Alan

"In a given city, the probability that a given person is taller than 180 cm is 0.26
 If 18 people are chosen, what is the probability that at least 3 are taller than 180 cm?"

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80 = 0.5v^1.5 

160 = v^1.5

160^(2/3) = v

v ≈ 29.472

"Find the remainder when f(x)=2x^3−x^2+x+1 is divided by 2x+1."

Here's another approach:

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Step 1 isn't so much wrong as incomplete. There is an additional solution, namely -(81)^(1/4)

(-3)^4 = 81 as well as 3^4 = 81

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Or simply:  y = 2^(x-1)

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Set y equal to zero and find the corresponding value of x.  This gives you the x-intercept.

Set x equal to zero and find the corresponding value of y.  This gives you the y-intercept.

Then multiply the two results together.

A graph often helps in these sort of problems:

Yes, I see. Annoying!

I think the question is meant to be interpreted as follows:

Total marbles = T

T = 36 + 72 +(5/8)T

(3/8)T = 108

T =  288

Thomas has (5/8)T → (5/8)*288 → 180

(no broken marbles!)

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2x-y-3z=7.           (1)

3x+y+z=10.         (2)

5x+y+2z=15.       (3)

Add equations (1) and (2) term by term:   5x - 2z = 17.       (4)

Add equations (1)and (3) term by term:    7x - z = 22.         (5)

From (5) we have:   z = 7x - 22.     (6)

Put this in (4):  5x - 2(7x-22) = 17

                        5x - 14x + 44 = 17

                        -9x = -27

                           x = 3.              (7)

Put (7) into (6):   z = -1.             (8)

Put (7) and (8) into (1):   6 - y + 3 = 7

                                       y = 2

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