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Go to this link and learn how to  use the Summation Calculator. I have already entered your problem into the calculator and see the answer at the bottom (10,600):

https://www.mathsisfun.com/numbers/sigma-calculator.html

1 year = 365 days x 14 hours(that he is awake) x 60 minutes per hour =306,600 minutes that is awake in 1 year.

306,600 x 3 blinks per minute =919,800 - number of blinks in 1 year.

So, the conclusion is: He does NOT blink more than 1,000,000 times in one year.

Sorry your pass/fail depends on this one question....you must have a really low score

3 blinks/min   x     60 min /hr   x 14 hr / day    x   365 days/yr   =   919800 blinks/yr

Let the positions in your current list be 1,2,3,4. So sqrt(21)=1, -cbrt(27)=2, -sqrt(16)=3, and 4th root (25)=4. These are just position placeholders, they aren't actually equal. Firstly, we find the ones that are integers. The negative of the cube root of 27 is -3 and the negative of the square root of 16 is -4. The fourth root of 25 is clearly smaller than the square root of 21 but it is nonnegative, so the list goes 3,2,4,1.

Calculate hours per test for each of them...see which is least

Kar  5/6 hr  /  2/3 test  = 5/6 * 3/2 = 15/12 = 1 1/4 hr per test  ( 75 minutes)

Hay 1/8 hr  / 1/10 test = 1/8 * 10 =  10/8   = 1 1/4 hr per test  ( 75 minutes)    It is a tie !

Interesting problem. I will denote the cube root of something as cbrt. Then you have cbrt((2x+3)/4)=2cbrt((x+3)/4). Now just cube both sides and you have an easy linear equation. The solution is x=-7/2, your answer.

Hint: What are the extremes of this equation in the given interval?

1 cup / 2/3  = 3/2 of a recipe

1/4 cup peanuts / recipe     x   3/2 recipe  = 3/8 cup of peanuts required

64 is the anwser

incorrect

the answer is  83/99

There are 480 possible arrangements.

3 1/3 =   10/3     and    4 =  4/1

10/3 /  4/1  =   10/3 * 1/4 = 10/12 = 5/6

At 3:20 it would be one hour...60 minutes

   3:14 is six minutes less than this....so 54 minutes.

Need to know the cheetah's speed in mph

  I suspect you messed up this question...

    as a cheetah's top speed IS 60 mph to almost 80 mph

As follows:

Lol that was solved pretty fast.

                                                      From,

                                                               Gust

Thanks Chris,      

It wasn't that much really.  Thinking it through required a bit of effort though.

I hope Willy, or any other interested person, can work through what I have said.    

Rearange  as

x^2   - x  +  y^2   - y    =   0      complete the square on x and  y

x^2  - x  +1/4    +  y^2  - y + 1/4 =   1/4  +  1/4       factor

(x - 1/2)^2  +  ( y -1/2)^2   =   1/2

x will be maximized  when  y = 1/2

So

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

(x  -1/2)^2    +   0     =   1/2

(x - 1/2)^2  = 1/2           take the positive root

x - 1/2 =  sqrt (1/2)

x - 1/2  =  sqrt (2) / 2

x =  [ 1 + sqrt (2)  ]  / 2

See the  following image  :

B is  point A  reflected over  one of the lines  and C  is  the reflection of A over the other line

Consider FCAB

Angle  CFB = Angle FBA  = Angle GHO = Angle AEG  = Angle CEG =  90°

Angle  OGH = 90 - 38 =  52°  = Angle EGC

So angle ECG  = 90  - 52  =  38°= angle ACF

Then the sum of  the interior angles of FCAB  =  360

So

angle BAC  = 360  -  angle FBA - angle CFB  - angle  ACF

angle  BAC  = 360  - 90  - 90 - 38 =  142°   [ supplemental to the original 38° angle  ]

Thanks, Melody.....that was a LOT of work   !!!!