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OOPS, too late to edit my above.   

I didn't read the problem properly.  

I didn't account for same color in 2 and 4. 

There are 4 ways.  

Red  Yellow  Red  Blue  Red  

Red  Blue  Red  Yellow  Red  

Red  Yellow  Red  Yellow  Red  

Red  Blue  Red  Blue  Red  

_.

السَّلاَمُ عَلَيْكُمْ وَرَحْمَةُ اللهِ وَبَرَكَاتُهُ

3/8+2/5+1/8=9/10

So Zakaria payed 1/10

google translate converts this to:  

Zakaria wants to buy a bicycle, so the grandfather paid 3/8 and 2/5,  

and the mother paid 1/8 of its price, and Zakaria paid the rest.  

Keihaku, I'm glad you've seen that so many of the guests who post only an "answer" without showing the steps / reasoning to get to their so-called answer, post an incorrect answer.  I hope others have noticed it as well, and don't believe these guests.  It happens so often, I believe that they're trolls and posting wrong answers on purpose, trying to get students to fall for it and get in trouble with their teacher.  

In a row of five squares, each square is to be colored either red, yellow, or blue, so that

no two consecutive squares have the same color, and at lest three of the squares are red.  

How many ways are there to color the five squares?  

Under the rules, reds can't be next to each other, so the three reds have to go in squares 1, 3, and 5.  

Square 2 can have either yellow or blue.  Each of those choices leaves only one color left for square 4. 

So there are only 2 ways to color the five squares.  

1st way         Red Yellow Red Blue Red   

2nd way        Red Blue Red Yellow Red   

_.

That's correct, thank you for not giving false answers like many other guests do

Students, please don't believe guests who post only an "answer" 

without showing you the way they obtained their so-called answer.  

Their "answers" are wrong so often, I think they're doing it on purpose.  

I believe that they're trolls, trying to get you in trouble with your teacher.  

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 + 6)(x + 3)  =  0    therefore u and v equal –6 and –3  (not necessarily in that order)      

–6 / –3  =  2   

–3 / –6  =  0.5           so their total is 2.5  

_.

A rectangular box has a volume of 108 cubic feet. How many cubic yards are in the volume of this box?  

Don't believe the first guest.  There are 27 cubic feet in 1 cubic yard. 

108 / 27 =  4 yds³  

_.

A positive integer k is called a "lucky" number if the units digit of k^4 is 6. How many lucky numbers smaller than 10 are there?  

1⁴      =            1  

2⁴      =          16  

3⁴      =          81  

4⁴      =        256  

5⁴      =        625  

6⁴      =      1,296  

7⁴      =      2,401  

8⁴      =      4,096  

9⁴      =      6,561            Looks like there are 4 of them.  

_.

The area of triangle ABC is 24*sqrt(5).

Guest, thank you for trying but that was incorrect.

u/v + v/u = 15

The  number of ways is 144.

sqrt(2*sqrt(8^2 + 15^2) + sqrt(9^2 + 40^2))

= sqrt(2*17 + 44)

= sqrt(78)

F(x) = (x^2 + 1)/(x^2 - 3x + 2)

One way of reasoning is as follows:

That should be 0.059 not 0.59.

See https://web2.0calc.com/questions/help-geometry_19961#r1

On the calculator on the Home page here, after you've entered -9 and then pressed the square root key, press enter (or the equals sign) twice.

If \(y=ax^2+bx+c\) then usingthe vertex values we have 

\(4=4a+2b+c\)        (1)

Using the point (7,7) we have

\(7=49a+7b+c\)      (2)

We need a thid equation.  Because of the symmetry about the vertex, the distance on the x-axis of point (7,7) from the vertex is matched by a point the same distance from th vertex in the opposite x direction.  Since point(7,7) is a distance of +5 in the x-direction from (2,4), we must have a point with y-value 7 at x-value 2 - 5 = -3. ie. the point (-3, 7) is also on the curve.  Hence our third equation becomes:

\(7=9a-3b+c\)        (3)

There are now three equations in three unknowns.  Can you take it from here?

AMOGUS!