+3+2+1=45\left(numbers\right)\)  satisfy the question.

The least possible number is the least number divisible by 2 of the following statements. Since  \(60⋮15\) in the 2 following statements e and a so the least possible number of k is 60.

We mustn't move the letters y and x.

So there are: \(3.2.1=6\left(arrangements\right)\)

There are: \(100\cdot\dfrac{1}{4}=25\left(liters\right)\) of maple syrup.

There are: \(100-25=75\left(liters\right)\) of base.

She need to add: \(75-25=50\left(liters\right)\) of maple syrup to bring the ratio of maple syrup to base up to 1:1

Because she has to evaporate 90% of maple sap to get maple syrup so 50 liters of maple syrup is 100%-90%=10%

She has to evaporate: \(50\cdot\left(90\%:10\%\right)=450\left(liters\right)\) of maple sap

So she need to start with: \(50+450=500\left(maple-sap\right)\)

The answer is: \(1-\dfrac{20\%}{80\%}=\dfrac{3}{4}\)

We have the numbers satisfy: 3; 43; 343; 433; 443.

So their sum is: \(3+43+343+433+443=1265\)

There are: \(3\cdot4\cdot5=60\left(combinations\right)\) that she can watch.

We have the sequence: 3;5;2;-3;-5;-2;3;5;2;...

So to the 198th number of the sequence, the sum of the sequence is still 0. 

We have: 199th number = 3 and 200th number = 5

So the sum of the first 200 terms of the sequence is: \(0+3+5=8\)

Because 2017 is a prime number

=> \(F\left(2017\right)=1;2017\)

So their sum is: \(1+2017=2018\)

The diameter of the table is: \(\sqrt{20^2+21^2}=\sqrt{400+441}=\sqrt{841}=29\left(ft\right)\)

Call + 1 binder with photos of celebrities on the cover: SB

        + 1 regular binder: RB

We have: \(1SB+8RB=32,60\left(dollars\right)\) and \(1SB+12RB=46,00\left(dollars\right)\)

So we have: \(\left(1SB+12RB\right)-\left(1SB-8RB\right)=4RB=46,00-32,60=13,40\left(dollars\right)\)

So \(1RB=13,40:4=3,35\left(dollars\right)\)

The cost of \(1SB=32,60-\left(3,35\cdot8\right)=5,80\left(dollars\right)\)

So it costs more to buy a celebrity binder than a regular binder: \(5,80-3,35=2,45\left(dollars\right)\)

Mr Smith makes the commission more than Mr Jones: \(5\%-3\%=2\%\)

Mr Smith sold: \(\left(500:2\%\right)\cdot3\%=750\left(widgets\right)\)

We can only solve this question with the equation: \(y=ax^b\)

We have: \(8=1\cdot2^3\) ; \(27=1\cdot3^3\) ; \(125=1\cdot5^3\) ; \(216=1\cdot6^3\)

So a = 1 and b = 3 satisfy this question.

So their sum is: 1 + 3 = 4

A part more than 4 fluid ounces: \(\left(32\cdot1\right):4=8times\)

So she expect to pay: \(3.00\times8=24.00\left(dollars\right)\)

We have the grid shown

=> \(18\cdot a\cdot b\cdot4=5184\)

<=> \(ab=5184:18:4\)

<=> \(ab=72\)

Because a and b are both positive integers so we have the possible ways for ab = 72:

a*b = 1*72 = 2*36 = 3*24 = 4*18 = 6*12 = 8*9 and backwards.

We have the least possible a + b = \(8+9=17\)

We have: 

1st,2nd and 3rd,4th row are given.

5th row: 11;12;13;14;15

6th row: 16;17;18;19;20;21

7th row: 22;23;24;25;26;27;28

So their sum is: \(22+23+24+25+26+27+28=175\)

The difference between the numbers is: \(\left(47-12\right):5=7\) (Arthimetric sequence's facts)

So we have the sequence: 12,19,26,33,... so y = 33.

The total measure of its width and length is: \(136:2=68\)

The width of the rectangle is: \(68:\left(1+3\right)\cdot1=17\left(cm\right)\)

The length of the rectangle is: \(68-17=51\left(cm\right)\)

So the area of the rectangle is: \(17\cdot51=867\left(cm^2\right)\)

Since the median of the sets is 88 so the greatest possible value for the lowest score of the next two tests is 88.

ANSWER: 88.