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not enough information

here is 1 solution:m=1,n=2

\(\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{1 + \cfrac{1}{4}}}}. \)

we simply 1+1/4 first which is 5/4

then 1/(5/4)=4/5

now 4+4/5=24/5

1/(24/5)=5/24

1+5/24=29/24

1/(29/24)=24/29

\(\cfrac{24}{29}\)

gcd(25,1)=1                              I hope you can count the 1s!

gcd(25,2)=1

gcd(25,3)=1

gcd(25,4)=1

gcd(25,5)=5

gcd(25,6)=1

gcd(25,7)=1

gcd(25,8)=1

gcd(25,9)=1

gcd(25,10)=5

gcd(25,11)=1

gcd(25,12)=1

gcd(25,13)=1

gcd(25,14)=1

gcd(25,15)=5

gcd(25,16)=1

gcd(25,17)=1

gcd(25,18)=1

gcd(25,19)=1

gcd(25,20)=5

gcd(25,21)=1

gcd(25,22)=1

gcd(25,23)=1

gcd(25,24)=1

gcd(25,25)=25

            what is 3/7 cubed     

            (3 / 7)³  =  3³ / 7³  =  27 / 343     

_.     

When 100 is divided by 12, the remainder is 4.     
When 100 is divided by a positive integer x, the remainder is 10.     
When 1000 is divided by x, the remainder is what?      

100 / 15  =  6 R 10      1000 / 15  =  66 R 10     

100 / 18  =  5 R 10      1000 / 18  =  55 R 10     

100 / 30  =  3 R 10      1000 / 30  =  33 R 10     

100 / 45  =  2 R 10      1000 / 45  =  22 R 10     

_.     

Parker and his three friends went trick-or-treating together. If Parker got 11 pieces of candy, and each of his friends got three times as much candy as he did, how many pieces of candy did Parker and his friends get in all?     

Parker  got 11 pieces     

Friend₁ got 33 pieces     

Friend₂ got 33 pieces     

Friend₃ got 33 pieces     

                  110 pieces total     

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is euqal to 10 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?     

(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6)  =  10 • (x+6)     

                                                                   7x + 21  =  10x + 60     

                                                                          –3x  =  39     

                                                                              x  =  –13     

check answer     

–13  +  –12  +  –11  +  –10  +  –9  +  –8  +  –7  =?  10 • –7     

                                                                   –70  =  –70     True     

_.     

How many integers n can be used such that the quantity |2n^2 + 3n + 11 - n^2 + 9n| results in a prime number?     

                                                                 |2n² + 3n + 11 – n² + 9n|     

                                                                    n² + 12n + 11     

                               factors to solutions       n  =   –1     

                                                                    n  =  –11     —>>  absolute value is +11     

One isn't a prime, so eleven is the only solution.     

So, the answer to "how many are there" is one,     

since absolute value limits it to its positive value.     

_.     

An aquarium tank is 1/6 full of water.     

When 2 gallons of water are added, the tank becomes 1/3 full.     

What is the total capacity of the aquarium tank, in gallons?      

Two gallons of water raises the level from 1/6 to 2/6,     

which means that 2 gallons accounts for 1/6 of a tank.     

So, it would take 12 gallons to account for 6/6 of a tank.     

_.     

Let u and v be the solutions to 3x^2 + 5x + 7 = 2x^2 - 4x - 11. Find u/v + v/u.      

                                      3x² + 5x + 7  =  2x² – 4x – 11     

                                        x² + 9x + 18  =  0     

                                       (x + 3)(x + 6)  =  0     

                                                          x  =  –3      call it u     

                                                          x  =  –6      call it v     

                                        u / v  +  v / u  =     

                                –3 / –6  +  –6 / –3  =     

                                    1 / 2   +   2         =  2 ¹/₂     

_.     

An aquarium tank is 1/6 full of water. When 2 gallons of water are added, the tank becomes 1/3 full. What is the total capacity of the aquarium tank, in gallons?     

Two gallons of water raises the level from 1/6 to 2/6,     

which means that 2 gallons accounts for 1/6 of a tank.     

So, it would take 12 gallons to account for 6/6 of a tank.     

_.     

                        x  =  –2y² + 12y – 15     

1st derivative           –4y + 12     

set = 0                     –4y + 12  =  0     

                                        –4y  =  –12     

                                            y  =  +3     

                                           x  =  –2y² + 12y – 15     

sub 3 for y                           x  =  –2(9) + 12(3) – 15     

                                            x  =  –18 + 36 – 15     

                                            x  =  –33 + 36     

                                            x  =  +3     

                                     Vertex at  (3, 3)     

_.     

The correct answer is [1,4] U (6,8).